diff --git a/v1.3.1/404.html b/v1.3.1/404.html new file mode 100644 index 000000000..226a44de3 --- /dev/null +++ b/v1.3.1/404.html @@ -0,0 +1,86 @@ + + + + + + + +Page not found (404) • rbmi + + + + + + + + + Skip to contents + + +
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Page not found (404)

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+ +Content not found. Please use links in the navbar. + +
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+ + + +
+ + + + + + + diff --git a/v1.3.1/CONTRIBUTING.html b/v1.3.1/CONTRIBUTING.html new file mode 100644 index 000000000..b45576115 --- /dev/null +++ b/v1.3.1/CONTRIBUTING.html @@ -0,0 +1,143 @@ + +Contributing to rbmi • rbmi + Skip to contents + + +
+
+
+

Contributing to rbmi

+ Source: CONTRIBUTING.md +
+ +
+ +

This file outlines how to propose and make changes to rbmi as well as providing details about more obscure aspects of the package’s development process.

+
+

Setup

+

In order to develop or contribute to rbmi you will need to access to a C/C++ compiler. If you are on Windows you should install rtools or if you are on macOS you should install Xcode. Likewise, you will also need to install all of the package’s development dependencies. This can be done by launching R from within the project root and executing:

+
devtools::install_dev_deps()
+
+
+

Code changes

+

If you want to make a code contribution, it’s a good idea to first file an issue and make sure someone from the team agrees that it’s needed. If you’ve found a bug, please file an issue that illustrates the bug with a minimal reprex (this will also help you write a unit test, if needed).

+
+

Pull request process

+

  • This project uses a simple GitHub flow model for development. That is, code changes should be done in their own feature branch based off of the main branch and merged back into the main branch once complete.

    • +

  • Pull Requests will not be accepted unless all CI/CD checks have passed. (See the CI/CD section for more information).

    • +

  • Pull Requests relating to any of the package’s core R code must be accompanied by a corresponding unit test. Any pull requests containing changes to the core R code that do not contain a unit test to demonstrate that it is working as intended will not be accepted. (See the Unit Testing section for more information).

    • +

  • Pull Requests should add a few lines about what has been changed to the NEWS.md file.

    • +
+
+

Coding Considerations

+

  • We use roxygen2, with Markdown syntax, for documentation.

    • +

  • Please ensure your code conforms to lintr. You can check this by running lintr::lint("FILE NAME") on any files you have modified and ensuring that the findings are kept to as few as possible. We do not have any hard requirements on following lintr’s conventions but do encourage developers to follow its guidance as closely as possible.

    • +

  • This project uses 4 space indents, contributions not following this will not be accepted.

    • +

  • This project makes use of S3 and R6 for OOP. Usage of S4 and other OOP systems should be avoided unless absolutely necessary to ensure consistency. Having said that it is recommended to stick to S3 unless modification in place or other R6 specific features are required.

    • +

  • The current desire of this package is to keep the dependency tree as small as possible. To that end you are discouraged from adding any additional packages to the “Depends” / “Imports” section unless absolutely essential. If you are importing a package just to use a single function then consider just copying the source code of that function instead, though please check the licence and include proper attribution/notices. There are no such expectations for “Suggests” and you are free to use any package in the vignettes / unit tests, though again please be mindful to not be unnecessarily excessive with this.

    • +
+
+
+

Unit Testing & CI/CD

+

This project uses testthat to perform unit testing in combination with GitHub Actions for CI/CD.

+
+

Scheduled Testing

+

Due to the stochastic nature of this package some unit tests take a considerable amount of time to execute. To avoid issues with usability, unit tests that take more than a couple of seconds to run should be deferred to the scheduled testing. These are tests that are only run occasionally on a periodic basis (currently twice a month) and not on every pull request / push event.

+

To defer a test to the scheduled build simply include skip_if_not(is_full_test()) to the top of the test_that() block i.e.

+
+test_that("some unit test", {
+    skip_if_not(is_full_test())
+    expect_equal(1,1)
+})
+

The scheduled tests can also be manually activated by going to “https://github.com/insightsengineering/rbmi” -> “Actions” -> “Bi-Weekly” -> “Run Workflow”. It is advisable to do this before releasing to CRAN.

+
+
+

Docker Images

+

To support CI/CD, in terms of reducing setup time, a Docker images has been created which contains all the packages and system dependencies required for this project. The image can be found at:

+
  • ghcr.io/insightsengineering/rbmi:latest
    • +

This image is automatically re-built once a month to contain the latest version of R and its packages. The code to create this images can be found in misc/docker.

+

To build the image locally run the following from the project root directory:

+
docker build -f misc/docker/Dockerfile  -t rbmi:latest .
+
+
+

Reproducibility, Print Tests & Snaps

+

A particular issue with testing this package is reproducibility. For the most part this is handled well via set.seed() however stan/rstan does not guarantee reproducibility even with the same seed if run on different hardware.

+

This issue surfaces itself when testing the print messages of the pool object which displays treatment estimates which are thus not identical when run on different machines. To address this issue pre-made pool objects have been generated and stored in R/sysdata.rda (which itself is generated by data-raw/create_print_test_data.R). The generated print messages are compared to expected values which are stored in tests/testthat/_snaps/ (which themselves are automatically created by testthat::expect_snapshot())

+
+
+
+

Fitting MMRM’s

+

This package currently uses the mmrm package to fit MMRM models. This package is still fairly new but has so far proven to be very stable, fast and reliable. If you do spot any issues with the MMRM package please do raise them in the corresponding GitHub Repository - link

+

As the mmrm package uses TMB it is not uncommon to see warnings about either inconsistent versions between what TMB and the Matrix package were compiled as. In order to resolve this you may wish to re-compile these packages from source using:

+
install.packages(c("TMB", "mmrm"), type = "source")
+

Note that you will need to have rtools installed if you are on a Windows machine or Xcode if you are running macOS (or somehow else have access to a C/C++ compiler).

+
+
+

rstan

+

The Bayesian models fitted by this package are implemented via stan/rstan. The code for this can be found in inst/stan/MMRM.stan. Note that the package will automatically take care of compiling this code when you install it or run devtools::load_all(). Please note that the package won’t recompile the code unless you have changed the source code or you delete the src directory.

+
+
+

Vignettes

+

CRAN imposes a 10-minute run limit on building, compiling and testing your package. To keep to this limit the vignettes are pre-built; that is to say that simply changing the source code will not automatically update the vignettes, you will need to manually re-build them.

+

To do this you need to run:

+
Rscript vignettes/build.R
+

Once re-built you will then need to commit the updated *.html files to the git repository.

+

For reference this static vignette process works by using the “asis” vignette engine provided by R.rsp. This works by getting R to only recognise vignettes as files ending in *.html.asis; it then builds them by simply copying the corresponding files ending in *.html to the relevent docs/ folder in the built package.

+
+
+

Misc & Local Folders

+

The misc/ folder in this project is used to hold useful scripts, analyses, simulations & infrastructure code that we wish to keep but isn’t essential to the build or deployment of the package. Feel free to store additional stuff in here that you feel is worth keeping.

+

Likewise, local/ has been added to the .gitignore file meaning anything stored in this folder won’t be committed to the repository. For example, you may find this useful for storing personal scripts for testing or more generally exploring the package during development.

+
+
+ +
+ + +
+ + + + + + + diff --git a/v1.3.1/LICENSE.html b/v1.3.1/LICENSE.html new file mode 100644 index 000000000..229921f44 --- /dev/null +++ b/v1.3.1/LICENSE.html @@ -0,0 +1,142 @@ + +Apache License • rbmi + Skip to contents + + +
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+ + + + + + + diff --git a/v1.3.1/articles/CondMean_Inference.html b/v1.3.1/articles/CondMean_Inference.html new file mode 100644 index 000000000..53320c398 --- /dev/null +++ b/v1.3.1/articles/CondMean_Inference.html @@ -0,0 +1,576 @@ + + + + + + + +rbmi: Inference with Conditional Mean Imputation • rbmi + + + + + + + + Skip to contents + + +
+ + +
+
+

rbmi: Inference with Conditional Mean Imputation

+

Alessandro Noci, Marcel Wolbers, Craig Gower-Page

+ + + Source: vignettes/CondMean_Inference.Rmd +
CondMean_Inference.Rmd
+
+ + + +
+

+1 Introduction +

+

As described in section 3.10.2 of the statistical specifications of the package (vignette(topic = "stat_specs", package = "rbmi")), two different types of variance estimators have been proposed for reference-based imputation methods in the statistical literature (Bartlett (2023)). +The first is the frequentist variance which describes the actual repeated sampling variability of the estimator and results in inference which is correct in the frequentist sense, i.e. hypothesis tests have accurate type I error control and confidence intervals have correct coverage probabilities under repeated sampling if the reference-based assumption is correctly specified (Bartlett (2023), Wolbers et al. (2022)). +Reference-based missing data assumption are strong and borrow information from the control arm for imputation in the active arm. +As a consequence, the size of frequentist standard errors for treatment effects may decrease with increasing amounts of missing data. +The second is the so-called “information-anchored” variance which was originally proposed in the context of sensitivity analyses (Cro, Carpenter, and Kenward (2019)). This variance estimator is based on disentangling point estimation and variance estimation altogether. +The resulting information-anchored variance is typically very similar to the variance under missing-at-random (MAR) imputation and increases with increasing amounts of missing data at approximately the same rate as MAR imputation. +However, the information-anchored variance does not reflect the actual variability of the reference-based estimator and the resulting frequentist inference is highly conservative resulting in a substantial power loss.

+

Reference-based conditional mean imputation combined with a resampling method such as the jackknife or the bootstrap was first introduced in Wolbers et al. (2022). +This approach naturally targets the frequentist variance. The information-anchored variance is typically estimated using Rubin’s rules for Bayesian multiple imputation which are not applicable within the conditional mean imputation framework. +However, an alternative information-anchored variance proposed by Lu (2021) can easily be obtained as we show below. +The basic idea of Lu (2021) is to obtain the information-anchored variance via a MAR imputation combined with a delta-adjustment where delta is selected in a data-driven way to match the reference-based estimator. +For conditional mean imputation, the proposal by Lu (2021) can be implemented by choosing the delta-adjustment as the difference between the conditional mean imputation under the chosen reference-based assumption and MAR on the original dataset. +The variance can then be obtained via the jackknife or the bootstrap while keeping the delta-adjustment fixed. The resulting variance estimate is very similar to Rubin’s variance. +Moreover, as shown in Cro, Carpenter, and Kenward (2019), the variance of MAR-imputation combined with a delta-adjustment achieves even better information-anchoring properties than Rubin’s variance for reference-based imputation. +Reference-based missing data assumptions are strong and borrow information from the control arm for imputation in the active arm.

+

This vignette demonstrates first how to obtain frequentist inference using reference-based conditional mean imputation using rbmi, and then shows that an information-anchored inference can also be easily implemented using the package.

+
+
+

+2 Data and model specification +

+

We use a publicly available example dataset from an antidepressant clinical trial of an active drug versus placebo. +The relevant endpoint is the Hamilton 17-item depression rating scale (HAMD17) which was assessed at baseline and at weeks 1, 2, 4, and 6. +Study drug discontinuation occurred in 24% of subjects from the active drug and 26% of subjects from placebo. +All data after study drug discontinuation are missing and there is a single additional intermittent missing observation.

+

We consider an imputation model with the mean change from baseline in the HAMD17 score as the outcome (variable CHANGE in the dataset). +The following covariates are included in the imputation model: the treatment group (THERAPY), the (categorical) visit (VISIT), treatment-by-visit interactions, the baseline HAMD17 score (BASVAL), and baseline HAMD17 score-by-visit interactions. +A common unstructured covariance matrix structure is assumed for both groups. The analysis model is an ANCOVA model with the treatment group as the primary factor and adjustment for the baseline HAMD17 score. +For this example, we assume that the imputation strategy after the ICE “study-drug discontinuation” is Jump To Reference (JR) for all subjects and the imputation is based on conditional mean imputation combined with jackknife resampling (but the bootstrap could also have been selected).

+
+
+

+3 Reference-based conditional mean imputation - frequentist inference +

+

Conditional mean imputation combined with a resampling method such as jackknife or bootstrap naturally targets a frequentist estimation of the standard error of the treatment effect, thus providing a valid frequentist inference. +Here we provide the code to obtain frequentist inference for reference-based conditional mean imputation using rbmi.

+

The code used in this section is almost identical to the code in the quickstart vignette (vignette(topic = "quickstart", package = "rbmi")) except that we use conditional mean imputation combined with the jackknife (method_condmean(type = "jackknife")) here rather than Bayesian multiple imputation (method_bayes()). +We therefore refer to that vignette and the help files for the individual functions for further explanations and details.

+
+

+3.1 Draws +

+

We will make use of rbmi::expand_locf() to expand the dataset in order to have one row per subject per visit with missing outcomes denoted as NA. We will then construct the data_ice, vars and method input arguments to the first core rbmi function, draws(). +Finally, we call the function draws() to derive the parameter estimates of the base imputation model for the full dataset and all leave-one-subject-out samples.

+
+library(rbmi)
+library(dplyr)
+#> 
+#> Attaching package: 'dplyr'
+#> The following objects are masked from 'package:stats':
+#> 
+#>     filter, lag
+#> The following objects are masked from 'package:base':
+#> 
+#>     intersect, setdiff, setequal, union
+
+dat <- antidepressant_data
+
+# Use expand_locf to add rows corresponding to visits with missing outcomes to
+# the dataset
+dat <- expand_locf(
+  dat,
+  PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT 
+  VISIT = levels(dat$VISIT),
+  vars = c("BASVAL", "THERAPY"), # fill with LOCF BASVAL and THERAPY
+  group = c("PATIENT"),
+  order = c("PATIENT", "VISIT")
+)
+
+# create data_ice and set the imputation strategy to JR for
+# each patient with at least one missing observation
+dat_ice <- dat %>% 
+  arrange(PATIENT, VISIT) %>% 
+  filter(is.na(CHANGE)) %>% 
+  group_by(PATIENT) %>% 
+  slice(1) %>%
+  ungroup() %>% 
+  select(PATIENT, VISIT) %>% 
+  mutate(strategy = "JR")
+
+# In this dataset, subject 3618 has an intermittent missing values which
+# does not correspond to a study drug discontinuation. We therefore remove
+# this subject from `dat_ice`. (In the later imputation step, it will
+# automatically be imputed under the default MAR assumption.)
+dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),]
+
+# Define the names of key variables in our dataset and
+# the covariates included in the imputation model using `set_vars()`
+vars <- set_vars(
+  outcome = "CHANGE",
+  visit = "VISIT",
+  subjid = "PATIENT",
+  group = "THERAPY",
+  covariates = c("BASVAL*VISIT", "THERAPY*VISIT")
+)
+
+# Define which imputation method to use (here: conditional mean imputation
+# with jackknife as resampling) 
+method <- method_condmean(type = "jackknife")
+
+# Create samples for the imputation parameters by running the draws() function
+drawObj <- draws(
+  data = dat,
+  data_ice = dat_ice,
+  vars = vars,
+  method = method,
+  quiet = TRUE
+)
+drawObj
+#> 
+#> Draws Object
+#> ------------
+#> Number of Samples: 1 + 172
+#> Number of Failed Samples: 0
+#> Model Formula: CHANGE ~ 1 + THERAPY + VISIT + BASVAL * VISIT + THERAPY * VISIT
+#> Imputation Type: condmean
+#> Method:
+#>     name: Conditional Mean
+#>     covariance: us
+#>     threshold: 0.01
+#>     same_cov: TRUE
+#>     REML: TRUE
+#>     type: jackknife
+
+
+

+3.2 Impute +

+

We can use now the function impute() to perform the imputation of the original dataset and of each leave-one-out samples using the results obtained at the previous step.

+
+references <- c("DRUG" = "PLACEBO", "PLACEBO" = "PLACEBO")
+imputeObj <- impute(drawObj, references)
+imputeObj
+#> 
+#> Imputation Object
+#> -----------------
+#> Number of Imputed Datasets: 1 + 172
+#> Fraction of Missing Data (Original Dataset):
+#>     4:   0%
+#>     5:   8%
+#>     6:  13%
+#>     7:  25%
+#> References:
+#>     DRUG    -> PLACEBO
+#>     PLACEBO -> PLACEBO
+
+
+

+3.3 Analyse +

+

Once the datasets have been imputed, we can call the analyse() function to apply the complete-data analysis model (here ANCOVA) to each imputed dataset.

+
+
+# Set analysis variables using `rbmi` function "set_vars"
+vars_an <- set_vars(
+  group = vars$group,
+  visit = vars$visit,
+  outcome = vars$outcome,
+  covariates = "BASVAL"
+)
+
+# Analyse MAR imputation with derived delta adjustment
+anaObj <- analyse(
+  imputeObj,
+  rbmi::ancova,
+  vars = vars_an
+)
+anaObj
+#> 
+#> Analysis Object
+#> ---------------
+#> Number of Results: 1 + 172
+#> Analysis Function: rbmi::ancova
+#> Delta Applied: FALSE
+#> Analysis Estimates:
+#>     trt_4
+#>     lsm_ref_4
+#>     lsm_alt_4
+#>     trt_5
+#>     lsm_ref_5
+#>     lsm_alt_5
+#>     trt_6
+#>     lsm_ref_6
+#>     lsm_alt_6
+#>     trt_7
+#>     lsm_ref_7
+#>     lsm_alt_7
+
+
+

+3.4 Pool +

+

Finally, we can extract the treatment effect estimates and perform inference using the jackknife variance estimator. This is done by calling the pool() function.

+
+poolObj <- pool(anaObj)
+poolObj
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 1 + 172
+#> Method: jackknife
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   ==================================================
+#>    parameter   est     se     lci     uci     pval  
+#>   --------------------------------------------------
+#>      trt_4    -0.092  0.695  -1.453   1.27   0.895  
+#>    lsm_ref_4  -1.616  0.588  -2.767  -0.464  0.006  
+#>    lsm_alt_4  -1.708  0.396  -2.484  -0.931  <0.001 
+#>      trt_5    1.305   0.878  -0.416  3.027   0.137  
+#>    lsm_ref_5  -4.133  0.688  -5.481  -2.785  <0.001 
+#>    lsm_alt_5  -2.828  0.604  -4.011  -1.645  <0.001 
+#>      trt_6    1.929   0.862  0.239   3.619   0.025  
+#>    lsm_ref_6  -6.088  0.671  -7.402  -4.773  <0.001 
+#>    lsm_alt_6  -4.159  0.686  -5.503  -2.815  <0.001 
+#>      trt_7    2.126   0.858  0.444   3.807   0.013  
+#>    lsm_ref_7  -6.965  0.685  -8.307  -5.622  <0.001 
+#>    lsm_alt_7  -4.839  0.762  -6.333  -3.346  <0.001 
+#>   --------------------------------------------------
+

This gives an estimated treatment effect of +2.13 (95% CI 0.44 to 3.81) +at the last visit with an associated p-value of 0.013.

+
+
+
+

+4 Reference-based conditional mean imputation - information-anchored inference +

+

In this section, we present how the estimation process based on conditional mean imputation combined with the jackknife can be adapted to obtain an information-anchored variance following the proposal by Lu (2021).

+
+

+4.1 Draws +

+

The code for the pre-processing of the dataset and for the “draws” step is equivalent to the code provided for the frequentist inference. Please refer to that section for details about this step.

+
+
+library(rbmi)
+library(dplyr)
+
+dat <- antidepressant_data
+
+# Use expand_locf to add rows corresponding to visits with missing outcomes to
+# the dataset
+dat <- expand_locf(
+  dat,
+  PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT 
+  VISIT = levels(dat$VISIT),
+  vars = c("BASVAL", "THERAPY"), # fill with LOCF BASVAL and THERAPY
+  group = c("PATIENT"),
+  order = c("PATIENT", "VISIT")
+)
+
+# create data_ice and set the imputation strategy to JR for
+# each patient with at least one missing observation
+dat_ice <- dat %>% 
+  arrange(PATIENT, VISIT) %>% 
+  filter(is.na(CHANGE)) %>% 
+  group_by(PATIENT) %>% 
+  slice(1) %>%
+  ungroup() %>% 
+  select(PATIENT, VISIT) %>% 
+  mutate(strategy = "JR")
+
+# In this dataset, subject 3618 has an intermittent missing values which
+# does not correspond to a study drug discontinuation. We therefore remove
+# this subject from `dat_ice`. (In the later imputation step, it will
+# automatically be imputed under the default MAR assumption.)
+dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),]
+
+# Define the names of key variables in our dataset and
+# the covariates included in the imputation model using `set_vars()`
+vars <- set_vars(
+  outcome = "CHANGE",
+  visit = "VISIT",
+  subjid = "PATIENT",
+  group = "THERAPY",
+  covariates = c("BASVAL*VISIT", "THERAPY*VISIT")
+)
+
+# Define which imputation method to use (here: conditional mean imputation
+# with jackknife as resampling) 
+method <- method_condmean(type = "jackknife")
+
+# Create samples for the imputation parameters by running the draws() function
+drawObj <- draws(
+  data = dat,
+  data_ice = dat_ice,
+  vars = vars,
+  method = method,
+  quiet = TRUE
+)
+drawObj
+
+
+

+4.2 Imputation step including calculation of delta-adjustment +

+

The proposal by Lu (2021) is to replace the reference-based imputation by a MAR imputation combined with a delta-adjustment where delta is selected in a data-driven way to match the reference-based estimator. +In rbmi, this is implemented by first performing the imputation under the defined reference-based imputation strategy (here JR) as well as under MAR separately. +Second, the delta-adjustment is defined as the difference between the conditional mean imputation under reference-based and MAR imputation, respectively, on the original dataset.

+

To simplify the implementation, we have written a function get_delta_match_refBased that performs this step. +The function takes as input arguments the draws object, data_ice (i.e. the data.frame containing the information about the intercurrent events and the imputation strategies), and references, a named vector that identifies the references to be used for reference-based imputation methods. +The function returns a list containing the imputation objects under both reference-based and MAR imputation, plus a data.frame which contains the delta-adjustment.

+
+
+#' Get delta adjustment that matches reference-based imputation
+#' 
+#' @param draws: A `draws` object created by `draws()`.
+#' @param data_ice: `data.frame` containing the information about the intercurrent
+#' events and the imputation strategies. Must represent the desired imputation
+#' strategy and not the MAR-variant.
+#' @param references: A named vector. Identifies the references to be used
+#' for reference-based imputation methods.
+#' 
+#' @return 
+#' The function returns a list containing the imputation objects under both
+#' reference-based and MAR imputation, plus a `data.frame` which contains the
+#' delta-adjustment.
+#' 
+#' @seealso `draws()`, `impute()`.
+get_delta_match_refBased <- function(draws, data_ice, references) {
+  
+  # Impute according to `data_ice`
+  imputeObj <- impute(
+    draws = drawObj,
+    update_strategy = data_ice,
+    references = references
+  )
+  
+  vars <- imputeObj$data$vars
+  
+  # Access imputed dataset (index=1 for method_condmean(type = "jackknife"))
+  cmi <- extract_imputed_dfs(imputeObj, index = 1, idmap = TRUE)[[1]]
+  idmap <- attributes(cmi)$idmap
+  cmi <- cmi[, c(vars$subjid, vars$visit, vars$outcome)]
+  colnames(cmi)[colnames(cmi) == vars$outcome] <- "y_imp"
+  
+  # Map back original patients id since `rbmi` re-code ids to ensure id uniqueness
+  
+  cmi[[vars$subjid]] <- idmap[match(cmi[[vars$subjid]], names(idmap))]
+  
+  # Derive conditional mean imputations under MAR
+  dat_ice_MAR <- data_ice 
+  dat_ice_MAR[[vars$strategy]] <- "MAR"
+  
+  # Impute under MAR 
+  # Note that in this specific context, it is desirable that an update   
+
+  # from a reference-based strategy to MAR uses the exact same data for 
+  # fitting the imputation models, i.e. that available post-ICE data are 
+  # omitted from the imputation model for both. This is the case when    
+  # using argument update_strategy in function impute(). 
+  # However, for other settings (i.e. if one is interested in switching to
+  # a standard MAR imputation strategy altogether), this behavior is  
+  # undesirable and, consequently, the function throws a warning which 
+  # we suppress here. 
+  suppressWarnings(
+    imputeObj_MAR <- impute(
+      draws,
+      update_strategy = dat_ice_MAR
+    )
+  ) 
+  
+  # Access imputed dataset (index=1 for method_condmean(type = "jackknife"))
+  cmi_MAR <- extract_imputed_dfs(imputeObj_MAR, index = 1, idmap = TRUE)[[1]]
+  idmap <- attributes(cmi_MAR)$idmap
+  cmi_MAR <- cmi_MAR[, c(vars$subjid, vars$visit, vars$outcome)]
+  colnames(cmi_MAR)[colnames(cmi_MAR) == vars$outcome] <- "y_MAR"
+  
+  # Map back original patients id since `rbmi` re-code ids to ensure id uniqueness
+  cmi_MAR[[vars$subjid]] <- idmap[match(cmi_MAR[[vars$subjid]], names(idmap))]
+  
+  # Derive delta adjustment "aligned with ref-based imputation",
+  # i.e. difference between ref-based imputation and MAR imputation
+  delta_adjust <- merge(cmi, cmi_MAR, by = c(vars$subjid, vars$visit), all = TRUE)
+  delta_adjust$delta <- delta_adjust$y_imp - delta_adjust$y_MAR
+
+  ret_obj <- list(
+    imputeObj = imputeObj,
+    imputeObj_MAR = imputeObj_MAR,
+    delta_adjust = delta_adjust
+  )
+  
+  return(ret_obj)
+}
+
+references <- c("DRUG" = "PLACEBO", "PLACEBO" = "PLACEBO")
+
+res_delta_adjust <- get_delta_match_refBased(drawObj, dat_ice, references)
+
+
+

+4.3 Analyse +

+

We use the function analyse() to add the delta-adjustment and perform the analysis of the imputed datasets under MAR. +analyse() will take as the input argument imputations = res_delta_adjust$imputeObj_MAR, i.e. the imputation object corresponding to the MAR imputation (and not the JR imputation). +The argument delta can be used to add a delta-adjustment prior to the analysis and we set this to the delta-adjustment obtained in the previous step: delta = res_delta_adjust$delta_adjust.

+
+
+# Set analysis variables using `rbmi` function "set_vars"
+vars_an <- set_vars(
+  group = vars$group,
+  visit = vars$visit,
+  outcome = vars$outcome,
+  covariates = "BASVAL"
+)
+
+# Analyse MAR imputation with derived delta adjustment
+anaObj_MAR_delta <- analyse(
+  res_delta_adjust$imputeObj_MAR,
+  rbmi::ancova,
+  delta = res_delta_adjust$delta_adjust,
+  vars = vars_an
+)
+
+
+

+4.4 Pool +

+

We can finally use the pool() function to extract the treatment effect estimate (as well as the estimated marginal means) at each visit and apply the jackknife variance estimator to the analysis estimates from all the imputed leave-one-out samples.

+
+
+poolObj_MAR_delta <- pool(anaObj_MAR_delta)
+poolObj_MAR_delta
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 1 + 172
+#> Method: jackknife
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   ==================================================
+#>    parameter   est     se     lci     uci     pval  
+#>   --------------------------------------------------
+#>      trt_4    -0.092  0.695  -1.453   1.27   0.895  
+#>    lsm_ref_4  -1.616  0.588  -2.767  -0.464  0.006  
+#>    lsm_alt_4  -1.708  0.396  -2.484  -0.931  <0.001 
+#>      trt_5    1.305   0.944  -0.545  3.156   0.167  
+#>    lsm_ref_5  -4.133  0.738  -5.579  -2.687  <0.001 
+#>    lsm_alt_5  -2.828  0.603  -4.01   -1.646  <0.001 
+#>      trt_6    1.929   0.993  -0.018  3.876   0.052  
+#>    lsm_ref_6  -6.088  0.758  -7.574  -4.602  <0.001 
+#>    lsm_alt_6  -4.159  0.686  -5.504  -2.813  <0.001 
+#>      trt_7    2.126   1.123  -0.076  4.327   0.058  
+#>    lsm_ref_7  -6.965  0.85   -8.63   -5.299  <0.001 
+#>    lsm_alt_7  -4.839  0.763  -6.335  -3.343  <0.001 
+#>   --------------------------------------------------
+

This gives an estimated treatment effect of +2.13 (95% CI -0.08 to 4.33) +at the last visit with an associated p-value of 0.058. +Per construction of the delta-adjustment, the point estimate is identical to the frequentist analysis. However, its standard error is much larger (1.12 vs. 0.86). +Indeed, the information-anchored standard error (and the resulting inference) is very similar to the results for Baysesian multiple imputation using Rubin’s rules for which a standard error of 1.13 was reported in the quickstart vignette (vignette(topic = "quickstart", package = "rbmi"). +Of note, as shown e.g. in Wolbers et al. (2022), hypothesis testing based on the information-anchored inference is very conservative, i.e. the actual type I error is much lower than the nominal value. Hence, confidence intervals and \(p\)-values based on information-anchored inference should be interpreted with caution.

+
+
+
+

References +

+
+
+Bartlett, Jonathan W. 2023. “Reference-Based Multiple Imputation - What Is the Right Variance and How to Estimate It.” Statistics in Biopharmaceutical Research 15 (1): 178–86. +
+
+Cro, Suzie, James R Carpenter, and Michael G Kenward. 2019. “Information-Anchored Sensitivity Analysis: Theory and Application.” Journal of the Royal Statistical Society: Series A (Statistics in Society) 182 (2): 623–45. +
+
+Lu, Kaifeng. 2021. “An Alternative Implementation of Reference-Based Controlled Imputation Procedures.” Statistics in Biopharmaceutical Research 13 (4): 483–91. +
+
+Wolbers, Marcel, Alessandro Noci, Paul Delmar, Craig Gower-Page, Sean Yiu, and Jonathan W Bartlett. 2022. “Standard and Reference-Based Conditional Mean Imputation.” Pharmaceutical Statistics 21 (6): 1246–57. +
+
+
+
+
+ + + + +
+ + + + + + + diff --git a/v1.3.1/articles/FAQ.html b/v1.3.1/articles/FAQ.html new file mode 100644 index 000000000..d8fa06dfd --- /dev/null +++ b/v1.3.1/articles/FAQ.html @@ -0,0 +1,202 @@ + + + + + + + +rbmi: Frequently Asked Questions • rbmi + + + + + + + + Skip to contents + + +
+ + +
+
+

rbmi: Frequently Asked Questions

+

Alessandro Noci, Craig Gower-Page and Marcel Wolbers

+ + + Source: vignettes/FAQ.Rmd +
FAQ.Rmd
+
+ + + +
+

+1 Introduction +

+

This document provides answers to common questions about the rbmi package. +It is intended to be read after the rbmi: Quickstart vignette.

+


+
+

+1.1 Is rbmi validated? +

+

With regards to software in the pharmaceutical industry, validation is the act of ensuring that the software meets the needs and +requirements of users given the conditions of actual use. The FDA provides general principles and +guidance for validation but leaves it to individual sponsors to define their specific validation +processes. Therefore, no individual R package can claim to be ‘validated’ independently, as +validation depends on the entire software stack and the specific processes of each company.

+

That being said, some of the core components of any validation process are the design specification +(what is the software supposed to do) as well as the testing / test results that demonstrate that +the design specification has been met. For rbmi, the design specification is documented extensively, +both at a macro level in vignettes and literature publications, and at a micro level in detailed +function manuals. This is supported by our extensive suite of unit and integration tests, which +ensure the software consistently produces correct output across a wide range of input scenarios.

+

This documentation and test coverage enable rbmi to be easily installed and integrated into any +R system, in alignment with the system’s broader validation process.

+


+
+
+

+1.2 How do the methods in rbmi compare to the mixed model for repeated measures (MMRM) implemented in the mmrm package? +

+

rbmi was designed to complement and, occasionally, replace standard MMRM analyses for clinical trials with longitudinal endpoints.

+

Strengths of rbmi compared to the standard MMRM model are:

+
    +
  • +rbmi was designed to allow for analyses which are fully aligned with the the estimand definition. To facilitate this, it implements methods under a range of different missing data assumptions including standard missing-at-random (MAR), extended MAR (via inclusion of time-varying covariates), reference-based missingness, and not missing-at-random at random (NMAR; via \(\delta\)-adjustments). In contrast, the standard MMRM model is only valid under a standard MAR assumption which is not always plausible. For example, the standard MAR assumption is rather implausible for implementing a treatment policy strategy for the intercurrent event “treatment discontinuation” if a substantial proportion of subjects are lost-to-follow-up after discontinuation.
    • +
  • The \(\delta\)-adjustment methods implemented in rbmi can be used for sensitivity analyses of a primary MMRM- or rbmi-type analysis.
    • +
+

Weaknesses of rbmi compared to the standard MMRM model are:

+
    +
  • MMRM models have been the de-facto standard analysis method for more than a decade. rbmi is currently less established.
    • +
  • +rbmi is computationally more intensive and using it requires more careful planning.
    • +
+


+
+
+

+1.3 How does rbmi compare to general-purpose software for multiple imputation (MI) such as mice? +

+

rbmi covers only “MMRM-type” settings, i.e. settings with a single longitudinal continuous outcome which may be missing at some visits and hence require imputation.

+

For these settings, it has several advantages over general-purpose MI software:

+
    +
  • +rbmi supports imputation under a range of different missing data assumptions whereas general-purpose MI software is mostly focused on MAR-based imputation. In particular, it is unclear how to implement jump to reference (JR) or copy increments in reference (CIR) methods with such software.
    • +
  • The rbmi interface is fully streamlined to this setting which arguably makes the implementation more straightforward than for general-purpose MI software.
    • +
  • The MICE algorithm is stochastic and inference is always based on Rubin’s rules. In contrast, method “conditional mean imputation plus jackknifing” (method="method_condmean(type = "jackknife")") in rbmi does not require any tuning parameters, is fully deterministic, and provides frequentist-consistent inference also for reference-based imputations (where Rubin’s rule is very conservative leading to actual type I error rates which can be far below their nominal values).
    • +
+

However, rbmi is much more limited in its functionality than general-purpose MI software.

+


+
+
+

+1.4 How to handle missing data in baseline covariates in rbmi? +

+

rbmi does not support imputation of missing baseline covariates. Therefore, missing baseline covariates need to be handled outside of rbmi. +The best approach for handling missing baseline covariates needs to be made on a case-by-case basis but in the context of randomized trials, relatively simple approach are often sufficient (White and Thompson (2005)).

+


+
+
+

+1.5 Why does rbmi by default use an ANCOVA analysis model and not an MMRM analysis model? +

+

The theoretical justification for the conditional mean imputation method requires that the analysis model leads to a point estimator which is a linear function of the outcome vector (Wolbers et al. (2022)). This is the case for ANCOVA but not for general MMRM models. For the other imputation methods, both ANCOVA and MMRM are valid analysis methods. An MMRM analysis model could be implemented by providing a custom analysis function to the analyse() function.

+

For further expalanations, we also cite the end of section 2.4 of the conditional mean imputation paper (Wolbers et al. (2022)):

+
+

The proof relies on the fact that the ANCOVA estimator is a linear function of the outcome vector. +For complete data, the ANCOVA estimator leads to identical parameter estimates as an MMRM model of all longitudinal outcomes with an arbitrary common covariance structure across treatment groups if treatment-by-visit interactions as well as covariate-by-visit-interactions are included in the analysis model for all covariates,17 (p. 197). +Hence, the same proof also applies to such MMRM models. +We expect that conditional mean imputation is also valid if a general MMRM model is used for the analysis but more involved argument would be required to formally justify this.

+
+


+
+
+

+1.6 How can I analyse the change-from-baseline in the analysis model when imputation was done on the original outcomes? +

+

This can be achieved using custom analysis functions as outlined in Section 7 of the Advanced Vignette. e.g.

+
+ancova_modified <- function(data, ...) {
+    data2 <- data %>% mutate(ENDPOINT = ENDPOINT - BASELINE)
+    rbmi::ancova(data2, ...)
+}
+
+anaObj <- rbmi::analyse(
+    imputeObj,
+    ancova_modified,
+    vars = vars
+ )
+


+
+
+White, Ian R, and Simon G Thompson. 2005. “Adjusting for Partially Missing Baseline Measurements in Randomized Trials.” Statistics in Medicine 24 (7): 993–1007. +
+
+Wolbers, Marcel, Alessandro Noci, Paul Delmar, Craig Gower-Page, Sean Yiu, and Jonathan W Bartlett. 2022. “Standard and Reference-Based Conditional Mean Imputation.” Pharmaceutical Statistics 21 (6): 1246–57. +
+
+
+
+
+
+ + + + +
+ + + + + + + diff --git a/v1.3.1/articles/advanced.html b/v1.3.1/articles/advanced.html new file mode 100644 index 000000000..34dc18105 --- /dev/null +++ b/v1.3.1/articles/advanced.html @@ -0,0 +1,915 @@ + + + + + + + +rbmi: Advanced Functionality • rbmi + + + + + + + + Skip to contents + + +
+ + +
+
+

rbmi: Advanced Functionality

+

Alessandro Noci, Craig Gower-Page, and Marcel Wolbers

+ + + Source: vignettes/advanced.Rmd +
advanced.Rmd
+
+ + + +
+

+1 Introduction +

+

The purpose of this vignette is to provide an overview of some more advanced features of the rbmi package. +The sections of the vignette are relatively self-contained, i.e. readers should be able to jump directly to the section which covers the functionality that they are most interested in.

+
+
+

+2 Data simulation using function simulate_data() +

+

In order to demonstrate the advanced functions we will first create a simulated dataset with the rbmi function simulate_data(). +The simulate_data() function generates data from a randomized clinical trial with longitudinal continuous outcomes and up to two different types of intercurrent events (ICEs). +One intercurrent event (ICE1) may be thought of as a discontinuation from study treatment due to study drug or condition related (SDCR) reasons. +The other event (ICE2) may be thought of as discontinuation from study treatment due to not study drug or condition related (NSDCR) reasons. +For the purpose of this vignette, we simulate data similarly to the simulation study reported in Wolbers et al. (2022) (though we change some of the simulation parameters) and include only one ICE type (ICE1).

+

Specifically, we simulate a 1:1 randomized trial of an active drug (intervention) versus placebo (control) with 100 subjects per group and 6 post-baseline assessments (bi-monthly visits until 12 months) under the following assumptions:

+
    +
  • The mean outcome trajectory in the placebo group increases linearly from 50 at baseline (visit 0) to 60 at visit 6, i.e. the slope is 10 points/year.
    • +
  • The mean outcome trajectory in the intervention group is identical to the placebo group up to visit 2. From visit 2 onward, the slope decreases by 50% to 5 points/year.
    • +
  • The covariance structure of the baseline and follow-up values in both groups is implied by a random intercept and slope model with a standard deviation of 5 for both the intercept and the slope, and a correlation of 0.25. In addition, an independent residual error with standard deviation 2.5 is added to each assessment.
    +
    • +
  • The probability of study drug discontinuation after each visit is calculated according to a logistic model which depends on the observed outcome at that visit. Specifically, a visit-wise discontinuation probability of 2% and 3% in the control and intervention group, respectively, is specified in case the observed outcome is equal to 50 (the mean value at baseline). The odds of a discontinuation is simulated to increase by +10% for each +1 point increase of the observed outcome.
    • +
  • Study drug discontinuation is simulated to have no effect on the mean trajectory in the placebo group. In the intervention group, subjects who discontinue follow the slope of the mean trajectory from the placebo group from that time point onward. This is compatible with a copy increments in reference (CIR) assumption.
    • +
  • Study drop-out at the study drug discontinuation visit occurs with a probability of 50% leading to missing outcome data from that time point onward.
    • +
+

The function simulate_data() requires 3 arguments (see the function documentation help(simulate_data) for more details):

+
    +
  • +pars_c: The simulation parameters of the control group
    • +
  • +pars_t: The simulation parameters of the intervention group
    • +
  • +post_ice1_traj: Specifies how observed outcomes after ICE1 are simulated
    • +
+

Below, we report how data according to the specifications above can be simulated with function simulate_data():

+
+library(rbmi)
+library(dplyr)
+library(ggplot2)
+library(purrr)
+
+set.seed(122)
+
+n <- 100
+time <- c(0, 2, 4, 6, 8, 10, 12)
+
+# Mean trajectory control
+muC <- c(50.0, 51.66667, 53.33333, 55.0, 56.66667, 58.33333, 60.0)
+
+# Mean trajectory intervention
+muT <- c(50.0, 51.66667, 53.33333, 54.16667, 55.0, 55.83333, 56.66667)
+
+# Create Sigma
+sd_error <- 2.5
+covRE <- rbind(
+  c(25.0, 6.25),
+  c(6.25, 25.0)
+)
+
+Sigma <- cbind(1, time / 12) %*% covRE %*% rbind(1, time / 12) + diag(sd_error^2, nrow = length(time))
+
+# Set probability of discontinuation
+probDisc_C <- 0.02
+probDisc_T <- 0.03
+or_outcome <- 1.10 # +1 point increase => +10% odds of discontinuation
+
+# Set drop-out rate following discontinuation
+prob_dropout <- 0.5
+
+# Set simulation parameters of the control group
+parsC <- set_simul_pars(
+    mu = muC,
+    sigma = Sigma,
+    n = n,
+    prob_ice1 = probDisc_C,
+    or_outcome_ice1 = or_outcome,
+    prob_post_ice1_dropout = prob_dropout
+)
+
+# Set simulation parameters of the intervention group
+parsT <- parsC
+parsT$mu <- muT
+parsT$prob_ice1 <- probDisc_T
+
+# Set assumption about post-ice trajectory
+post_ice_traj <- "CIR"
+
+# Simulate data
+data <- simulate_data(
+    pars_c = parsC,
+    pars_t = parsT,
+    post_ice1_traj = post_ice_traj
+)
+
+head(data)
+#>     id visit   group outcome_bl outcome_noICE ind_ice1 ind_ice2 dropout_ice1
+#> 1 id_1     0 Control   57.32704      57.32704        0        0            0
+#> 2 id_1     1 Control   57.32704      54.69751        1        0            1
+#> 3 id_1     2 Control   57.32704      58.60702        1        0            1
+#> 4 id_1     3 Control   57.32704      61.50119        1        0            1
+#> 5 id_1     4 Control   57.32704      56.68363        1        0            1
+#> 6 id_1     5 Control   57.32704      66.14799        1        0            1
+#>    outcome
+#> 1 57.32704
+#> 2       NA
+#> 3       NA
+#> 4       NA
+#> 5       NA
+#> 6       NA
+
+# As a simple descriptive of the simulated data, summarize the number of subjects with ICEs and missing data 
+data %>%
+  group_by(id) %>%
+  summarise(
+    group = group[1],
+    any_ICE = (any(ind_ice1 == 1)),
+    any_NA = any(is.na(outcome))) %>%
+  group_by(group) %>%
+  summarise(
+      subjects_with_ICE = sum(any_ICE),
+      subjects_with_missings = sum(any_NA)
+  )
+#> # A tibble: 2 × 3
+#>   group        subjects_with_ICE subjects_with_missings
+#>   <fct>                    <int>                  <int>
+#> 1 Control                     18                      8
+#> 2 Intervention                25                     14
+
+
+

+3 Handling of observed post-ICE data in rbmi under reference-based imputation +

+

rbmi always uses all non-missing outcome data from the input data set, i.e. such data are never overwritten during the imputation step or removed from the analysis step. This implies that if there are data which are considered to be irrelevant for treatment effect estimation (e.g. data after an ICE for which the estimand specified a hypothetical strategy), then such data need to be removed from the input data set by the user prior to calling the rbmi functions.

+

For imputation under a missing at random (MAR) strategy, all observed outcome data is also included in the fitting of the base imputation model. However, for ICEs handled using reference-based imputation methods (such as CIR, CR, and JR), rbmi excludes observed post-ICE data from the base imputation model. If these data were not excluded, then the base imputation model would mistakenly estimate mean trajectories based on a mixture of observed pre- and post-ICE data which are not relevant for reference-based imputations. However, any observed post-ICE data are added back into the data set after the fitting of the base imputation model and included as is in the subsequent imputation and analysis steps.

+

Post-ICE data in the control or reference group are also excluded from the base imputation model if the user specifies a reference-based imputation strategy for such ICEs. This ensures that an ICE has the same impact on the data included in the base imputation model regardless whether the ICE occurred in the control or the intervention group. On the other hand, imputation in the reference group is based on a MAR assumption even for reference-based imputation methods and it may be preferable in some settings to include such post-ICE data from the control group in the base imputation model. This can be implemented by specifying a MAR strategy for the ICE in the control group and a reference-based strategy for the same ICE in the intervention group. We will use this latter approach in our example below.

+

The simulated trial data from section 2 assumed that outcomes in the intervention group observed after the ICE “treatment discontinuation” follow the increments observed in the control group. Thus the imputation of missing data in the intervention group after treatment discontinuation might be performed under a reference-based copy increments in reference (CIR) assumption.

+

Specifically, we implement an estimator under the following assumptions:

+
    +
  • The endpoint of interest is the change in the outcome from baseline at each visit.
    • +
  • The imputation model includes the treatment group, the (categorical) visit, treatment-by-visit interactions, the baseline outcome, and baseline outcome-by-visit interactions as covariates.
    • +
  • The imputation model assumes a common unstructured covariance matrix in both treatment groups
    • +
  • In the control group, all missing data are imputed under MAR whereas in the intervention group, missing post-ICE data are imputed under a CIR assumption
    • +
  • The analysis model of the endpoint in the imputed datasets is a separate ANCOVA model for each visit with the treatment group as the primary covariate and adjustment for the baseline outcome value.
    • +
+

For illustration purposes, we chose MI based on approximate Bayesian posterior draws with 20 random imputations which is not very demanding from a computational perspective. In practical applications, the number of random imputations may need to be increased. Moreover, other imputations are also supported in rbmi. For guidance regarding the choice of the imputation approach, we refer the user to a comparison between all implemented approaches in Section 3.9 of the “Statistical Specifications” vignette (vignette("stat_specs", package = "rbmi")).

+

We first report the code to set the variables of the imputation and analysis models. If you are not yet familiar with the syntax, we recommend that you first check the “quickstart” vignette (vignette("quickstart", package = "rbmi")).

+
+# Create data_ice including the subject's first visit affected by the ICE and the imputation strategy
+# Imputation strategy for post-ICE data is CIR in the intervention group and MAR for the control group 
+# (note that ICEs which are handled using MAR are optional and do not impact the analysis
+#  because imputation of missing data under MAR is the default)
+data_ice_CIR <- data %>%
+    group_by(id) %>%
+    filter(ind_ice1 == 1) %>% # select visits with ICEs
+    mutate(strategy = ifelse(group == "Intervention", "CIR", "MAR")) %>%
+    summarise(
+        visit = visit[1], # Select first visit affected by the ICE
+        strategy = strategy[1]
+    )
+
+# Compute endpoint of interest: change from baseline and
+# remove rows corresponding to baseline visits
+data <- data %>% 
+    filter(visit != 0) %>% 
+    mutate(
+        change = outcome - outcome_bl,
+        visit = factor(visit, levels = unique(visit))
+    )
+
+# Define key variables for the imputation and analysis models
+vars <- set_vars(
+    subjid = "id",
+    visit = "visit",
+    outcome = "change",
+    group = "group",
+    covariates = c("visit*outcome_bl", "visit*group"),
+    strategy = "strategy"
+)
+
+vars_an <- vars
+vars_an$covariates <- "outcome_bl"
+

The chosen imputation method can be set with the function method_approxbayes() as follows:

+
+method <- method_approxbayes(n_sample = 20)
+

We can now sequentially call the 4 key functions of rbmi to perform the multiple imputation. Please note that the management of observed post-ICE data is performed without additional complexity for the user. draws() automatically excludes post-ICE data handled with a reference-based method (but keeps post-ICE data handled using MAR) using information provided by the argument data_ice. impute() will impute only truly missing data in data[[vars$outcome]].

+
+draw_obj <- draws(
+    data = data,
+    data_ice = data_ice_CIR,
+    vars = vars,
+    method = method,
+    quiet = TRUE,
+    ncores = 2
+)
+
+impute_obj_CIR <- impute(
+    draw_obj,
+    references = c("Control" = "Control", "Intervention" = "Control")
+)
+
+ana_obj_CIR <- analyse(
+    impute_obj_CIR,
+    vars = vars_an
+)
+
+pool_obj_CIR <- pool(ana_obj_CIR)
+pool_obj_CIR
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 20
+#> Method: rubin
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   ==================================================
+#>    parameter   est     se     lci     uci     pval  
+#>   --------------------------------------------------
+#>      trt_1    -0.486  0.512  -1.496  0.524   0.343  
+#>    lsm_ref_1   2.62   0.362  1.907   3.333   <0.001 
+#>    lsm_alt_1  2.133   0.362   1.42   2.847   <0.001 
+#>      trt_2    -0.066  0.542  -1.135  1.004   0.904  
+#>    lsm_ref_2  3.707   0.384   2.95   4.464   <0.001 
+#>    lsm_alt_2  3.641   0.383  2.885   4.397   <0.001 
+#>      trt_3    -1.782  0.607  -2.979  -0.585  0.004  
+#>    lsm_ref_3  5.841   0.428  4.997   6.685   <0.001 
+#>    lsm_alt_3  4.059   0.428  3.214   4.904   <0.001 
+#>      trt_4    -2.518  0.692  -3.884  -1.152  <0.001 
+#>    lsm_ref_4  7.656   0.492  6.685   8.627   <0.001 
+#>    lsm_alt_4  5.138   0.488  4.176    6.1    <0.001 
+#>      trt_5    -3.658  0.856  -5.346  -1.97   <0.001 
+#>    lsm_ref_5  9.558   0.598  8.379   10.737  <0.001 
+#>    lsm_alt_5   5.9    0.608  4.699   7.101   <0.001 
+#>      trt_6    -4.537  0.954  -6.42   -2.655  <0.001 
+#>    lsm_ref_6  11.048  0.666  9.735   12.362  <0.001 
+#>    lsm_alt_6  6.511   0.674  5.181   7.841   <0.001 
+#>   --------------------------------------------------
+

This last output gives an estimated difference of +-4.537 (95% CI -6.420 to -2.655) +between the two groups at the last visit with an associated p-value lower than 0.001.

+
+
+

+4 Efficiently changing reference-based imputation strategies +

+

The draws() function is by far the most computationally intensive function in rbmi. +In some settings, it may be important to explore the impact of a change in the +reference-based imputation strategy on the results. +Such a change does not affect the imputation model but it does +affect the subsequent imputation step. +In order to allow changes in the imputation strategy without having to re-run the +draws() function, the function impute() has an additional argument update_strategies.

+

However, please note that this functionality comes with some important limitations: +As described at the beginning of Section 3, post-ICE outcomes are included in the input dataset for the base imputation model if the imputation method is MAR but they are excluded for reference-based imputation methods (such as CIR, CR, and JR). +Therefore, updata_strategies cannot be applied if the imputation strategy is changed from a MAR to a non-MAR strategy in the presence of observed post-ICE outcomes. Similarly, a change from a non-MAR strategy to MAR triggers a warning in the presence of observed post-ICE outcomes because the base imputation model was not fitted to all relevant data under MAR. +Finally, update_strategies cannot be applied if the timing of any of the ICEs is changed (in argument data_ice) in addition to the imputation strategy.

+

As an example, we described an analysis under a copy increments in reference (CIR) assumption in the previous section. Let’s assume we want to change this strategy to a jump to reference imputation strategy for a sensitivity analysis. This can be efficiently implemented using update_strategies as follows:

+
+# Change ICE strategy from CIR to JR
+data_ice_JR <- data_ice_CIR %>% 
+    mutate(strategy = ifelse(strategy == "CIR", "JR", strategy))
+
+impute_obj_JR <- impute(
+    draw_obj,
+    references = c("Control" = "Control", "Intervention" = "Control"),
+    update_strategy = data_ice_JR
+)
+
+ana_obj_JR <- analyse(
+    impute_obj_JR,
+    vars = vars_an
+)
+
+pool_obj_JR <- pool(ana_obj_JR)
+pool_obj_JR
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 20
+#> Method: rubin
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   ==================================================
+#>    parameter   est     se     lci     uci     pval  
+#>   --------------------------------------------------
+#>      trt_1    -0.485  0.513  -1.496  0.526   0.346  
+#>    lsm_ref_1  2.609   0.363  1.892   3.325   <0.001 
+#>    lsm_alt_1  2.124   0.361  1.412   2.836   <0.001 
+#>      trt_2    -0.06   0.535  -1.115  0.995   0.911  
+#>    lsm_ref_2  3.694   0.378  2.948   4.441   <0.001 
+#>    lsm_alt_2  3.634   0.381  2.882   4.387   <0.001 
+#>      trt_3    -1.767  0.598  -2.948  -0.587  0.004  
+#>    lsm_ref_3  5.845   0.422  5.012   6.677   <0.001 
+#>    lsm_alt_3  4.077   0.432  3.225    4.93   <0.001 
+#>      trt_4    -2.529  0.686  -3.883  -1.175  <0.001 
+#>    lsm_ref_4  7.637   0.495  6.659   8.614   <0.001 
+#>    lsm_alt_4  5.108   0.492  4.138   6.078   <0.001 
+#>      trt_5    -3.523  0.856  -5.212  -1.833  <0.001 
+#>    lsm_ref_5  9.554   0.61   8.351   10.758  <0.001 
+#>    lsm_alt_5  6.032   0.611  4.827   7.237   <0.001 
+#>      trt_6    -4.36   0.952  -6.238  -2.482  <0.001 
+#>    lsm_ref_6  11.003  0.676  9.669   12.337  <0.001 
+#>    lsm_alt_6  6.643   0.687  5.287     8     <0.001 
+#>   --------------------------------------------------
+

For imputations under a jump to reference assumption, we get an estimated difference of +-4.360 (95% CI -6.238 to -2.482) +between the two groups at the last visit with an associated p-value of +<0.001.

+
+
+

+5 Imputation under MAR with time-varying covariates +

+

The rbmi package supports the inclusion of time-varying covariates in the imputation model. This is particularly useful for implementing so-called retrieved dropout models. +The vignette “Implementation of retrieved-dropout models using rbmi” (vignette(topic = "retrieved_dropout", package = "rbmi")) contains examples of such models.

+
+
+

+6 Custom imputation strategies +

+

The following imputation strategies are implemented in rbmi:

+
    +
  • Missing at Random (MAR)
    • +
  • Jump to Reference (JR)
    • +
  • Copy Reference (CR)
    • +
  • Copy Increments in Reference (CIR)
    • +
  • Last Mean Carried Forward (LMCF)
    • +
+

In addition, rbmi allows the user to implement their own imputation strategy. +To do this, the user needs to do three things:

+
    +
  1. Define a function implementing the new imputation strategy.
    2. +
  2. Specify which patients use this strategy in the data_ice dataset provided to draws().
    3. +
  3. Provide the imputation strategy function to impute().
    4. +
+

The imputation strategy function must take 3 arguments (pars_group, pars_ref, and index_mar) and calculates the mean and covariance matrix of the subject’s marginal imputation distribution which will then be applied to subjects to which the strategy applies. +Here, pars_group contains the predicted mean trajectory (pars_group$mu, a numeric vector) and covariance matrix (pars_group$sigma) for a subject conditional on their assigned treatment group and covariates. +pars_ref contains the corresponding mean trajectory and covariance matrix conditional on the reference group and the subject’s covariates. +index_mar is a logical vector which specifies for each visit whether the visit is unaffected by an ICE handled using a non-MAR method or not. +As an example, the user can check how the CIR strategy was implemented by looking at function strategy_CIR().

+
+strategy_CIR
+#> function (pars_group, pars_ref, index_mar) 
+#> {
+#>     if (all(index_mar)) {
+#>         return(pars_group)
+#>     }
+#>     else if (all(!index_mar)) {
+#>         return(pars_ref)
+#>     }
+#>     mu <- pars_group$mu
+#>     last_mar <- which(!index_mar)[1] - 1
+#>     increments_from_last_mar_ref <- pars_ref$mu[!index_mar] - 
+#>         pars_ref$mu[last_mar]
+#>     mu[!index_mar] <- mu[last_mar] + increments_from_last_mar_ref
+#>     sigma <- compute_sigma(sigma_group = pars_group$sigma, sigma_ref = pars_ref$sigma, 
+#>         index_mar = index_mar)
+#>     pars <- list(mu = mu, sigma = sigma)
+#>     return(pars)
+#> }
+#> <bytecode: 0x55697a7e04b8>
+#> <environment: namespace:rbmi>
+

To further illustrate this for a simple example, assume that a new strategy is to be implemented as follows: +- The marginal mean of the imputation distribution is equal to the marginal mean trajectory for the subject according to their assigned group and covariates up to the ICE. +- After the ICE the marginal mean of the imputation distribution is equal to the average of the visit-wise marginal means based on the subjects covariates and the assigned group or the reference group, respectively. +- For the covariance matrix of the marginal imputation distribution, the covariance matrix from the assigned group is taken.

+

To do this, we first need to define the imputation function which for this example could be coded as follows:

+
+strategy_AVG <- function(pars_group, pars_ref, index_mar) {
+    mu_mean <- (pars_group$mu + pars_ref$mu) / 2
+    x <- pars_group
+    x$mu[!index_mar] <- mu_mean[!index_mar]
+    return(x)
+}
+

And an example showing its use:

+
+pars_group <- list(
+    mu = c(1, 2, 3),
+    sigma = as_vcov(c(1, 3, 2), c(0.4, 0.5, 0.45))
+)
+
+pars_ref <- list(
+    mu = c(5, 6, 7),
+    sigma = as_vcov(c(2, 1, 1), c(0.7, 0.8, 0.5))
+)
+
+index_mar <- c(TRUE, TRUE, FALSE)
+
+strategy_AVG(pars_group, pars_ref, index_mar)
+#> $mu
+#> [1] 1 2 5
+#> 
+#> $sigma
+#>      [,1] [,2] [,3]
+#> [1,]  1.0  1.2  1.0
+#> [2,]  1.2  9.0  2.7
+#> [3,]  1.0  2.7  4.0
+

To incorporate this into rbmi, data_ice needs to be updated such that the strategy AVG is specified for visits affected by the ICE. Additionally, the function needs +to be provided to impute() via the getStrategies() function as shown below:

+
+data_ice_AVG <- data_ice_CIR %>% 
+    mutate(strategy = ifelse(strategy == "CIR", "AVG", strategy))
+
+
+draw_obj <- draws(
+    data = data,
+    data_ice = data_ice_AVG,
+    vars = vars,
+    method = method,
+    quiet = TRUE
+)
+
+impute_obj <- impute(
+    draw_obj,
+    references = c("Control" = "Control", "Intervention" = "Control"),
+    strategies = getStrategies(AVG = strategy_AVG)
+)
+

Then, the analysis could proceed by calling analyse() and pool() as before.

+
+
+

+7 Custom analysis functions +

+

By default rbmi will analyse the data by using the ancova() function. +This analysis function fits an ANCOVA model to the outcomes from each visit separately, +and returns the “treatment effect” estimate as well as the corresponding least square means +for each group. If the user wants to perform a different analysis, or return different +statistics from the analysis, then this can be done by using a custom analysis function. +Beware that the validity of the conditional mean imputation method has only been formally established for analysis functions corresponding to linear models (such as ANCOVA) and caution is +required when applying alternative analysis functions for this method.

+

The custom analysis function must take a data.frame as its +first argument and return a named list with each element itself being a list +containing at a minimum a point estimate, called est. +For method method_bayes() or method_approxbayes(), the list must additionally contain a +standard error (element se) and, if available, the degrees of freedom of the complete-data analysis model (element df).

+

As a simple example, we replicate the ANCOVA analysis at the last visit for the CIR-based imputations with a user-defined analysis function below:

+
+compare_change_lastvisit <- function(data, ...) {
+    fit <- lm(change ~ group + outcome_bl, data = data, subset = (visit == 6) )
+    res <- list(
+        trt = list(
+            est = coef(fit)["groupIntervention"],
+            se = sqrt(vcov(fit)["groupIntervention", "groupIntervention"]),
+            df = df.residual(fit)
+        )
+    )
+    return(res)
+}
+
+ana_obj_CIR6 <- analyse(
+  impute_obj_CIR,
+  fun = compare_change_lastvisit,
+  vars = vars_an
+)
+
+pool(ana_obj_CIR6)
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 20
+#> Method: rubin
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   =================================================
+#>    parameter   est     se     lci    uci     pval  
+#>   -------------------------------------------------
+#>       trt     -4.537  0.954  -6.42  -2.655  <0.001 
+#>   -------------------------------------------------
+

As a second example, assume that for a supplementary analysis the user wants to compare the proportion of subjects with a change from baseline of >10 points at the last +visit between the treatment groups with the baseline outcome as an additional covariate. This could lead to the following basic analysis function:

+
+compare_prop_lastvisit <- function(data, ...) {
+    fit <- glm(
+        I(change > 10) ~ group + outcome_bl,
+        family = binomial(),
+        data = data,
+        subset = (visit == 6)
+    )
+    res <- list(
+        trt = list(
+            est = coef(fit)["groupIntervention"],
+            se = sqrt(vcov(fit)["groupIntervention", "groupIntervention"]),
+            df = NA
+        )
+    )
+    return(res)
+}
+    
+ana_obj_prop <- analyse(
+  impute_obj_CIR,
+  fun = compare_prop_lastvisit,
+  vars = vars_an
+)
+
+pool_obj_prop <- pool(ana_obj_prop)
+pool_obj_prop
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 20
+#> Method: rubin
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   =================================================
+#>    parameter   est     se     lci     uci    pval  
+#>   -------------------------------------------------
+#>       trt     -1.052  0.314  -1.667  -0.438  0.001 
+#>   -------------------------------------------------
+
+tmp <- as.data.frame(pool_obj_prop) %>% 
+    mutate(
+        OR = exp(est),
+        OR.lci = exp(lci),
+        OR.uci = exp(uci)
+    ) %>% 
+    select(parameter, OR, OR.lci, OR.uci)
+tmp
+#>   parameter        OR   OR.lci    OR.uci
+#> 1       trt 0.3491078 0.188807 0.6455073
+

Note that if the user wants rbmi to use a normal approximation to the pooled test statistics, then the degrees of freedom need to be set to df = NA (as per the above example). If the degrees of freedom of the complete data test statistics are known or if the degrees of freedom are set to df = Inf, then rbmi pools the degrees of freedom across imputed datasets according to the rule by Barnard and Rubin (see the “Statistical Specifications” vignette (vignette("stat_specs", package = "rbmi") for details). According to this rule, infinite degrees of freedom for the complete data analysis do not imply that the pooled degrees of freedom are also infinite. +Rather, in this case the pooled degrees of freedom are (M-1)/lambda^2, where M is the number of imputations and lambda is the fraction of missing information (see Barnard and Rubin (1999) for details).

+
+
+

+8 Sensitivity analyses: Delta adjustments and tipping point analyses +

+

Delta-adjustments are used to impute missing data under a not missing at random (NMAR) assumption. This reflects the belief that unobserved outcomes would have been systematically “worse” (or “better”) than “comparable” observed outcomes. For an extensive discussion of delta-adjustment methods, we refer to Cro et al. (2020).

+

In rbmi, a marginal delta-adjustment approach is implemented. This means that the delta-adjustment is applied to the dataset after data imputation under MAR or reference-based missing data assumptions and prior to the analysis of the imputed data. +Sensitivity analysis using delta-adjustments can therefore be performed without having to re-fit the imputation model. In rbmi, they are implemented via the delta argument of the analyse() function.

+
+

+8.1 Simple delta adjustments and tipping point analyses +

+

The delta argument of analyse() allows users to modify the outcome variable prior to the analysis. +To do this, the user needs to provide a data.frame which contains columns for the subject and visit (to identify the observation to be adjusted) plus an additional column called delta which specifies the value which will be added to the outcomes prior to the analysis.

+

The delta_template() function supports the user in creating this data.frame: it creates a skeleton data.frame containing one row per subject and visit with the value of delta set to 0 for all observations:

+
+dat_delta <- delta_template(imputations = impute_obj_CIR)
+head(dat_delta)
+#>     id visit   group is_mar is_missing is_post_ice strategy delta
+#> 1 id_1     1 Control   TRUE       TRUE        TRUE      MAR     0
+#> 2 id_1     2 Control   TRUE       TRUE        TRUE      MAR     0
+#> 3 id_1     3 Control   TRUE       TRUE        TRUE      MAR     0
+#> 4 id_1     4 Control   TRUE       TRUE        TRUE      MAR     0
+#> 5 id_1     5 Control   TRUE       TRUE        TRUE      MAR     0
+#> 6 id_1     6 Control   TRUE       TRUE        TRUE      MAR     0
+

Note that the output of delta_template() contains additional information which can be used to properly re-set variable delta.

+

For example, assume that the user wants to implement a delta-adjustment to the imputed values under CIR described in section 3.
+Specifically, assume that a fixed “worsening adjustment” of +5 points is applied to all imputed values regardless of the treatment group. This could be programmed as follows:

+
+# Set delta-value to 5 for all imputed (previously missing) outcomes and 0 for all other outcomes
+dat_delta <- delta_template(imputations = impute_obj_CIR) %>%
+    mutate(delta = is_missing * 5)
+
+# Repeat the analyses with the delta-adjusted values and pool results
+ana_delta <- analyse(
+    impute_obj_CIR,
+    delta = dat_delta,
+    vars = vars_an
+)
+pool(ana_delta)
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 20
+#> Method: rubin
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   ==================================================
+#>    parameter   est     se     lci     uci     pval  
+#>   --------------------------------------------------
+#>      trt_1    -0.482  0.524  -1.516  0.552   0.359  
+#>    lsm_ref_1  2.718   0.37   1.987   3.448   <0.001 
+#>    lsm_alt_1  2.235   0.37   1.505   2.966   <0.001 
+#>      trt_2    -0.016  0.56   -1.12   1.089   0.978  
+#>    lsm_ref_2  3.907   0.396  3.125   4.688   <0.001 
+#>    lsm_alt_2  3.891   0.395  3.111   4.671   <0.001 
+#>      trt_3    -1.684  0.641  -2.948  -0.42   0.009  
+#>    lsm_ref_3  6.092   0.452  5.201   6.983   <0.001 
+#>    lsm_alt_3  4.408   0.452  3.515    5.3    <0.001 
+#>      trt_4    -2.359  0.741  -3.821  -0.897  0.002  
+#>    lsm_ref_4  7.951   0.526  6.913    8.99   <0.001 
+#>    lsm_alt_4  5.593   0.522  4.563   6.623   <0.001 
+#>      trt_5    -3.34   0.919  -5.153  -1.526  <0.001 
+#>    lsm_ref_5  9.899   0.643  8.631   11.168  <0.001 
+#>    lsm_alt_5  6.559   0.653  5.271   7.848   <0.001 
+#>      trt_6    -4.21   1.026  -6.236  -2.184  <0.001 
+#>    lsm_ref_6  11.435  0.718  10.019  12.851  <0.001 
+#>    lsm_alt_6  7.225   0.725  5.793   8.656   <0.001 
+#>   --------------------------------------------------
+

The same approach can be used to implement a tipping point analysis. Here, we apply different delta-adjustments to imputed data from the control and the intervention group, respectively. Assume that delta-adjustments by less then -5 points or by more than +15 points are considered implausible from a clinical perspective. Therefore, we vary the delta-values in each group between -5 to +15 points to investigate which delta combinations lead to a “tipping” of the primary analysis result, defined here as an analysis p-value \(\geq 0.05\).

+
+
+
+
+perform_tipp_analysis <- function(delta_control, delta_intervention, cl) {
+
+    # Derive delta offset based on control and intervention specific deltas
+    delta_df <-  delta_df_init %>%
+        mutate(
+            delta_ctl = (group == "Control") * is_missing * delta_control,
+            delta_int = (group == "Intervention") * is_missing * delta_intervention,
+            delta = delta_ctl + delta_int
+        )
+
+    ana_delta <- analyse(
+        impute_obj_CIR,
+        fun = compare_change_lastvisit,
+        vars = vars_an,
+        delta = delta_df,
+        ncores = cl
+    )
+
+    pool_delta <- as.data.frame(pool(ana_delta))
+
+    list(
+        trt_effect_6 = pool_delta[["est"]],
+        pval_6 = pool_delta[["pval"]]
+    )
+}
+
+# Get initial delta template
+delta_df_init <- delta_template(impute_obj_CIR)
+
+tipp_frame_grid <- expand.grid(
+    delta_control = seq(-5, 15, by = 2),
+    delta_intervention = seq(-5, 15, by = 2)
+) %>%
+    as_tibble()
+
+# parallelise to speed up computation
+cl <- make_rbmi_cluster(2)
+
+tipp_frame <- tipp_frame_grid %>%
+    mutate(
+        results_list = map2(delta_control, delta_intervention, perform_tipp_analysis, cl = cl),
+        trt_effect_6 = map_dbl(results_list, "trt_effect_6"),
+        pval_6 = map_dbl(results_list, "pval_6")
+    ) %>%
+    select(-results_list) %>%
+    mutate(
+        pval = cut(
+            pval_6,
+            c(0, 0.001, 0.01, 0.05, 0.2, 1),
+            right = FALSE,
+            labels = c("<0.001", "0.001 - <0.01", "0.01- <0.05", "0.05 - <0.20", ">= 0.20")
+        )
+    )
+
+# Close cluster when done with it
+parallel::stopCluster(cl)
+
+# Show delta values which lead to non-significant analysis results
+tipp_frame %>%
+    filter(pval_6 >= 0.05)
+#> # A tibble: 3 × 5
+#>   delta_control delta_intervention trt_effect_6 pval_6 pval        
+#>           <dbl>              <dbl>        <dbl>  <dbl> <fct>       
+#> 1            -5                 15        -1.99 0.0935 0.05 - <0.20
+#> 2            -3                 15        -2.15 0.0704 0.05 - <0.20
+#> 3            -1                 15        -2.31 0.0527 0.05 - <0.20
+
+ggplot(tipp_frame, aes(delta_control, delta_intervention, fill = pval)) +
+    geom_raster() +
+    scale_fill_manual(values = c("darkgreen", "lightgreen", "lightyellow", "orange", "red"))
+

+

According to this analysis, the significant test result from the primary analysis under CIR could only be tipped to a non-significant result for rather extreme delta-adjustments. Please note that for a real analysis it is recommended to use a smaller step size in the grid than what has been used here.

+
+
+

+8.2 More flexible delta-adjustments using the dlag and delta arguments of delta_template() +

+

So far, we have only discussed simple delta arguments which add the same value to all imputed values. +However, the user may want to apply more flexible delta-adjustments to missing values after an intercurrent event (ICE) and vary the magnitude of the delta adjustment depending on the how far away the visit in question is from the ICE visit.

+

To facilitate the creation of such flexible delta-adjustments, the delta_template() function has two optional additional arguments delta +and dlag. The delta argument specifies the default amount of delta +that should be applied to each post-ICE visit, whilst +dlag specifies the scaling coefficient to be applied based upon the visits proximity +to the first visit affected by the ICE. By default, the delta will only be added to unobserved (i.e. imputed) post-ICE +outcomes but this can be changed by setting the optional argument missing_only = FALSE.

+

The usage of the delta and dlag arguments is best illustrated with a few examples:

+

Assume a setting with 4 visits and that the user specified delta = c(5,6,7,8) and dlag=c(1,2,3,4).

+

For a subject for whom the first visit affected by the ICE is visit 2, these values of delta and dlag would imply the following delta offset:

+
v1  v2  v3  v4
+--------------
+ 5   6   7   8  # delta assigned to each visit
+ 0   1   2   3  # scaling starting from the first visit after the subjects ICE
+--------------
+ 0   6  14  24  # delta * scaling
+--------------
+ 0   6  20  44  # cumulative sum (i.e. delta) to be applied to each visit
+

That is, the subject would have a delta offset of 0 applied to visit v1, 6 for visit v2, 20 for visit v3 and 44 for visit v4.

+

Assume instead, that the subject’s first visit affected by the ICE was visit 3. Then, the above values of delta and dlag would imply the following delta offset:

+
v1  v2  v3  v4
+--------------
+ 5   6   7   8  # delta assigned to each visit
+ 0   0   1   2  # scaling starting from the first visit after the subjects ICE
+--------------
+ 0   0   7  16  # delta * scaling
+--------------
+ 0   0   7  23  # cumulative sum (i.e. delta) to be applied to each visit
+

To apply a constant delta value of +5 to all visits affected by the ICE +regardless of their proximity to the first ICE visit, one could set delta = c(5,5,5,5) and dlag = c(1,0,0,0). +Alternatively, it may be more straightforward for this setting to call the delta_template() function without the delta and dlag arguments and then overwrite the delta column of the resulting data.frame as described in the previous section (and additionally relying on the is_post_ice variable).

+

Another way of using these arguments is to set delta to the difference in time +between visits and dlag to be the amount of delta per unit of time. For example, +let’s say that visits occur on weeks 1, 5, 6 and 9 and that we want a delta of 3 +to be applied for each week after an ICE. +For simplicity, we assume that the ICE occurs immediately after the subject’s last visit which +is not affected by the ICE. This this could be achieved by setting +delta = c(1,4,1,3) (the difference in weeks between each visit) and dlag = c(3, 3, 3, 3).

+

Assume a subject’s first visit affected by the ICE was visit v2, then these values of delta and dlag would imply the following delta offsets:

+
v1  v2  v3  v4
+--------------
+ 1   4   1   3  # delta assigned to each visit
+ 0   3   3   3  # scaling starting from the first visit after the subjects ICE 
+--------------
+ 0  12   3   9  # delta * scaling
+--------------
+ 0  12  15  24  # cumulative sum (i.e. delta) to be applied to each visit
+

To wrap up, we show this in action for our simulated dataset from section 2 and the imputed datasets +based on a CIR assumption from section 3. +The simulation setting specified follow-up visits at months 2, 4, 6, 8, 10, and 12.
+Assume that we want to apply a delta-adjustment of 1 for every month after an ICE to unobserved post-ICE visits from the intervention group only. (E.g. if the ICE occurred immediately after the month 4 visit, then the total delta applied to a missing value from the month 10 visit would be 6.)

+

To program this, we first use the delta and dlag arguments of delta_template() to set up a corresponding template data.frame:

+
+delta_df <- delta_template(
+    impute_obj_CIR,
+    delta = c(2, 2, 2, 2, 2, 2),
+    dlag = c(1, 1, 1, 1, 1, 1)
+)
+
+head(delta_df)
+#>     id visit   group is_mar is_missing is_post_ice strategy delta
+#> 1 id_1     1 Control   TRUE       TRUE        TRUE      MAR     2
+#> 2 id_1     2 Control   TRUE       TRUE        TRUE      MAR     4
+#> 3 id_1     3 Control   TRUE       TRUE        TRUE      MAR     6
+#> 4 id_1     4 Control   TRUE       TRUE        TRUE      MAR     8
+#> 5 id_1     5 Control   TRUE       TRUE        TRUE      MAR    10
+#> 6 id_1     6 Control   TRUE       TRUE        TRUE      MAR    12
+

Next, we can use the additional metadata variables provided by delta_template() to manually +reset the delta values for the control group back to 0:

+
+delta_df2 <- delta_df %>%
+    mutate(delta = if_else(group == "Control", 0, delta))
+
+head(delta_df2)
+#>     id visit   group is_mar is_missing is_post_ice strategy delta
+#> 1 id_1     1 Control   TRUE       TRUE        TRUE      MAR     0
+#> 2 id_1     2 Control   TRUE       TRUE        TRUE      MAR     0
+#> 3 id_1     3 Control   TRUE       TRUE        TRUE      MAR     0
+#> 4 id_1     4 Control   TRUE       TRUE        TRUE      MAR     0
+#> 5 id_1     5 Control   TRUE       TRUE        TRUE      MAR     0
+#> 6 id_1     6 Control   TRUE       TRUE        TRUE      MAR     0
+

Finally, we can use our delta data.frame to apply the desired delta offset to our analysis:

+
+ana_delta <- analyse(impute_obj_CIR, delta = delta_df2, vars = vars_an)
+pool(ana_delta)
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 20
+#> Method: rubin
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   ==================================================
+#>    parameter   est     se     lci     uci     pval  
+#>   --------------------------------------------------
+#>      trt_1    -0.446  0.514  -1.459  0.567   0.386  
+#>    lsm_ref_1   2.62   0.363  1.904   3.335   <0.001 
+#>    lsm_alt_1  2.173   0.363  1.458   2.889   <0.001 
+#>      trt_2    0.072   0.546  -1.006   1.15   0.895  
+#>    lsm_ref_2  3.708   0.387  2.945   4.471   <0.001 
+#>    lsm_alt_2   3.78   0.386  3.018   4.542   <0.001 
+#>      trt_3    -1.507  0.626  -2.743  -0.272  0.017  
+#>    lsm_ref_3  5.844   0.441  4.973   6.714   <0.001 
+#>    lsm_alt_3  4.336   0.442  3.464   5.209   <0.001 
+#>      trt_4    -2.062  0.731  -3.504  -0.621  0.005  
+#>    lsm_ref_4  7.658   0.519  6.634   8.682   <0.001 
+#>    lsm_alt_4  5.596   0.515   4.58   6.612   <0.001 
+#>      trt_5    -2.938  0.916  -4.746  -1.13   0.002  
+#>    lsm_ref_5  9.558   0.641  8.293   10.823  <0.001 
+#>    lsm_alt_5   6.62   0.651  5.335   7.905   <0.001 
+#>      trt_6    -3.53   1.045  -5.591  -1.469  0.001  
+#>    lsm_ref_6  11.045  0.73   9.604   12.486  <0.001 
+#>    lsm_alt_6  7.515   0.738  6.058   8.971   <0.001 
+#>   --------------------------------------------------
+
+
+
+

References +

+
+
+Barnard, John, and Donald B Rubin. 1999. “Miscellanea. Small-Sample Degrees of Freedom with Multiple Imputation.” Biometrika 86 (4): 948–55. +
+
+Cro, Suzie, Tim P Morris, Michael G Kenward, and James R Carpenter. 2020. “Sensitivity Analysis for Clinical Trials with Missing Continuous Outcome Data Using Controlled Multiple Imputation: A Practical Guide.” Statistics in Medicine 39 (21): 2815–42. +
+
+Wolbers, Marcel, Alessandro Noci, Paul Delmar, Craig Gower-Page, Sean Yiu, and Jonathan W Bartlett. 2022. “Standard and Reference-Based Conditional Mean Imputation.” Pharmaceutical Statistics 21 (6): 1246–57. +
+
+
+
+
+ + + + +
+ + + + + + + diff --git a/v1.3.1/articles/advanced_files/figure-html/unnamed-chunk-15-1.png b/v1.3.1/articles/advanced_files/figure-html/unnamed-chunk-15-1.png new file mode 100644 index 000000000..884f46538 Binary files /dev/null and b/v1.3.1/articles/advanced_files/figure-html/unnamed-chunk-15-1.png differ diff --git a/v1.3.1/articles/index.html b/v1.3.1/articles/index.html new file mode 100644 index 000000000..83de1477c --- /dev/null +++ b/v1.3.1/articles/index.html @@ -0,0 +1,77 @@ + +Articles • rbmi + Skip to contents + + +
+
+
+

Articles

+
+ +
+

All vignettes

+
+ +
rbmi: Advanced Functionality
+
+
rbmi: Inference with Conditional Mean Imputation
+
+
rbmi: Frequently Asked Questions
+
+
rbmi: Quickstart
+
+
rbmi: Implementation of retrieved-dropout models using rbmi
+
+
rbmi: Statistical Specifications
+
+
+
+ + +
+ + + + + + + diff --git a/v1.3.1/articles/quickstart.html b/v1.3.1/articles/quickstart.html new file mode 100644 index 000000000..3f81964f2 --- /dev/null +++ b/v1.3.1/articles/quickstart.html @@ -0,0 +1,630 @@ + + + + + + + +rbmi: Quickstart • rbmi + + + + + + + + Skip to contents + + +
+ + +
+
+

rbmi: Quickstart

+

Craig Gower-Page, Alessandro Noci, and Marcel Wolbers

+ + + Source: vignettes/quickstart.Rmd +
quickstart.Rmd
+
+ + + +
+

+1 Introduction +

+

The purpose of this vignette is to provide a 15 minute quickstart guide to the core functions of the rbmi package.

+

The rbmi package consists of 4 core functions (plus several helper functions) which are typically called in sequence:

+
    +
  • +draws() - fits the imputation models and stores their parameters
    • +
  • +impute() - creates multiple imputed datasets
    • +
  • +analyse() - analyses each of the multiple imputed datasets
    • +
  • +pool() - combines the analysis results across imputed datasets into a single statistic
    • +
+

This example in this vignette makes use of Bayesian multiuple imputation; this functionality +requires the installation of the suggested package rstan.

+
install.packages("rstan")
+
+
+

+2 The Data +

+

We use a publicly available example dataset from an antidepressant clinical trial of an active drug versus placebo. The relevant endpoint is the Hamilton 17-item depression rating scale (HAMD17) which was assessed at baseline and at weeks 1, 2, 4, and 6. Study drug discontinuation occurred in 24% of subjects from the active drug and 26% of subjects from placebo. All data after study drug discontinuation are missing and there is a single additional intermittent missing observation.

+
+library(rbmi)
+library(dplyr)
+#> 
+#> Attaching package: 'dplyr'
+#> The following objects are masked from 'package:stats':
+#> 
+#>     filter, lag
+#> The following objects are masked from 'package:base':
+#> 
+#>     intersect, setdiff, setequal, union
+
+data("antidepressant_data")
+dat <- antidepressant_data
+

We consider an imputation model with the mean change from baseline in the HAMD17 score as the outcome (variable CHANGE in the dataset). The following covariates are included in the imputation model: the treatment group (THERAPY), the (categorical) visit (VISIT), treatment-by-visit interactions, the baseline HAMD17 score (BASVAL), and baseline HAMD17 score-by-visit interactions. A common unstructured covariance matrix structure is assumed for both groups. The analysis model is an ANCOVA model with the treatment group as the primary factor and adjustment for the baseline HAMD17 score.

+

rbmi expects its input dataset to be complete; that is, there must be one row per subject for each visit. Missing outcome values should be coded as NA, while missing covariate values are not allowed. If the dataset is incomplete, then the expand_locf() helper function can be used to add any missing rows, using LOCF imputation to carry forward the observed baseline covariate values to visits with missing outcomes. Rows corresponding to missing outcomes are not present in the antidepressant trial dataset. To address this we will therefore use the expand_locf() function as follows:

+
+
+# Use expand_locf to add rows corresponding to visits with missing outcomes to the dataset
+dat <- expand_locf(
+    dat,
+    PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT 
+    VISIT = levels(dat$VISIT),
+    vars = c("BASVAL", "THERAPY"), # fill with LOCF BASVAL and THERAPY
+    group = c("PATIENT"),
+    order = c("PATIENT", "VISIT")
+)
+
+
+

+3 Draws +

+

The draws() function fits the imputation models and stores the corresponding parameter estimates or Bayesian posterior parameter draws. +The three main inputs to the draws() function are:

+
    +
  • +data - The primary longitudinal data.frame containing the outcome variable and all covariates.
    • +
  • +data_ice - A data.frame which specifies the first visit affected by an intercurrent event (ICE) and the imputation strategy for handling missing outcome data after the ICE. At most one ICE which is to be imputed by a non-MAR strategy is allowed per subject.
    • +
  • +method - The statistical method used to fit the imputation models and to create imputed datasets.
    • +
+

For the antidepressant trial data, the dataset data_ice is not provided. However, it can be derived because, in this dataset, +the subject’s first visit affected by the ICE “study drug discontinuation” corresponds to the first terminal missing observation. +We first derive the dateset data_ice and then create 150 Bayesian posterior draws of the imputation model parameters.

+

For this example, we assume that the imputation strategy after the ICE is Jump To Reference (JR) for all subjects +and that 150 multiple imputed datasets using Bayesian posterior draws from the imputation model are to be created.

+
+# create data_ice and set the imputation strategy to JR for
+# each patient with at least one missing observation
+dat_ice <- dat %>% 
+    arrange(PATIENT, VISIT) %>% 
+    filter(is.na(CHANGE)) %>% 
+    group_by(PATIENT) %>% 
+    slice(1) %>%
+    ungroup() %>% 
+    select(PATIENT, VISIT) %>% 
+    mutate(strategy = "JR")
+
+# In this dataset, subject 3618 has an intermittent missing values which does not correspond
+# to a study drug discontinuation. We therefore remove this subject from `dat_ice`. 
+# (In the later imputation step, it will automatically be imputed under the default MAR assumption.)
+dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),]
+
+dat_ice
+#> # A tibble: 43 × 3
+#>    PATIENT VISIT strategy
+#>    <fct>   <fct> <chr>   
+#>  1 1513    5     JR      
+#>  2 1514    5     JR      
+#>  3 1517    5     JR      
+#>  4 1804    7     JR      
+#>  5 2104    7     JR      
+#>  6 2118    5     JR      
+#>  7 2218    6     JR      
+#>  8 2230    6     JR      
+#>  9 2721    5     JR      
+#> 10 2729    5     JR      
+#> # ℹ 33 more rows
+
+# Define the names of key variables in our dataset and
+# the covariates included in the imputation model using `set_vars()`
+# Note that the covariates argument can also include interaction terms
+vars <- set_vars(
+    outcome = "CHANGE",
+    visit = "VISIT",
+    subjid = "PATIENT",
+    group = "THERAPY",
+    covariates = c("BASVAL*VISIT", "THERAPY*VISIT")
+)
+
+# Define which imputation method to use (here: Bayesian multiple imputation with 150 imputed datsets) 
+method <- method_bayes(
+    burn_in = 200,
+    burn_between = 5,
+    n_samples = 150
+)
+
+# Create samples for the imputation parameters by running the draws() function
+set.seed(987)
+drawObj <- draws(
+    data = dat,
+    data_ice = dat_ice,
+    vars = vars,
+    method = method,
+    quiet = TRUE
+)
+drawObj
+#> 
+#> Draws Object
+#> ------------
+#> Number of Samples: 150
+#> Number of Failed Samples: 0
+#> Model Formula: CHANGE ~ 1 + THERAPY + VISIT + BASVAL * VISIT + THERAPY * VISIT
+#> Imputation Type: random
+#> Method:
+#>     name: Bayes
+#>     burn_in: 200
+#>     burn_between: 5
+#>     same_cov: TRUE
+#>     n_samples: 150
+

Note the use of set_vars() which specifies the names of the key variables +within the dataset and the imputation model. Additionally, note that whilst vars$group and vars$visit +are added as terms to the imputation model by default, their interaction is not, +thus the inclusion of group * visit in the list of covariates.

+

Available imputation methods include:

+
    +
  • Bayesian multiple imputation - method_bayes() +
    • +
  • Approximate Bayesian multiple imputation - method_approxbayes() +
    • +
  • Conditional mean imputation (bootstrap) - method_condmean(type = "bootstrap") +
    • +
  • Conditional mean imputation (jackknife) - method_condmean(type = "jackknife") +
    • +
  • Bootstrapped multiple imputation - method = method_bmlmi() +
    • +
+

For a comparison of these methods, we refer to the stat_specs vignette (Section 3.10).

+

“statistical specifications” vignette (Section 3.10): vignette("stat_specs",package="rbmi").

+

Available imputation strategies include:

+
    +
  • Missing At Random - "MAR" +
    • +
  • Jump to Reference - "JR" +
    • +
  • Copy Reference - "CR" +
    • +
  • Copy Increments from Reference - "CIR" +
    • +
  • Last Mean Carried Forward - "LMCF" +
    • +
+
+
+

+4 Impute +

+

The next step is to use the parameters from the imputation model to generate the imputed datasets. This is +done via the impute() function. The function only has two key inputs: the imputation +model output from draws() and the reference groups relevant to reference-based imputation methods. It’s usage is thus:

+
+imputeObj <- impute(
+    drawObj,
+    references = c("DRUG" = "PLACEBO", "PLACEBO" = "PLACEBO")
+)
+imputeObj
+#> 
+#> Imputation Object
+#> -----------------
+#> Number of Imputed Datasets: 150
+#> Fraction of Missing Data (Original Dataset):
+#>     4:   0%
+#>     5:   8%
+#>     6:  13%
+#>     7:  25%
+#> References:
+#>     DRUG    -> PLACEBO
+#>     PLACEBO -> PLACEBO
+

In this instance, we are specifying that the PLACEBO group should be the reference group for itself as well as for the DRUG group (as is standard for imputation using reference-based methods).

+

Generally speaking, there is no need to see or directly interact with the imputed +datasets. However, if you do wish to inspect them, they can be extracted from the imputation +object using the extract_imputed_dfs() helper function, i.e.:

+
+imputed_dfs <- extract_imputed_dfs(imputeObj)
+head(imputed_dfs[[10]], 12) # first 12 rows of 10th imputed dataset
+#>     PATIENT HAMATOTL PGIIMP RELDAYS VISIT THERAPY GENDER POOLINV BASVAL
+#> 1  new_pt_1       21      2       7     4    DRUG      F     006     32
+#> 2  new_pt_1       19      2      14     5    DRUG      F     006     32
+#> 3  new_pt_1       21      3      28     6    DRUG      F     006     32
+#> 4  new_pt_1       17      4      42     7    DRUG      F     006     32
+#> 5  new_pt_2       18      3       7     4 PLACEBO      F     006     14
+#> 6  new_pt_2       18      2      15     5 PLACEBO      F     006     14
+#> 7  new_pt_2       14      3      29     6 PLACEBO      F     006     14
+#> 8  new_pt_2        8      2      42     7 PLACEBO      F     006     14
+#> 9  new_pt_3       18      3       7     4    DRUG      F     006     21
+#> 10 new_pt_3       17      3      14     5    DRUG      F     006     21
+#> 11 new_pt_3       12      3      28     6    DRUG      F     006     21
+#> 12 new_pt_3        9      3      44     7    DRUG      F     006     21
+#>    HAMDTL17 CHANGE
+#> 1        21    -11
+#> 2        20    -12
+#> 3        19    -13
+#> 4        17    -15
+#> 5        11     -3
+#> 6        14      0
+#> 7         9     -5
+#> 8         5     -9
+#> 9        20     -1
+#> 10       18     -3
+#> 11       16     -5
+#> 12       13     -8
+

Note that in the case of method_bayes() or method_approxbayes(), all imputed datasets correspond to random imputations on the original dataset. +For method_condmean(), the first imputed dataset will always correspond to the completed original dataset containing all subjects. +For method_condmean(type="jackknife"), the remaining datasets correspond to conditional mean imputations on leave-one-subject-out datasets, +whereas for method_condmean(type="bootstrap"), each subsequent dataset corresponds to a conditional mean imputation on a bootstrapped datasets. +For method_bmlmi(), all the imputed datasets correspond to sets of random imputations on bootstrapped datasets.

+
+
+

+5 Analyse +

+

The next step is to run the analysis model on each imputed dataset. This is done by defining +an analysis function and then calling analyse() to apply this function to each +imputed dataset. For this vignette we use the ancova() function provided by the rbmi +package which fits a separate ANCOVA model for the outcomes from each visit and returns a treatment +effect estimate and corresponding least square means for each group per visit.

+
+anaObj <- analyse(
+    imputeObj,
+    ancova,
+    vars = set_vars(
+        subjid = "PATIENT",
+        outcome = "CHANGE",
+        visit = "VISIT",
+        group = "THERAPY",
+        covariates = c("BASVAL")
+    )
+)
+anaObj
+#> 
+#> Analysis Object
+#> ---------------
+#> Number of Results: 150
+#> Analysis Function: ancova
+#> Delta Applied: FALSE
+#> Analysis Estimates:
+#>     trt_4
+#>     lsm_ref_4
+#>     lsm_alt_4
+#>     trt_5
+#>     lsm_ref_5
+#>     lsm_alt_5
+#>     trt_6
+#>     lsm_ref_6
+#>     lsm_alt_6
+#>     trt_7
+#>     lsm_ref_7
+#>     lsm_alt_7
+

Note that, similar to draws(), the ancova() function uses the set_vars() +function which determines the names of the key variables within the data and the covariates +(in addition to the treatment group) for which the analysis model will be adjusted.

+

Please also note that the names of the analysis estimates contain “ref” and “alt” to refer to the two treatment arms. In particular “ref” refers to the first factor level of vars$group which does not necessarily +coincide with the control arm. In this example, since levels(dat[[vars$group]]) = c("DRUG", PLACEBO), the results associated with “ref” correspond to the intervention arm, while those associated with “alt” correspond to the control arm.

+

Additionally, we can use the delta argument of analyse() to perform a delta adjustments of the imputed datasets prior to the analysis. +In brief, this is implemented by specifying a data.frame that contains the amount +of adjustment to be added to each longitudinal outcome for each subject and visit, i.e.  +the data.frame must contain the columns subjid, visit, and delta.

+

It is appreciated that carrying out this procedure is potentially tedious, therefore the +delta_template() helper function has been provided to simplify it. In particular, +delta_template() returns a shell data.frame where the delta-adjustment is set to 0 for all +patients. Additionally delta_template() adds several meta-variables onto the shell +data.frame which can be used for manual derivation or manipulation of the delta-adjustment.

+

For example lets say we want to add a delta-value of 5 to all imputed values (i.e. those values +which were missing in the original dataset) in the drug arm. That could then be implemented as follows:

+
+# For reference show the additional meta variables provided
+delta_template(imputeObj) %>% as_tibble()
+#> # A tibble: 688 × 8
+#>    PATIENT VISIT THERAPY is_mar is_missing is_post_ice strategy delta
+#>    <fct>   <fct> <fct>   <lgl>  <lgl>      <lgl>       <chr>    <dbl>
+#>  1 1503    4     DRUG    TRUE   FALSE      FALSE       NA           0
+#>  2 1503    5     DRUG    TRUE   FALSE      FALSE       NA           0
+#>  3 1503    6     DRUG    TRUE   FALSE      FALSE       NA           0
+#>  4 1503    7     DRUG    TRUE   FALSE      FALSE       NA           0
+#>  5 1507    4     PLACEBO TRUE   FALSE      FALSE       NA           0
+#>  6 1507    5     PLACEBO TRUE   FALSE      FALSE       NA           0
+#>  7 1507    6     PLACEBO TRUE   FALSE      FALSE       NA           0
+#>  8 1507    7     PLACEBO TRUE   FALSE      FALSE       NA           0
+#>  9 1509    4     DRUG    TRUE   FALSE      FALSE       NA           0
+#> 10 1509    5     DRUG    TRUE   FALSE      FALSE       NA           0
+#> # ℹ 678 more rows
+
+delta_df <- delta_template(imputeObj) %>%
+    as_tibble() %>% 
+    mutate(delta = if_else(THERAPY == "DRUG" & is_missing , 5, 0)) %>% 
+    select(PATIENT, VISIT, delta)
+    
+delta_df
+#> # A tibble: 688 × 3
+#>    PATIENT VISIT delta
+#>    <fct>   <fct> <dbl>
+#>  1 1503    4         0
+#>  2 1503    5         0
+#>  3 1503    6         0
+#>  4 1503    7         0
+#>  5 1507    4         0
+#>  6 1507    5         0
+#>  7 1507    6         0
+#>  8 1507    7         0
+#>  9 1509    4         0
+#> 10 1509    5         0
+#> # ℹ 678 more rows
+
+anaObj_delta <- analyse(
+    imputeObj,
+    ancova,
+    delta = delta_df,
+    vars = set_vars(
+        subjid = "PATIENT",
+        outcome = "CHANGE",
+        visit = "VISIT",
+        group = "THERAPY",
+        covariates = c("BASVAL")
+    )
+)
+
+
+

+6 Pool +

+

Finally, the pool() function can be used to summarise the analysis results across multiple +imputed datasets to provide an overall statistic with a standard error, confidence intervals and a p-value for +the hypothesis test of the null hypothesis that the effect is equal to 0.

+

Note that the pooling method is automatically derived based on the method that was specified +in the original call to draws():

+
    +
  • For method_bayes() or method_approxbayes() pooling and inference are based on Rubin’s rules.
    • +
  • For method_condmean(type = "bootstrap") inference is either based on a normal approximation using the bootstrap standard error (pool(..., type = "normal")) or on the bootstrap percentiles (pool(..., type = "percentile")).
    • +
  • For method_condmean(type = "jackknife") inference is based on a normal approximation using the jackknife estimate of the standard error.
    • +
  • For method = method_bmlmi() inference is according to the methods described by von Hippel and Bartlett (see the stat_specs vignette for details)
    • +
+

Since we have used Bayesian multiple imputation in this vignette, the pool() function will automatically use Rubin’s rules.

+
+poolObj <- pool(
+    anaObj, 
+    conf.level = 0.95, 
+    alternative = "two.sided"
+)
+poolObj
+#> 
+#> Pool Object
+#> -----------
+#> Number of Results Combined: 150
+#> Method: rubin
+#> Confidence Level: 0.95
+#> Alternative: two.sided
+#> 
+#> Results:
+#> 
+#>   ==================================================
+#>    parameter   est     se     lci     uci     pval  
+#>   --------------------------------------------------
+#>      trt_4    -0.092  0.683  -1.439  1.256   0.893  
+#>    lsm_ref_4  -1.616  0.486  -2.576  -0.656  0.001  
+#>    lsm_alt_4  -1.708  0.475  -2.645  -0.77   <0.001 
+#>      trt_5    1.332   0.925  -0.495  3.159   0.152  
+#>    lsm_ref_5  -4.157  0.661  -5.462  -2.852  <0.001 
+#>    lsm_alt_5  -2.825  0.646   -4.1   -1.55   <0.001 
+#>      trt_6    1.927   1.005  -0.059  3.913   0.057  
+#>    lsm_ref_6  -6.097  0.721  -7.522  -4.671  <0.001 
+#>    lsm_alt_6  -4.17    0.7   -5.553  -2.786  <0.001 
+#>      trt_7     2.18   1.143  -0.08   4.439   0.059  
+#>    lsm_ref_7  -6.994  0.826  -8.628  -5.36   <0.001 
+#>    lsm_alt_7  -4.815  0.791  -6.379  -3.25   <0.001 
+#>   --------------------------------------------------
+

The table of values shown in the print message for poolObj can also be extracted using the as.data.frame() function:

+
+as.data.frame(poolObj)
+#>    parameter         est        se         lci        uci         pval
+#> 1      trt_4 -0.09180645 0.6826279 -1.43949684  1.2558839 8.931772e-01
+#> 2  lsm_ref_4 -1.61581996 0.4862316 -2.57577141 -0.6558685 1.093708e-03
+#> 3  lsm_alt_4 -1.70762640 0.4749573 -2.64531931 -0.7699335 4.262148e-04
+#> 4      trt_5  1.33217342 0.9248889 -0.49452471  3.1588715 1.517381e-01
+#> 5  lsm_ref_5 -4.15685743 0.6607638 -5.46196249 -2.8517524 2.982856e-09
+#> 6  lsm_alt_5 -2.82468402 0.6455730 -4.09978956 -1.5495785 2.197441e-05
+#> 7      trt_6  1.92723926 1.0050687 -0.05860912  3.9130876 5.706399e-02
+#> 8  lsm_ref_6 -6.09679600 0.7213490 -7.52226719 -4.6713248 2.489617e-14
+#> 9  lsm_alt_6 -4.16955674 0.7003707 -5.55341225 -2.7857012 1.784937e-08
+#> 10     trt_7  2.17964370 1.1426199 -0.07965819  4.4389456 5.852211e-02
+#> 11 lsm_ref_7 -6.99418014 0.8260358 -8.62803604 -5.3603242 4.048404e-14
+#> 12 lsm_alt_7 -4.81453644 0.7913711 -6.37916058 -3.2499123 1.067031e-08
+

These outputs gives an estimated difference of +2.180 (95% CI -0.080 to 4.439) +between the two groups at the last visit with an associated p-value of 0.059.

+
+
+

+7 Code +

+

We report below all the code presented in this vignette.

+
+library(rbmi)
+library(dplyr)
+
+data("antidepressant_data")
+dat <- antidepressant_data
+
+# Use expand_locf to add rows corresponding to visits with missing outcomes to the dataset
+dat <- expand_locf(
+    dat,
+    PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT 
+    VISIT = levels(dat$VISIT),
+    vars = c("BASVAL", "THERAPY"), # fill with LOCF BASVAL and THERAPY
+    group = c("PATIENT"),
+    order = c("PATIENT", "VISIT")
+)
+
+# Create data_ice and set the imputation strategy to JR for
+# each patient with at least one missing observation
+dat_ice <- dat %>% 
+    arrange(PATIENT, VISIT) %>% 
+    filter(is.na(CHANGE)) %>% 
+    group_by(PATIENT) %>% 
+    slice(1) %>%
+    ungroup() %>% 
+    select(PATIENT, VISIT) %>% 
+    mutate(strategy = "JR")
+
+# In this dataset, subject 3618 has an intermittent missing values which does not correspond
+# to a study drug discontinuation. We therefore remove this subject from `dat_ice`. 
+# (In the later imputation step, it will automatically be imputed under the default MAR assumption.)
+dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),]
+
+# Define the names of key variables in our dataset using `set_vars()`
+# and the covariates included in the imputation model
+# Note that the covariates argument can also include interaction terms
+vars <- set_vars(
+    outcome = "CHANGE",
+    visit = "VISIT",
+    subjid = "PATIENT",
+    group = "THERAPY",
+    covariates = c("BASVAL*VISIT", "THERAPY*VISIT")
+)
+
+# Define which imputation method to use (here: Bayesian multiple imputation with 150 imputed datsets) 
+method <- method_bayes(
+    burn_in = 200,
+    burn_between = 5,
+    n_samples = 150
+)
+
+
+# Create samples for the imputation parameters by running the draws() function
+set.seed(987)
+drawObj <- draws(
+    data = dat,
+    data_ice = dat_ice,
+    vars = vars,
+    method = method,
+    quiet = TRUE
+)
+
+# Impute the data
+imputeObj <- impute(
+    drawObj,
+    references = c("DRUG" = "PLACEBO", "PLACEBO" = "PLACEBO")
+)
+
+# Fit the analysis model on each imputed dataset
+anaObj <- analyse(
+    imputeObj,
+    ancova,
+    vars = set_vars(
+        subjid = "PATIENT",
+        outcome = "CHANGE",
+        visit = "VISIT",
+        group = "THERAPY",
+        covariates = c("BASVAL")
+    )
+)
+
+# Apply a delta adjustment
+
+# Add a delta-value of 5 to all imputed values (i.e. those values
+# which were missing in the original dataset) in the drug arm.
+delta_df <- delta_template(imputeObj) %>%
+    as_tibble() %>% 
+    mutate(delta = if_else(THERAPY == "DRUG" & is_missing , 5, 0)) %>% 
+    select(PATIENT, VISIT, delta)
+
+# Repeat the analyses with the adjusted values
+anaObj_delta <- analyse(
+    imputeObj,
+    ancova,
+    delta = delta_df,
+    vars = set_vars(
+        subjid = "PATIENT",
+        outcome = "CHANGE",
+        visit = "VISIT",
+        group = "THERAPY",
+        covariates = c("BASVAL")
+    )
+)
+
+# Pool the results
+poolObj <- pool(
+    anaObj, 
+    conf.level = 0.95, 
+    alternative = "two.sided"
+)
+
+
+
+ + + + +
+ + + + + + + diff --git a/v1.3.1/articles/retrieved_dropout.html b/v1.3.1/articles/retrieved_dropout.html new file mode 100644 index 000000000..1647bc5bb --- /dev/null +++ b/v1.3.1/articles/retrieved_dropout.html @@ -0,0 +1,500 @@ + + + + + + + +rbmi: Implementation of retrieved-dropout models using rbmi • rbmi + + + + + + + + Skip to contents + + +
+ + +
+
+

rbmi: Implementation of retrieved-dropout models using rbmi

+

Alessandro Noci, Marcel Wolbers

+ +

2024-07-30

+ + Source: vignettes/retrieved_dropout.Rmd +
retrieved_dropout.Rmd
+
+ + + +

This vignette describes how retrieved dropout models which include time-varying intercurrent event (ICE) indicators can be +implemented in the rbmi package.

+
+

+1 Retrieved dropout models in a nutshell +

+

Retrieved dropout models have been proposed for the analysis of estimands using the treatment policy strategy for addressing an ICE. +In these models, missing outcomes are multiply imputed conditional upon whether they occur pre- or post-ICE. Retrieved dropout models +typically rely on an extended missing-at-random (MAR) assumption, i.e., they assume that missing outcome data is similar to observed +data from subjects in the same treatment group with the same observed outcome history, and the same ICE status. For a more +comprehensive description and evaluation of retrieved dropout models, we refer to Guizzaro et al. (2021), Polverejan and Dragalin (2020), Noci et al. (2023), +Drury et al. (2024), and Bell et al. (2024). Broadly, these publications find that retrieved dropout models reduce bias compared to alternative +analysis approaches based on imputation under a basic MAR assumption or a reference-based missing data assumption. However, several +issues of retrieved dropout models have also been highlighted. Retrieved dropout models require that enough post-ICE data is +collected to inform the imputation model. Even with relatively small amounts of missingness, complex retrieved dropout models may +face identifiability issues. Another drawback to these models in general is the loss of power relative to reference-based imputation methods, which +becomes meaningful for post-ICE observation percentages below 50% and increases at an accelerating rate as this percentage decreases (Bell et al. 2024).

+
+
+

+2 Data simulation using function simulate_data() +

+

For the purposes of this vignette we will first create a simulated dataset with the rbmi function simulate_data(). +The simulate_data() function generates data from a randomized clinical trial with longitudinal continuous outcomes and up to two +different types of ICEs.

+

Specifically, we simulate a 1:1 randomized trial of an active drug (intervention) versus placebo (control) with 100 subjects per +group and 4 post-baseline assessments (3-monthly visits until 12 months):

+
    +
  • The mean outcome trajectory in the placebo group increases linearly from 50 at baseline (visit 0) to 60 at visit 4, i.e. the slope is 10 points/year (or 2.5 points every 3 months).
    • +
  • The mean outcome trajectory in the intervention group is identical to the placebo group up to month 6. From month 6 onward, the slope decreases by 50% to 5 points/year (i.e. 1.25 points every 3 months).
    • +
  • The covariance structure of the baseline and follow-up values in both groups is implied by a random intercept and slope model +with a standard deviation of 5 for both the intercept and the slope, and a correlation of 0.25. In addition, an independent +residual error with standard deviation 2.5 is added to each assessment.
    +
    • +
  • The probability of the intercurrent event study drug discontinuation after each visit is calculated according to a logistic model which depends on the observed outcome at that visit. +Specifically, a visit-wise discontinuation probability of 3% and 4% in the control and intervention group, respectively, is specified in case the observed outcome is equal to 50 (the mean value at baseline). +The odds of a discontinuation is simulated to increase by +10% for each +1 point increase of the observed outcome.
    • +
  • Study drug discontinuation is simulated to have no effect on the mean trajectory in the placebo group. +In the intervention group, subjects who discontinue follow the slope of the mean trajectory from the placebo group +from that time point onward. This is compatible with a copy increments in reference (CIR) assumption.
    • +
  • Study dropout at the study drug discontinuation visit occurs with a probability of 50% leading to missing outcome +data from that time point onward.
    • +
+

The function simulate_data() requires 3 arguments (see the function documentation help(simulate_data) for more details):

+
    +
  • +pars_c: The simulation parameters of the control group.
    • +
  • +pars_t: The simulation parameters of the intervention group.
    • +
  • +post_ice1_traj: Specifies how observed outcomes after ICE1 are simulated.
    • +
+

Below, we report how data according to the specifications above can be simulated with function simulate_data():

+ +
## 
+## Attaching package: 'dplyr'
+
## The following objects are masked from 'package:stats':
+## 
+##     filter, lag
+
## The following objects are masked from 'package:base':
+## 
+##     intersect, setdiff, setequal, union
+
+set.seed(1392)
+
+time <- c(0, 3, 6, 9, 12)
+
+# Mean trajectory control
+muC <- c(50.0, 52.5, 55.0, 57.5, 60.0)
+
+# Mean trajectory intervention
+muT <- c(50.0, 52.5, 55.0, 56.25, 57.50)
+
+# Create Sigma
+sd_error <- 2.5
+covRE <- rbind(
+  c(25.0, 6.25),
+  c(6.25, 25.0)
+)
+
+Sigma <- cbind(1, time / 12) %*%
+    covRE %*% rbind(1, time / 12) +
+    diag(sd_error^2, nrow = length(time))
+
+# Set simulation parameters of the control group
+parsC <- set_simul_pars(
+    mu = muC,
+    sigma = Sigma,
+    n = 100, # sample size
+    prob_ice1 = 0.03, # prob of discontinuation for outcome equal to 50
+    or_outcome_ice1 = 1.10,  # +1 point increase => +10% odds of discontinuation
+    prob_post_ice1_dropout = 0.5 # dropout rate following discontinuation
+)
+
+# Set simulation parameters of the intervention group
+parsT <- parsC
+parsT$mu <- muT
+parsT$prob_ice1 <- 0.04
+
+# Simulate data
+data <- simulate_data(
+    pars_c = parsC,
+    pars_t = parsT,
+    post_ice1_traj = "CIR" # Assumption about post-ice trajectory
+) %>%
+  select(-c(outcome_noICE, ind_ice2)) # remove unncessary columns
+  
+
+head(data)
+
##     id visit   group outcome_bl ind_ice1 dropout_ice1  outcome
+## 1 id_1     0 Control   53.35397        0            0 53.35397
+## 2 id_1     1 Control   53.35397        0            0 55.15100
+## 3 id_1     2 Control   53.35397        0            0 59.81038
+## 4 id_1     3 Control   53.35397        0            0 61.59709
+## 5 id_1     4 Control   53.35397        0            0 67.08044
+## 6 id_2     0 Control   53.31025        0            0 53.31025
+

The frequency of the ICE and proportion of data collected after the ICE impacts the variance of the treatment effect for +retrieved dropout models. For example, a large proportion of ICE combined with a small proportion of data collected after the +ICE might result in substantial variance inflation, especially for more complex retrieved dropout models.

+

The proportion of subjects with an ICE and the proportion of subjects who withdrew from the simulated study is summarized below:

+
+# Compute endpoint of interest: change from baseline
+data <- data %>% 
+  filter(visit != "0") %>%
+  mutate(
+    change = outcome - outcome_bl,
+    visit = factor(visit, levels = unique(visit))
+  )
+      
+
+data %>%
+  group_by(visit) %>% 
+  summarise(
+    freq_disc_ctrl = mean(ind_ice1[group == "Control"] == 1),
+    freq_dropout_ctrl = mean(dropout_ice1[group == "Control"] == 1),
+    freq_disc_interv = mean(ind_ice1[group == "Intervention"] == 1),
+    freq_dropout_interv = mean(dropout_ice1[group == "Intervention"] == 1)
+  )
+
## # A tibble: 4 × 5
+##   visit freq_disc_ctrl freq_dropout_ctrl freq_disc_interv freq_dropout_interv
+##   <fct>          <dbl>             <dbl>            <dbl>               <dbl>
+## 1 1               0.03              0.01             0.06                0.03
+## 2 2               0.1               0.03             0.1                 0.04
+## 3 3               0.19              0.09             0.17                0.06
+## 4 4               0.23              0.12             0.24                0.1
+

For this study 23% of the study participants discontinued from study treatment in the control arm and 24% in the intervention +arm. Approximately half of the participants who discontinued from treatment dropped-out from the study at the discontinuation +visit leading to missing outcomes at subsequent visits.

+
+
+

+3 Estimators based on retrieved dropout models +

+

We consider retrieved dropout methods which model pre- and post-ICE outcomes jointly by including time-varying ICE indicators in +the imputation model, i.e. we allow the occurrence of the ICE to impact the mean structure but not the covariance matrix. +Imputation of missing outcomes is then performed under a MAR assumption including all observed data. For the analysis of the +completed data, we use a standard ANCOVA model of the outcome at each follow-up visit, respectively, with treatment assignment +as the main covariate and adjustment for the baseline outcome.

+

Specifically, we consider the following imputation models:

+
    +
  • +Imputation under a basic MAR assumption (basic MAR): This model ignores whether an outcome is observed pre- or post-ICE, +i.e. it is not a retrieved dropout model. Rather, it is asymptotically equivalent to a standard MMRM model and analogous to the +“MI1” model in Bell et al. (2024). The only difference to the “MI1” model is that rbmi is not based on sequential imputation but +rather, all missing outcomes are imputed simultaneously based on a MMRM-type imputation model. We include baseline outcome by +visit and treatment group by visit interaction terms in the imputation model which is of the form: +change ~ outcome_bl*visit + group*visit.
    • +
  • +Retrieved dropout model 1 (RD1): This model uses the following imputation model: +change ~ outcome_bl*visit + group*visit + time_since_ice1*group, where time_since_ice1 is set to 0 up to +the treatment discontinuation and to the time from treatment +discontinuation (in months) at subsequent visits. This implies a change in the slope of the outcome trajectories after the ICE, which +is modeled separately for each treatment arm. This model is similar to the “TV2-MAR” estimator in Noci et al. (2023). Compared to the basic +MAR model, this model requires estimation of 2 additional parameters.
    • +
  • +Retrieved dropout model 2 (RD2): This model uses the following imputation model: change ~ outcome_bl*visit + group*visit + ind_ice1*group*visit. This assumes a constant shift in outcomes after the ICE, which is modeled separately for each treatment arm +and each visit. This model is analogous to the “MI2” model in Bell et al. (2024). Compared to the basic MAR model, this model requires +estimation of 2 times “number of visits” additional parameters. It makes different though rather weaker assumptions than the RD1 +model but might also be harder to fit if post-ICE data collection is sparse at some visits.
    • +
+
+
+

+4 Implementation of the defined retrieved dropout models in rbmi +

+

rbmi supports the inclusion of time-varying covariates in the imputation model. The only requirement is that the time-varying +covariate is non-missing at all visits including those where the outcome might be missing. +Imputation is performed under a (extended) MAR assumption. Therefore, all imputation approaches implemented in rbmi are valid and +should yield comparable estimators and standard errors. +For this vignette, we used the conditional mean imputation approach combined with the jackknife.

+
+

+4.1 Basic MAR model +

+
+# Define key variables for the imputation and analysis models
+vars <- set_vars(
+  subjid = "id",
+  visit = "visit",
+  outcome = "change",
+  group = "group",
+  covariates = c("outcome_bl*visit", "group*visit")
+)
+
+vars_an <- vars
+vars_an$covariates <- "outcome_bl"
+
+# Define imputation method
+method <- method_condmean(type = "jackknife")
+
+draw_obj <- draws(
+  data = data,
+  data_ice = NULL,
+  vars = vars,
+  method = method,
+  quiet = TRUE
+)
+
+impute_obj <- impute(
+  draw_obj
+)
+
+ana_obj <- analyse(
+  impute_obj,
+  vars = vars_an
+)
+
+pool_obj_basicMAR <- pool(ana_obj)
+pool_obj_basicMAR
+
## 
+## Pool Object
+## -----------
+## Number of Results Combined: 1 + 200
+## Method: jackknife
+## Confidence Level: 0.95
+## Alternative: two.sided
+## 
+## Results:
+## 
+##   ==================================================
+##    parameter   est     se     lci     uci     pval  
+##   --------------------------------------------------
+##      trt_1    -0.991  0.557  -2.083  0.101   0.075  
+##    lsm_ref_1  3.117   0.401  2.331   3.902   <0.001 
+##    lsm_alt_1  2.126   0.391   1.36   2.892   <0.001 
+##      trt_2    -0.937  0.611  -2.134   0.26   0.125  
+##    lsm_ref_2  5.814   0.447  4.938    6.69   <0.001 
+##    lsm_alt_2  4.877   0.414  4.066   5.688   <0.001 
+##      trt_3    -1.491  0.743  -2.948  -0.034  0.045  
+##    lsm_ref_3  7.725   0.526  6.694   8.757   <0.001 
+##    lsm_alt_3  6.234   0.522  5.211   7.258   <0.001 
+##      trt_4    -2.872  0.945  -4.723  -1.02   0.002  
+##    lsm_ref_4  10.787  0.661  9.491   12.083  <0.001 
+##    lsm_alt_4  7.915   0.67   6.603   9.228   <0.001 
+##   --------------------------------------------------
+
+
+

+4.2 Retrieved dropout model 1 (RD1) +

+
+# derive variable "time_since_ice1" (time since ICE in months)
+data <- data %>% 
+  group_by(id) %>% 
+  mutate(time_since_ice1 = cumsum(ind_ice1)*3)
+
+vars$covariates <- c("outcome_bl*visit", "group*visit", "time_since_ice1*group")
+
+draw_obj <- draws(
+  data = data,
+  data_ice = NULL,
+  vars = vars,
+  method = method,
+  quiet = TRUE
+)
+
+impute_obj <- impute(
+  draw_obj
+)
+
+ana_obj <- analyse(
+  impute_obj,
+  vars = vars_an
+)
+
+pool_obj_RD1 <- pool(ana_obj)
+pool_obj_RD1
+
## 
+## Pool Object
+## -----------
+## Number of Results Combined: 1 + 200
+## Method: jackknife
+## Confidence Level: 0.95
+## Alternative: two.sided
+## 
+## Results:
+## 
+##   ==================================================
+##    parameter   est     se     lci     uci     pval  
+##   --------------------------------------------------
+##      trt_1    -0.931  0.558  -2.025  0.163   0.095  
+##    lsm_ref_1  3.119    0.4   2.334   3.903   <0.001 
+##    lsm_alt_1  2.188   0.393  1.419   2.957   <0.001 
+##      trt_2    -0.805  0.616  -2.013  0.403   0.192  
+##    lsm_ref_2  5.822   0.445  4.949   6.695   <0.001 
+##    lsm_alt_2  5.017   0.424  4.186   5.849   <0.001 
+##      trt_3    -1.263  0.758  -2.748  0.222   0.096  
+##    lsm_ref_3  7.749   0.52   6.729   8.768   <0.001 
+##    lsm_alt_3  6.486   0.549   5.41   7.562   <0.001 
+##      trt_4    -2.506  0.969  -4.406  -0.606   0.01  
+##    lsm_ref_4  10.837  0.653  9.558   12.116  <0.001 
+##    lsm_alt_4  8.331   0.718  6.924   9.737   <0.001 
+##   --------------------------------------------------
+
+
+

+4.3 Retrieved dropout model 2 (RD2) +

+
+vars$covariates <- c("outcome_bl*visit", "group*visit", "ind_ice1*group*visit")
+
+draw_obj <- draws(
+  data = data,
+  data_ice = NULL,
+  vars = vars,
+  method = method,
+  quiet = TRUE
+)
+
+impute_obj <- impute(
+  draw_obj
+)
+
+ana_obj <- analyse(
+  impute_obj,
+  vars = vars_an
+)
+
+pool_obj_RD2 <- pool(ana_obj)
+pool_obj_RD2
+
## 
+## Pool Object
+## -----------
+## Number of Results Combined: 1 + 200
+## Method: jackknife
+## Confidence Level: 0.95
+## Alternative: two.sided
+## 
+## Results:
+## 
+##   ==================================================
+##    parameter   est     se     lci     uci     pval  
+##   --------------------------------------------------
+##      trt_1    -0.927  0.558  -2.021  0.167   0.097  
+##    lsm_ref_1  3.125    0.4   2.341   3.908   <0.001 
+##    lsm_alt_1  2.198   0.395  1.424   2.972   <0.001 
+##      trt_2    -0.889  0.612  -2.089  0.311   0.146  
+##    lsm_ref_2  5.837   0.443   4.97   6.705   <0.001 
+##    lsm_alt_2  4.948   0.421  4.124   5.772   <0.001 
+##      trt_3    -1.305  0.757  -2.788  0.178   0.085  
+##    lsm_ref_3  7.648   0.54    6.59   8.707   <0.001 
+##    lsm_alt_3  6.343   0.528  5.308   7.378   <0.001 
+##      trt_4    -2.617  0.975  -4.528  -0.706  0.007  
+##    lsm_ref_4  10.883  0.665   9.58   12.186  <0.001 
+##    lsm_alt_4  8.267   0.715  6.866   9.667   <0.001 
+##   --------------------------------------------------
+
+
+

+4.4 Brief summary of results +

+

The point estimators of the treatment effect at the last visit were +-2.872, +-2.506, and +-2.617 for the basic MAR, RD1, and RD2 estimators, respectively, i.e. slightly +smaller for the retrieved dropout models compared to the basic MAR model. +The corresponding standard errors of the 3 estimators were +0.945, +0.969, and +0.975, i.e. slightly larger for the retrieved dropout models compared to the +basic MAR model.

+
+
+
+

References +

+
+
+Bell, James, Thomas Drury, Tobias Mütze, Christian Bressen Pipper, Lorenzo Guizzaro, Marian Mitroiu, Khadija Rerhou Rantell, Marcel Wolbers, and David Wright. 2024. “Estimation Methods for Estimands Using the Treatment Policy Strategy; a Simulation Study Based on the PIONEER 1 Trial.” arXiv Preprint. https://arxiv.org/abs/2402.12850. +
+
+Drury, Thomas, Juan J Abellan, Nicky Best, and Ian R White. 2024. “Estimation of Treatment Policy Estimands for Continuous Outcomes Using Off-Treatment Sequential Multiple Imputation.” Pharmaceutical Statistics. +
+
+Guizzaro, Lorenzo, Frank Pétavy, Robin Ristl, and Ciro Gallo. 2021. “The Use of a Variable Representing Compliance Improves Accuracy of Estimation of the Effect of Treatment Allocation Regardless of Discontinuation in Trials with Incomplete Follow-up.” Statistics in Biopharmaceutical Research 13 (1): 119–27. +
+
+Noci, Alessandro, Marcel Wolbers, Markus Abt, Corine Baayen, Hans Ulrich Burger, Man Jin, and Weining Zhao Robieson. 2023. “A Comparison of Estimand and Estimation Strategies for Clinical Trials in Early Parkinson’s Disease.” Statistics in Biopharmaceutical Research 15 (3): 491–501. +
+
+Polverejan, Elena, and Vladimir Dragalin. 2020. “Aligning Treatment Policy Estimands and Estimators—a Simulation Study in Alzheimer’s Disease.” Statistics in Biopharmaceutical Research 12 (2): 142–54. +
+
+
+
+
+ + + + +
+ + + + + + + diff --git a/v1.3.1/articles/stat_specs.html b/v1.3.1/articles/stat_specs.html new file mode 100644 index 000000000..3ce94e49a --- /dev/null +++ b/v1.3.1/articles/stat_specs.html @@ -0,0 +1,714 @@ + + + + + + + +rbmi: Statistical Specifications • rbmi + + + + + + + + Skip to contents + + +
+ + +
+
+

rbmi: Statistical Specifications

+

Alessandro Noci, Craig Gower-Page, and Marcel Wolbers

+ + + Source: vignettes/stat_specs.Rmd +
stat_specs.Rmd
+
+ + + +
+

+1 Scope of this document +

+

This document describes the statistical methods implemented in the rbmi R package for standard and reference-based multiple imputation of continuous longitudinal outcomes. +The package implements three classes of multiple imputation (MI) approaches:

+
    +

  1. Conventional MI methods based on Bayesian (or approximate Bayesian) posterior draws of model parameters combined with Rubin’s rules to make inferences as described in Carpenter, Roger, and Kenward (2013) and Cro et al. (2020).

    2. +

  2. Conditional mean imputation methods combined with re-sampling techniques as described in Wolbers et al. (2022).

    3. +

  3. Bootstrapped MI methods as described in von Hippel and Bartlett (2021).

    4. +
+

The document is structured as follows: we first provide an informal introduction to estimands and corresponding treatment effect estimation based on MI (section 2). The core of this document consists of section 3 which describes the statistical methodology in detail and also contains a comparison of the implemented approaches (section 3.10). The link between theory and the functions included in package rbmi is described in section 4. We conclude with a comparison of our package to some alternative software implementations of reference-based imputation methods (section 5).

+
+
+

+2 Introduction to estimands and estimation methods +

+
+

+2.1 Estimands +

+

The ICH E9(R1) addendum on estimands and sensitivity analyses describes a systematic approach to ensure alignment among clinical trial objectives, trial execution/conduct, statistical analyses, and interpretation of results (ICH E9 working group (2019)). +As per the addendum, an estimand is a precise description of the treatment effect reflecting the clinical question posed by the trial objective which summarizes at a population-level what the outcomes would be in the same patients under different +treatment conditions being compared. +One important attribute of an estimand is a list of possible intercurrent events (ICEs), i.e. of events occurring after treatment initiation that affect either the interpretation or the existence of the measurements associated with the clinical question of interest, and the definition of appropriate strategies to deal with ICEs. The three most relevant strategies for the purpose of this document are the hypothetical strategy, the treatment policy strategy, and the composite strategy. For the hypothetical strategy, a scenario is envisaged in which the ICE would not occur. Under this scenario, endpoint values after the ICE are not directly observable and treated using models for missing data. +For the treatment policy strategy, the treatment effect in the presence of the ICEs is targeted and analyses are based on the observed outcomes regardless whether the subject had an ICE or not. +For the composite strategy, the ICE itself is included as a component of the endpoint.

+
+
+

+2.2 Alignment between the estimand and the estimation method +

+

The ICH E9(R1) addendum distinguishes between ICEs and missing data (ICH E9 working group (2019)). Whereas ICEs such as treatment discontinuations reflect clinical practice, the amount of missing data can be minimized in the conduct of a clinical trial. However, there are many connections between missing data and ICEs. For example, it is often difficult to retain subjects in a clinical trial after treatment discontinuation and a subject’s dropout from the trial leads to missing data. As another example, outcome values after ICEs addressed using a hypothetical strateg are not directly observable under the hypothetical scenario. Consequently, any observed outcome values after such ICEs are typically discarded and treated as missing data.

+

The addendum proposes that estimation methods to address the problem presented by missing data should be selected to align with the estimand. A recent overview of methods to align the estimator with the estimand is Mallinckrodt et al. (2020). A short introduction on estimation methods for studies with longitudinal endpoints can also be found in Wolbers et al. (2022). One prominent statistical method for this purpose is multiple imputation (MI), which is the target of the rbmi package.

+
+

+2.2.1 Missing data prior to ICEs +

+

Missing data may occur in subjects without an ICE or prior to the occurrence of an ICE. As such missing outcomes are not associated with an ICE, it is often plausible to impute them under a missing-at-random (MAR) assumption using a standard MMRM imputation model of the longitudinal outcomes. Informally, MAR occurs if the missing data can be fully accounted for by the baseline variables included in the model and the observed longitudinal outcomes, and if the model is correctly specified.

+
+
+

+2.2.2 Implementation of the hypothetical strategy +

+

The MAR imputation model described above is often also a good starting point for imputing data after an ICE handled using a hypothetical strategy (Mallinckrodt et al. (2020)). +Informally, this assumes that unobserved values after the ICE would have been similar to the observed data from subjects who did not have the ICE and remained under follow-up. +However, in some situations, it may be more reasonable to assume that missingness is “informative” and indicates a systematically better or worse outcome than in observed subjects. In such situations, MNAR imputation with a \(\delta\)-adjustment could be explored as a sensitivity analysis. \(\delta\)-adjustments add a fixed or random quantity to the imputations in order to make the imputed outcomes systematically worse or better than those observed as described in Cro et al. (2020). In rbmi only fixed \(\delta\)-adjustments are implemented.

+
+
+

+2.2.3 Implementation of the treatment policy strategy +

+

Ideally, data collection continues after an ICE handled with a treatment policy strategy and no missing data arises. +Indeed, such post-ICE data are increasingly systematically collected in RCTs. +However, despite best efforts, missing data after an ICE such as study treatment discontinuation may still occur because the subject drops out from the study after discontinuation. It is difficult to give definite recommendations regarding the implementation of the treatment policy strategy in the presence of missing data at this stage because the optimal method is highly context dependent and a topic of ongoing statistical research.

+

For ICEs which are thought to have a negligible effect on efficacy outcomes, standard MAR-based imputation which ignores whether an outcome is observed pre- or post-ICE may be appropriate. +In contrast, an ICE such as treatment discontinuation may be expected to have a more substantial impact on efficacy outcomes. In such settings, the MAR assumption may still be plausible after conditioning on the subject’s time-varying treatment status (Guizzaro et al. (2021)). In this case, one option is to impute missing post-discontinuation data based on subjects who also discontinued treatment but continued to be followed up. Another option which may require somewhat less post-discontinuation data is to include all subjects in the imputation procedure but to model post-discontinuation data by using time-varying treatment status indicators (Guizzaro et al. (2021), Polverejan and Dragalin (2020), Noci et al. (2023), Drury et al. (2024), Bell et al. (2024)). In this approach, post-ICE outcomes are included in every step of the analysis, including in the fitting of the imputation model. It assumes that ICEs may impact post-ICE outcomes but that otherwise missingness is non-informative. The approach also assumes that the time-varying covariates do not contain missing values, deviations in outcomes after the ICE are correctly modeled by these time-varying covariates, and that sufficient post-ICE data are available to inform the regression coefficients of the time-varying covariates. +The resulting imputation models are called “retrieved dropout models” in the statistical literature. These models tend to have less bias than alternative analysis approaches based on imputation under a basic MAR assumption or a reference-based missing data assumption. However, retrieved dropout models have been associated with inflated standard errors of associated treatment effect estimators which has a detrimental effect on study power. In particular, it has been observed that once the post-ICE observation percentages falls below 50%, the power loss can be quite dramatic (Bell et al. 2024). We illustrate the implementation of retrieved dropout models in the vignette “Implementation of retrieved-dropout models using rbmi” (vignette(topic = "retrieved_dropout", package = "rbmi")).

+

In some trial settings, only few subjects discontinue the randomized treatment. In other settings, treatment discontinuation rates are higher but it is difficult to retain subjects in the trial after treatment discontinuation leading to sparse data collection after treatment discontinuation. In both settings, the amount of available data after treatment discontinuation may be insufficient to inform an imputation model which explicitly models post-discontinuation data. Depending on the disease area and the anticipated mechanism of action of the intervention, it may be plausible to assume that subjects in the intervention group behave similarly to subjects in the control group after the ICE treatment discontinuation. In this case, reference-based imputation methods are an option (Mallinckrodt et al. (2020)). Reference-based imputation methods formalize the idea to impute missing data in the intervention group based on data from a control or reference group. For a general description and review of reference-based imputation methods, we refer to Carpenter, Roger, and Kenward (2013), Cro et al. (2020), I. White, Royes, and Best (2020) and Wolbers et al. (2022). For a technical description of the implemented statistical methodology for reference-based imputation, we refer to section 3 (in particular section 3.4).

+
+
+

+2.2.4 Implementation of the composite strategy +

+

The composite strategy is typically applied to binary or time-to-event outcomes but it can also be used for continuous outcomes by ascribing a suitably unfavorable value to patients who experience ICEs for which a composite strategy has been defined. One possibility to implement this is to use MI with a \(\delta\)-adjustment for post-ICE data as described in Darken et al. (2020).

+
+
+
+
+

+3 Statistical methodology +

+
+

+3.1 Overview of the imputation procedure +

+

Analyses of datasets with missing data always rely on missing data assumptions. The methods described here can be used to produce valid imputations under a MAR assumption or under reference-based imputation assumptions. MNAR imputation based on fixed \(\delta\)-adjustments as typically used in sensitivity analyses such as tipping-point analyses are also supported.

+

Three general imputation approaches are implemented in rbmi:

+
    +

  1. Conventional MI based on Bayesian (or approximate Bayesian) posterior draws from the imputation model combined with Rubin’s rules for inference as described in Carpenter, Roger, and Kenward (2013) and Cro et al. (2020).

    2. +

  2. Conditional mean imputation based on the REML estimate of the imputation model combined with resampling techniques (the jackknife or the bootstrap) for inference as described in Wolbers et al. (2022).

    3. +

  3. Bootstrapped MI methods based on REML estimates of the imputation model as described in von Hippel and Bartlett (2021).

    4. +
+
+

+3.1.1 Conventional MI +

+

Conventional MI approaches include the following steps:

+
    +
  1. +Base imputation model fitting step (Section 3.3)
    2. +
+
    +

  • Fit a Bayesian multivariate normal mixed model for repeated measures (MMRM) to the observed longitudinal outcomes after exclusion of data after ICEs for which reference-based missing data imputation is desired (Section 3.3.3). Draw \(M\) posterior samples of the estimated parameters (regression coefficients and covariance matrices) from this model.

    • +

  • Alternatively, \(M\) approximate posterior draws from the posterior distribution can be sampled by repeatedly applying conventional restricted maximum-likelihood (REML) parameter estimation of the MMRM model to nonparametric bootstrap samples from the original dataset (Section 3.3.4).

    • +
+
    +
  1. +Imputation step (Section 3.4)
    2. +
+
    +

  • Take a single sample \(m\) (\(m\in 1,\ldots, M)\) from the posterior distribution of the imputation model parameters.

    • +

  • For each subject, use the sampled parameters and the defined imputation strategy to determine the mean and covariance matrix describing the subject’s marginal outcome distribution for all longitudinal outcome assessments (i.e. observed and missing outcomes).

    • +

  • For each subjects, construct the conditional multivariate normal distribution of their missing outcomes given their observed outcomes (including observed outcomes after ICEs for which a reference-based assumption is desired).

    • +

  • For each subject, draw a single sample from this conditional distribution to impute their missing outcomes leading to a complete imputed dataset.

    • +

  • For sensitivity analyses, a pre-defined \(\delta\)-adjustment may be applied to the imputed data prior to the analysis step. (Section 3.5).

    • +
+
    +
  1. +Analysis step (Section 3.6)
    2. +
+
    +
  • Analyze the imputed dataset using an analysis model (e.g. ANCOVA) resulting in a point estimate and a standard error (with corresponding degrees of freedom) of the treatment effect.
    • +
+
    +
  1. +Pooling step for inference (Section 3.7)
    2. +
+
    +
  • Repeat steps 2. and 3. for each posterior sample \(m\), resulting in \(M\) complete datasets, \(M\) point estimates of the treatment effect, and \(M\) standard errors (with corresponding degrees of freedom). Pool the \(M\) treatment effect estimates, standard errors, and degrees of freedom using the rules by Barnard and Rubin to obtain the final pooled treatment effect estimator, standard error, and degrees of freedom.
    • +
+
+
+

+3.1.2 Conditional mean imputation +

+

The conditional mean imputation approach includes the following steps:

+
    +
  1. +Base imputation model fitting step (Section 3.3)
    2. +
+
    +
  • Fit a conventional multivariate normal/MMRM model using restricted maximum likelihood (REML) to the observed longitudinal outcomes after exclusion of data after ICEs for which reference-based missing data imputation is desired (Section 3.3.2).
    • +
+
    +
  1. +Imputation step (Section 3.4)
    2. +
+
    +

  • For each subject, use the fitted parameters from step 1. to construct the conditional distribution of missing outcomes given observed outcomes (including observed outcomes after ICEs for which reference-based missing data imputation is desired) as described above.

    • +

  • For each subject, impute their missing data deterministically by the mean of this conditional distribution leading to a complete imputed dataset.

    • +

  • For sensitivity analyses, a pre-defined \(\delta\)-adjustment may be applied to the imputed data prior to the analysis step. (Section 3.5).

    • +
+
    +
  1. +Analysis step (Section 3.6)
    2. +
+
    +
  • Apply an analysis model (e.g. ANCOVA) to the completed dataset resulting in a point estimate of the treatment effect.
    • +
+
    +
  1. +Jackknife or bootstrap inference step (Section 3.8)
    2. +
+
    +
  • Inference for the treatment effect estimate from 3. is based on re-sampling techniques. Both the jackknife and the bootstrap are supported. Importantly, these methods require repeating all steps of the imputation procedure (i.e. imputation, conditional mean imputation, and analysis steps) on each of the resampled datasets.
    • +
+
+
+

+3.1.3 Bootstrapped MI +

+

The bootstrapped MI approach includes the following steps:

+
    +
  1. +Base imputation model fitting step (Section 3.3)
    2. +
+
    +
  • Apply conventional restricted maximum-likelihood (REML) parameter estimation of the MMRM model to \(B\) nonparametric bootstrap samples from the original dataset using the observed longitudinal outcomes after exclusion of data after ICEs for which reference-based missing data imputation is desired.
    • +
+
    +
  1. +Imputation step (Section 3.4)
    2. +
+
    +

  • Take a bootstrapped dataset \(b\) (\(b\in 1,\ldots, B)\) and its corresponding imputation model parameter estimates.

    • +

  • For each subject (from the bootstrapped dataset), use the parameter estimates and the defined strategy for dealing with their ICEs to determine the mean and covariance matrix describing the subject’s marginal outcome distribution for all longitudinal outcome assessments (i.e. observed and missing outcomes).

    • +

  • For each subjects (from the bootstrapped dataset), construct the conditional multivariate normal distribution of their missing outcomes given their observed outcomes (including observed outcomes after ICEs for which reference-based missing data imputation is desired).

    • +

  • For each subject (from the bootstrapped dataset), draw \(D\) samples from this conditional distributions to impute their missing outcomes leading to \(D\) complete imputed dataset for bootstrap sample \(b\).

    • +

  • For sensitivity analyses, a pre-defined \(\delta\)-adjustment may be applied to the imputed data prior to the analysis step. (Section 3.5).

    • +
+
    +
  1. +Analysis step (Section 3.6)
    2. +
+
    +
  • Analyze each of the \(B\times D\) imputed datasets using an analysis model (e.g. ANCOVA) resulting in \(B\times D\) point estimates of the treatment effect.
    • +
+
    +
  1. +Pooling step for inference (Section 3.9)
    2. +
+
    +
  • Pool the \(B\times D\) treatment effect estimates as described in von Hippel and Bartlett (2021) to obtain the final pooled treatment effect estimate, standard error, and degrees of freedom.
    • +
+
+
+
+

+3.2 Setting, notation, and missing data assumptions +

+

Assume that the data are from a study with \(n\) subjects in total and that each subject \(i\) (\(i=1,\ldots,n\)) has \(J\) scheduled follow-up visits at which the outcome of interest is assessed. +In most applications, the data will be from a randomized trial of an intervention vs a control group and the treatment effect of interest is a comparison in outcomes at a specific visit between these randomized groups. However, single-arm trials or multi-arm trials are in principle also supported by the rbmi implementation.

+

Denote the observed outcome vector of length \(J\) for subject \(i\) by \(Y_i\) (with missing assessments coded as NA (not available)) and its non-missing and missing components by \(Y_{i!}\) and \(Y_{i?}\), respectively. +By default, imputation of missing outcomes in \(Y_{i}\) is performed under a MAR assumption in rbmi. Therefore, if missing data following an ICE are to be handled using MAR imputation, this is compatible with the default assumption. As discussed in Section 2, the MAR assumption is often a good starting point for implementing a hypothetical strategy. But also note that observed outcome data after an ICE handled using a hypothetical strategy is not compatible with this strategy. Therefore, we assume that all post-ICE data after ICEs handled using a hypothetical strategy are already set to NA in \(Y_i\) prior calling any rbmi functions. However, any observed outcomes after ICEs handled using a treatment policy strategy should be included in \(Y_i\) as they are compatible with this strategy.

+

Subjects may also experience up to one ICE after which missing data imputation according to a reference-based imputation method is foreseen. For a subject \(i\) with such an ICE, denote their first visit which is affected by the ICE by \(\tilde{t}_i \in \{1,\ldots,J\}\). For all other subjects, set \(\tilde{t}_i=\infty\). A subject’s outcome vector after setting observed outcomes from visit \(\tilde{t}_i\) onwards to missing (i.e. NA) is denoted as \(Y'_i\) and the corresponding data vector after removal of NA elements as \(Y'_{i!}\).

+

MNAR \(\delta\)-adjustments are added to the imputed datasets after the formal imputation steps. This is covered in a separate section (Section 3.5).

+
+
+

+3.3 The base imputation model +

+
+

+3.3.1 Included data and model specification +

+

The purpose of the imputation model is to estimate (covariate-dependent) mean trajectories and covariance matrices for each group in the absence of ICEs handled using reference-based imputation methods. Conventionally, +publications on reference-based imputation methods have implicitly assumed that the corresponding post-ICE +data is missing for all subjects (Carpenter, Roger, and Kenward (2013)). We also allow the situation where post-ICE data +is available for some subjects but needs to be imputed using reference-based methods for others. However, +any observed data after ICEs for which reference-based imputation methods are specified is not compatible +with the imputation model described below and they are therefore removed and considered as missing for +the purpose of estimating the imputation model, and for this purpose only. For example, if a patient has an ICE addressed with a reference-based method but outcomes after the ICE are collected, these post-ICE outcomes will be excluded when fitting the base imputation model (but they will be included again in the following steps). +That is, the base imputation model is fitted to \(Y'_{i!}\) and not to \(Y_{i!}\). +If we did not exclude these data, then the imputation model would mistakenly estimate mean trajectories based on a mixture of observed pre- and post-ICE data which are not relevant for reference-based imputations.

+

Observed post-ICE outcomes in the control or reference group are also excluded from the base imputation model if the user specifies a reference-based imputation strategy for such ICEs. This ensures that an ICE has the same impact on the data included in the imputation model regardless whether the ICE occurred in the control or the intervention group. On the other hand, imputation in the reference group is based on a MAR assumption even for reference-based imputation methods and it may be preferable in some settings to include post-ICE data from the control group in the base imputation model. This can be implemented by specifying a MAR strategy for the ICE in the control group and a reference-based strategy for the same ICE in the intervention group.

+

The base imputation model of the longitudinal outcomes \(Y'_i\) assumes that the mean structure is a linear function of covariates. Full flexibility for the specification of the linear predictor of the model is supported. At a minimum the covariates should include the treatment group, the (categorical) visit, and treatment-by-visit interactions. Typically, other covariates including the baseline outcome are also included. +External time-varying covariates (e.g. calendar time of the visit) as well as internal time-varying (e.g. time-varying indicators of treatment discontinuation or initiation of rescue treatment) may in principle also be included if indicated (Guizzaro et al. (2021)). Missing covariate values are not allowed. This means that the values of time-varying covariates must be non-missing at every visit regardless of whether the outcome is measured or missing.

+

Denote the \(J\times p\) design matrix for subject \(i\) corresponding to the mean structure model by \(X_i\) and the same matrix after removal of rows corresponding to missing outcomes in \(Y'_{i!}\) by \(X'_{i!}\). +Here \(p\) is the number of parameters in the mean structure of the model for the elements of \(Y'_{i!}\). +The base imputation model for the observed outcomes is defined as: +\[ Y'_{i!} = X'_{i!}\beta + \epsilon_{i!} \mbox{ with } \epsilon_{i!}\sim N(0,\Sigma_{i!!})\] +where \(\beta\) is the vector of regression coefficients and \(\Sigma_{i!!}\) is a covariance matrix which is obtained from the complete-data \(J\times J\)-covariance matrix \(\Sigma\) by omitting rows and columns corresponding to missing outcome assessments for subject \(i\).

+

Typically, a common unstructured covariance matrix for all subjects is assumed for \(\Sigma\) but separate covariate matrices per treatment group are also supported. Indeed, the implementation also supports the specification of separate covariate matrices according to an arbitrarily defined categorical variable which groups the subjects into disjoint subset. For example, this could be useful if different covariance matrices are suspected in different subject strata. Finally, for all imputation methods described below that do not rely on Bayesian model fitting through MCMC, there is further flexibility in the choice of the covariance structure, i.e. unstructured (default), heterogeneous Toeplitz, heterogeneous compound symmetry, and AR(1) covariance structures are supported.

+
+
+

+3.3.2 Restricted maximum likelihood estimation (REML) +

+

Frequentist parameter estimation for the base imputation is based on REML. The use of REML as an improved alternative to maximum likelihood (ML) for covariance parameter estimation was originally proposed by Patterson and Thompson (1971). Since then, it has become the default method for parameter estimation in linear mixed effects models. rbmi allows to choose between ML and REML methods to estimate the model parameters, with REML being the default option.

+
+
+

+3.3.3 Bayesian model fitting +

+

The Bayesian imputation model is fitted with the R package rstan (Stan Development Team (2020)). rstan is the R interface of Stan. Stan is a powerful and flexible statistical software developed by a dedicated team and implements Bayesian inference with state-of-the-art MCMC sampling procedures. The multivariate normal model with missing data specified in section 3.3.1 can be considered a generalization of the models described in the Stan user’s guide (see Stan Development Team (2020, sec. 3.5)).

+

The same prior distributions as in the SAS implementation of the “five macros” are used (Roger (2021)), i.e. an improper flat priors for the regression coefficients and a weakly informative inverse Wishart prior for the covariance matrix (or matrices). Specifically, let \(S \in \mathbb{R}^{J \times J}\) be a symmetric positive definite matrix and \(\nu \in (J-1, \infty)\). Then the symmetric positive definite matrix \(x \in \mathbb{R}^{J \times J}\) has density: +\[ +\text{InvWish}(x \vert \nu, S) = \frac{1}{2^{\nu J/2}} \frac{1}{\Gamma_J(\frac{\nu}{2})} \vert S \vert^{\nu/2} \vert x \vert ^{-(\nu + J + 1)/2} \text{exp}(-\frac{1}{2} \text{tr}(Sx^{-1})). +\] +For \(\nu > J+1\) the mean is given by: +\[ +E[x] = \frac{S}{\nu - J - 1}. +\] +We choose \(S\) equal to the estimated covariance matrix from the frequentist REML fit and \(\nu = J+2\) as these are the lowest degrees of freedom that guarantee a finite mean. Setting the degrees of freedom with such a low \(\nu\) ensures that the prior has little impact on the posterior. Moreover, this choice allows to interpret the parameter \(S\) as the mean of the prior distribution.

+

As in the “five macros”, the MCMC algorithm is initialized at the parameters from a frequentist REML fit (see section 3.3.2). As described above, we are using only weakly informative priors for the parameters. Therefore, the Markov chain is essentially starting from the targeted stationary posterior distribution and only a minimal amount of burn-in of the chain is required.

+
+
+

+3.3.4 Approximate Bayesian posterior draws via the bootstrap +

+

Several authors have suggested that a stabler way to get Bayesian posterior draws from the imputation model is to bootstrap the incomplete data and to calculate REML estimates for each bootstrap sample (Little and Rubin (2002), Efron (1994), Honaker and King (2010), von Hippel and Bartlett (2021)). This method is proper in that the REML estimates from the bootstrap samples are asymptotically equivalent to a sample from the posterior distribution and may provide additional robustness to model misspecification (Little and Rubin (2002, sec. 10.2.3, part 6), Honaker and King (2010)). In order to retain balance between treatment groups and stratification factors across bootstrap samples, the user is able to provide stratification variables for the bootstrap in the rbmi implementation.

+
+
+
+

+3.4 Imputation step +

+
+

+3.4.1 Marginal imputation distribution for a subject - MAR case +

+

For each subject \(i\), the marginal distribution of the complete \(J\)-dimensional outcome vector from all assessment visits according to the imputation model is a multivariate normal distribution. Its mean \(\tilde{\mu}_i\) is given by the predicted mean from the imputation model conditional on the subject’s baseline characteristics, group, and, optionally, time-varying covariates. Its covariance matrix \(\tilde{\Sigma}_i\) is given by the overall estimated covariance matrix or, if different covariance matrices are assumed for different groups, the covariance matrix corresponding to subject \(i\)’s group.

+
+
+

+3.4.2 Marginal imputation distribution for a subject - reference-based imputation methods +

+

For each subject \(i\), we calculate the mean and covariance matrix of the complete \(J\)-dimensional outcome vector from all assessment visits as for the MAR case and denote them by \(\mu_i\) and \(\Sigma_i\). +For reference-based imputation methods, a corresponding reference group is also required for each group. Typically, the reference group for the intervention group will be the control group. +The reference mean \(\mu_{ref,i}\) is defined as the predicted mean from the imputation model conditional on the reference group (rather than the actual group subject \(i\) belongs to) and the subject’s baseline characteristics. +The reference covariance matrix \(\Sigma_{ref,i}\) is the overall estimated covariance matrix or, if different covariance matrices are assumed for different groups, the estimated covariance matrix corresponding to the reference group. In principle, time-varying covariates could also be included in reference-based imputation methods. However, this is only sensible for external time-varying covariates (e.g. calendar time of the visit) and not for internal time-varying covariates (e.g. treatment discontinuation) because the latter likely depend on the actual treatment group and it is typically not sensible to assume the same trajectory of the time-varying covariate for the reference group.

+

Based on these means and covariance matrices, the subject’s marginal imputation distribution for the reference-based imputation methods is then calculated as detailed in Carpenter, Roger, and Kenward (2013, sec. 4.3). +Denote the mean and covariance matrix of this marginal imputation distribution by \(\tilde{\mu}_i\) and \(\tilde{\Sigma}_i\). Recall that the subject’s first visit which is affected by the ICE is denoted by \(\tilde{t}_i \in \{1,\ldots,J\}\) (and visit \(\tilde{t}_i-1\) is the last visit unaffected by the ICE). The marginal distribution for the patient \(i\) is then built according to the specific assumption for the data up to and post the ICE as follows:

+
    +

  1. Jump to reference (JR): the patient’s outcome distribution is normally distributed with the following mean: +\[\tilde{\mu}_i = (\mu_i[1], \dots, \mu_i[\tilde{t}_i-1], \mu_{ref,i}[\tilde{t}_i], \dots, \mu_{ref,i}[J])^T.\] +The covariance matrix is constructed as follows. First, we partition the covariance matrices \(\Sigma_i\) and \(\Sigma_{ref,i}\) in blocks according to the time of the ICE \(\tilde{t}_i\): +\[ +\Sigma_{i} = \begin{bmatrix} \Sigma_{i, 11} & \Sigma_{i, 12} \\ +\Sigma_{i, 21} & \Sigma_{i,22} \\ +\end{bmatrix} +\] +\[ +\Sigma_{ref,i} = \begin{bmatrix} \Sigma_{ref, i, 11} & \Sigma_{ref, i, 12} \\ +\Sigma_{ref, i, 21} & \Sigma_{ref, i,22} \\ +\end{bmatrix}. +\] +We want the covariance matrix \(\tilde{\Sigma}_i\) to match \(\Sigma_i\) for the pre-deviation measurements, and \(\Sigma_{ref,i}\) for the conditional components for the post-deviation given the pre-deviation measurements. The solution is derived in Carpenter, Roger, and Kenward (2013, sec. 4.3) and is given by: +\[ +\begin{matrix} +\tilde{\Sigma}_{i,11} = \Sigma_{i, 11} \\ +\tilde{\Sigma}_{i, 21} = \Sigma_{ref,i, 21} \Sigma^{-1}_{ref,i, 11} \Sigma_{i, 11} \\ +\tilde{\Sigma}_{i, 22} = \Sigma_{ref, i, 22} - \Sigma_{ref,i, 21} \Sigma^{-1}_{ref,i, 11} (\Sigma_{ref,i, 11} - \Sigma_{i,11}) \Sigma^{-1}_{ref,i, 11} \Sigma_{ref,i, 12}. +\end{matrix} +\]

    2. +

  2. Copy increments in reference (CIR): the patient’s outcome distribution is normally distributed with the following mean: +\[ +\begin{split} +\tilde{\mu}_i =& (\mu_i[1], \dots, \mu_i[\tilde{t}_i-1], \mu_i[\tilde{t}_i-1] + (\mu_{ref,i}[\tilde{t}_i] - \mu_{ref,i}[\tilde{t}_i-1]), \dots,\\ & +\mu_i[\tilde{t}_i-1]+(\mu_{ref,i}[J] - \mu_{ref,i}[\tilde{t}_i-1]))^T. +\end{split} +\] +The covariance matrix is derived as for the JR method.

    3. +

  3. Copy reference (CR): the patient’s outcome distribution is normally distributed with mean and covariance matrix taken from the reference group: +\[ +\tilde{\mu}_i = \mu_{ref,i} +\] +\[ +\tilde{\Sigma}_i = \Sigma_{ref,i}. +\]

    4. +

  4. Last mean carried forward (LMCF): the patient’s outcome distribution is normally distributed with the following mean: +\[ \tilde{\mu}_i = (\mu_i[1], \dots, \mu_i[\tilde{t}_i-1], \mu_i[\tilde{t}_i-1], \dots, \mu_i[\tilde{t}_i-1])'\] +and covariance matrix: \[ \tilde{\Sigma}_i = \Sigma_i.\]

    5. +
+
+
+

+3.4.3 Imputation of missing outcome data +

+

The joint marginal multivariate normal imputation distribution of subject \(i\)’s observed and missing outcome data has mean \(\tilde{\mu}_i\) and covariance matrix \(\tilde{\Sigma}_i\) as defined above. The actual imputation of the missing outcome data is obtained by conditioning this marginal distribution on the subject’s observed outcome data. Of note, this approach is valid regardless whether the subject has intermittent or terminal missing data.

+

The conditional distribution used for the imputation is again a multivariate normal distribution and explicit formulas for the conditional mean and covariance are readily available. For completeness, we report them here with the notation and terminology of our setting. The marginal distribution for the outcome of patient \(i\) is \(Y_i \sim N(\tilde{\mu}_i, \tilde{\Sigma}_i)\) and the outcome \(Y_i\) can be decomposed in the observed (\(Y_{i,!}\)) and the unobserved (\(Y_{i,?}\)) components. Analogously the mean \(\tilde{\mu}_i\) can be decomposed as \((\tilde{\mu}_{i,!},\tilde{\mu}_{i,?})\) and the covariance \(\tilde{\Sigma}_i\) as: +\[ +\tilde{\Sigma}_i = +\begin{bmatrix} +\tilde{\Sigma}_{i, !!} & \tilde{\Sigma}_{i,!?} \\ +\tilde{\Sigma}_{i, ?!} & \tilde{\Sigma}_{i, ??} +\end{bmatrix}. +\] +The conditional distribution of \(Y_{i,?}\) conditional on \(Y_{i,!}\) is then a multivariate normal distribution with expectation +\[ +E(Y_{i,?} \vert Y_{i,!})= \tilde{\mu}_{i,?} + \tilde{\Sigma}_{i, ?!} \tilde{\Sigma}_{i,!!}^{-1} (Y_{i,!} - \tilde{\mu}_{i,!}) +\] +and covariance matrix +\[ +Cov(Y_{i,?} \vert Y_{i,!}) = \tilde{\Sigma}_{i,??} - \tilde{\Sigma}_{i,?!} \tilde{\Sigma}_{i,!!}^{-1} \tilde{\Sigma}_{i,!?}. +\]

+

Conventional random imputation consists in sampling from this conditional multivariate normal distribution. Conditional mean imputation imputes missing values with the deterministic conditional expectation \(E(Y_{i,?} \vert Y_{i,!})\).

+
+
+
+

+3.5 \(\delta\)-adjustment +

+

A marginal \(\delta\)-adjustment approach similar to the “five macros” in SAS is implemented (Roger (2021)), i.e. fixed non-stochastic values are added after the multivariate normal imputation step and prior to the analysis. +This is relevant for sensitivity analyses in order to make imputed data systematically worse or better, respectively, than observed data. In addition, some authors have suggested \(\delta\)-type adjustments to implement a composite strategy for continuous outcomes (Darken et al. (2020)).

+

The implementation provides full flexibility regarding the specific implementation of the \(\delta\)-adjustment, i.e. the value that is added may depend on the randomized treatment group, the timing of the subject’s ICE, and other factors. For suggestions and case studies regarding this topic, we refer to Cro et al. (2020).

+
+
+

+3.6 Analysis step +

+

After data imputation, a standard analysis model can be applied to the completed data resulting in a treatment effect estimate. As the imputed data no longer contains missing values, the analysis model is often simple. For example, it can be an analysis of covariance (ANCOVA) model with the outcome (or the change in the outcome from baseline) at a specific visit j as the dependent variable, the randomized treatment group as the primary covariate and, typically, adjustment for the same baseline covariates as for the imputation model.

+
+
+

+3.7 Pooling step for inference of (approximate) Bayesian MI and Rubin’s rules +

+

Assume that the analysis model has been applied to \(M\) multiple imputed random datasets which resulted in \(m\) treatment effect estimates \(\hat{\theta}_m\) (\(m=1,\ldots,M\)) with corresponding standard error \(SE_m\) and (if available) degrees of freedom \(\nu_{com}\). If degrees of freedom are not available for an analysis model, set \(\nu_{com}=\infty\) for inference based on the normal distribution.

+

Rubin’s rules are used for pooling the treatment effect estimates and corresponding variances estimates from the analysis steps across the \(M\) multiple imputed datasets. According to Rubin’s rules, the final estimate of the treatment effect is calculated as the sample mean over the \(M\) treatment effect estimates: +\[ +\hat{\theta} = \frac{1}{M} \sum_{m = 1}^M \hat{\theta}_m. +\] +The pooled variance is based on two components that reflect the within and the between variance of the treatment effects across the multiple imputed datasets: +\[ +V(\hat{\theta}) = V_W(\hat{\theta}) + (1 + \frac{1}{M}) V_B(\hat{\theta}) +\] +where \(V_W(\hat{\theta}) = \frac{1}{M}\sum_{m = 1}^M SE^2_m\) is the within-variance and \(V_B(\hat{\theta}) = \frac{1}{M-1} \sum_{m = 1}^M (\hat{\theta}_m - \hat{\theta})^2\) is the between-variance.

+

Confidence intervals and tests of the null hypothesis \(H_0: \theta=\theta_0\) are based on the \(t\)-statistics \(T\):

+

\[ T= (\hat{\theta}-\theta_0)/\sqrt{V(\hat{\theta})}. \] +Under the null hypothesis, \(T\) has an approximate \(t\)-distribution with \(\nu\) degrees of freedom. \(\nu\) is calculated according to the Barnard and Rubin approximation, see Barnard and Rubin (1999) (formula 3) or Little and Rubin (2002) (formula (5.24), page 87):

+

\[ +\nu = \frac{\nu_{old}* \nu_{obs}}{\nu_{old} + \nu_{obs}} +\] +with +\[ +\nu_{old} = \frac{M-1}{\lambda^2} \quad\mbox{and}\quad \nu_{obs} = \frac{\nu_{com} + 1}{\nu_{com} + 3} \nu_{com} (1 - \lambda) +\] +where \(\lambda = \frac{(1 + \frac{1}{M})V_B(\hat{\theta})}{V(\hat{\theta})}\) is the fraction of missing information.

+
+
+

+3.8 Bootstrap and jackknife inference for conditional mean imputation +

+
+

+3.8.1 Point estimate of the treatment effect +

+

The point estimator is obtained by applying the analysis model (Section 3.6) to a single conditional mean imputation of the missing data (see Section 3.4.3) based on the REML estimator of the parameters of the imputation model (see Section 3.3.2). We denote this treatment effect estimator by \(\hat{\theta}\).

+

As demonstrated in Wolbers et al. (2022) (Section 2.4), this treatment effect estimator is valid if the analysis model is an ANCOVA model or, more generally, if the treatment effect estimator is a linear function of the imputed outcome vector. Indeed, if this is the case, then the estimator is identical to the pooled treatment effect across multiple random REML imputation with an infinite number of imputations and corresponds to a computationally efficient implementation of a proposal by von Hippel and Bartlett (2021). We expect that the conditional mean imputation method is also applicable to some other analysis models (e.g. for general MMRM analysis models) but this has not been formally justified.

+
+
+

+3.8.2 Jackknife standard errors, confidence intervals (CI) and tests for the treatment effect +

+

For a dataset containing \(n\) subjects, the jackknife standard error depends on treatment effect estimates \(\hat{\theta}_{(-b)}\) (\(b=1,\ldots,n\)) from samples of the original dataset which leave out the observation from subject \(b\). As described previously, to obtain treatment effect estimates for leave-one-subject-out datasets, all +steps of the imputation procedure (i.e. imputation, conditional mean imputation, and analysis steps) need to be repeated on this new dataset.

+

Then, the jackknife standard error is defined as +\[\hat{se}_{jack}=[\frac{(n-1)}{n}\cdot\sum_{b=1}^{n} (\hat{\theta}_{(-b)}-\bar{\theta}_{(.)})^2]^{1/2}\] +where \(\bar{\theta}_{(.)}\) denotes the mean of all jackknife estimates (Efron and Tibshirani (1994), chapter 10). The corresponding two-sided normal approximation \(1-\alpha\) CI is defined as \(\hat{\theta}\pm z^{1-\alpha/2}\cdot \hat{se}_{jack}\) where \(\hat{\theta}\) is the treatment effect estimate from the original dataset. Tests of the null hypothesis \(H_0: \theta=\theta_0\) are then based on the \(Z\)-score \(Z=(\hat{\theta}-\theta_0)/\hat{se}_{jack}\) using a standard normal approximation.

+

A simulation study reported in Wolbers et al. (2022) demonstrated exact protection of the type I error for jackknife-based inference with a relatively low sample size (n = 100 per group) and a substantial amount of missing data (>25% of subjects with an ICE).

+
+
+

+3.8.3 Bootstrap standard errors, confidence intervals (CI) and tests for the treatment effect +

+

As an alternative to the jackknife, the bootstrap has also been implemented in rbmi (Efron and Tibshirani (1994), Davison and Hinkley (1997)).

+

Two different bootstrap methods are implemented in rbmi: Methods based on the bootstrap standard error and the normal approximation and percentile bootstrap methods. Denote the treatment effect estimates from \(B\) bootstrap samples by \(\hat{\theta}^*_b\) (\(b=1,\ldots,B\)). The bootstrap standard error \(\hat{se}_{boot}\) is defined as the empirical standard deviation of the bootstrapped treatment effect estimates. Confidence intervals and tests based on the bootstrap standard error can then be constructed in the same way as for the jackknife. Confidence intervals using the percentile bootstrap are based on empirical quantiles of the bootstrap distribution and corresponding statistical tests are implemented in rbmi via inversion of the confidence interval. Explicit formulas for bootstrap inference as implemented in the rbmi package and some considerations regarding the required number of bootstrap samples are included in the Appendix of Wolbers et al. (2022).

+

A simulation study reported in Wolbers et al. (2022) demonstrated a small inflation of the type I error rate for inference based on the bootstrap standard error (up to \(5.3\%\) for a nominal type I error rate of \(5\%\)) for a sample size of n = 100 per group and a substantial amount of missing data (>25% of subjects with an ICE). Based on this simulations, we recommend the jackknife over the bootstrap for inference because it performed better in our simulation study and is typically much faster to +compute than the bootstrap.

+
+
+
+

+3.9 Pooling step for inference of the bootstrapped MI methods +

+

Assume that the analysis model has been applied to \(B\times D\) multiple imputed random datasets which resulted in \(B\times D\) treatment effect estimates \(\hat{\theta}_{bd}\) (\(b=1,\ldots,B\); \(d=1,\ldots,D\)).

+

The final estimate of the treatment effect is calculated as the sample mean over the \(B*D\) treatment effect estimates: +\[ +\hat{\theta} = \frac{1}{BD} \sum_{b = 1}^B \sum_{d = 1}^D \hat{\theta}_{bd}. +\] +The pooled variance is based on two components that reflect the variability within and between imputed bootstrap samples (von Hippel and Bartlett (2021), formula 8.4): +\[ +V(\hat{\theta}) = (1 + \frac{1}{B})\frac{MSB - MSW}{D} + \frac{MSW}{BD} +\]

+

where \(MSB\) is the mean square between the bootstrapped datasets, and \(MSW\) is the mean square within the bootstrapped datasets and between the imputed datasets:

+

\[ +\begin{align*} +MSB &= \frac{D}{B-1} \sum_{b = 1}^B (\bar{\theta_{b}} - \hat{\theta})^2 \\ +MSW &= \frac{1}{B(D-1)} \sum_{b = 1}^B \sum_{d = 1}^D (\theta_{bd} - \bar{\theta_b})^2 +\end{align*} +\] +where \(\bar{\theta_{b}}\) is the mean across the \(D\) estimates obtained from random imputation of the \(b\)-th bootstrap sample.

+

The degrees of freedom are estimated with the following formula (von Hippel and Bartlett (2021), formula 8.6):

+

\[ +\nu = \frac{(MSB\cdot (B+1) - MSW\cdot B)^2}{\frac{MSB^2\cdot (B+1)^2}{B-1} + \frac{MSW^2\cdot B}{D-1}} +\]

+

Confidence intervals and tests of the null hypothesis \(H_0: \theta=\theta_0\) are based on the \(t\)-statistics \(T\):

+

\[ T= (\hat{\theta}-\theta_0)/\sqrt{V(\hat{\theta})}. \] +Under the null hypothesis, \(T\) has an approximate \(t\)-distribution with \(\nu\) degrees of freedom.

+
+
+

+3.10 Comparison between the implemented approaches +

+
+

+3.10.1 Treatment effect estimation +

+

All approaches provide consistent treatment effect estimates for standard and reference-based imputation methods in case the analysis model of the completed datasets is a general linear model such as ANCOVA. Methods other than conditional mean imputation should also be valid for other analysis models. The validity of conditional mean imputation has only been formally demonstrated for analyses using the general linear model (Wolbers et al. (2022, sec. 2.4)) though it may also be applicable more widely (e.g. for general MMRM analysis models).

+

Treatment effects based on conditional mean imputation are deterministic. All other methods are affected by Monte Carlo sampling error and the precision of estimates depends on the number of imputations or bootstrap samples, respectively.

+
+
+

+3.10.2 Standard errors of the treatment effect +

+

All approaches for imputation under a MAR assumption provide consistent estimates of the frequentist standard error.

+

For reference-based imputation methods, the situation is more complicated and two different types of variance estimators have been proposed in the statistical literature (Bartlett (2023)). +The first is the frequentist variance which describes the actual repeated sampling variability of the estimator. +If the reference-based missing data assumption is correctly specified, then the resulting inference based on this variance is correct in the frequentist sense, i.e. hypothesis tests have asymptotically correct type I error control and confidence intervals have correct coverage probabilities under repeated sampling (Bartlett (2023), Wolbers et al. (2022)). +Reference-based missing data assumptions are strong and borrow information from the reference arm for imputation in the active arm. As a consequence, the size of frequentist standard errors for treatment effects may decrease with increasing amounts of missing data. +The second proposal is the so-called “information-anchored” variance which was originally proposed in the context of sensitivity analyses (Cro, Carpenter, and Kenward (2019)). This variance estimator is based on disentangling point estimation and variance estimation altogether. +The information-anchoring principle described in Cro, Carpenter, and Kenward (2019) states that the relative increase in the variance of the treatment effect estimator under MAR imputation with increasing amounts of missing data should be preserved for reference-based imputation methods. +The resulting information-anchored variance is typically very similar to the variance under MAR imputation and typically increases with increasing amounts of missing data. +However, the information-anchored variance does not reflect the actual variability of the reference-based estimator under repeated sampling and the resulting inference is highly conservative resulting in a substantial power loss (Wolbers et al. (2022)). +Moreover, to date, no Bayesian or frequentist framework has been developed under which the information-anchored variance provides correct inference for reference-based missingness assumptions, nor is it clear whether such a framework can even be developed.

+

Reference-based conditional mean imputation (method_condmean()) and bootstrapped likelihood-based multiple methods (method = method_bmlmi()) obtain standard errors via resampling and hence target the frequentist variance (Wolbers et al. (2022), von Hippel and Bartlett (2021)). +For finite samples, simulations for a sample size of \(n=100\) per group reported in Wolbers et al. (2022) demonstrated that conditional mean imputation combined with the jackknife (method_condmean(type = "jackknife")) provided exact protection of the type one error rate whereas the bootstrap (method_condmean(type = "bootstrap")) was associated with a small type I error inflation (between 5.1% to 5.3% for a nominal level of 5%). +For reference-based conditional mean imputation, an alternative information-anchored variance can be obtained by following a proposal by Lu (2021). +The basic idea of Lu (2021) is to obtain the information-anchored variance via a MAR imputation combined with a delta-adjustment where delta is selected in a data-driven way to match the reference-based estimator. +For conditional mean imputation, the proposal by Lu (2021) can be implemented by choosing the delta-adjustment as the difference between the conditional mean imputation under the chosen reference-based assumption and MAR on the original dataset. +An illustration of how the different variances can be obtained for conditional mean imputation in rbmi is provided in the vignette “Frequentist and information-anchored inference for reference-based conditional mean imputation” (vignette(topic = "CondMean_Inference", package = "rbmi")).

+

Reference-based Bayesian (or approximate Bayesian) multiple imputation methods combined with Rubin’s rules (method_bayes() and method_approxbayes()) target the information-anchored variance (Cro, Carpenter, and Kenward (2019)). +A frequentist variance for these methods could in principle be obtained via bootstrap or jackknife re-sampling of the treatment effect estimates but this would be very computationally intensive and is not directly supported by rbmi.

+

Our view is that for primary analyses, accurate type I error control (which can be obtained by using the frequentist variance) is more important than adherence to the information anchoring principle which, to us, is +not fully compatible with the strong reference-based assumptions. In any case, if reference-based imputation is used for the primary analysis, it is critical that the chosen +reference-based assumption can be clinically justified, and that suitable sensitivity analyses are conducted to stress-test these assumptions.

+

Conditional mean imputation combined with the jackknife is the only method which leads to deterministic standard error estimates and, consequently, confidence intervals and \(p\)-values are also deterministic. This is particularly important in a regulatory setting where it is important to ascertain whether a calculated \(p\)-value which is close to the critical boundary of 5% is truly below or above that threshold rather than being uncertain about this because of Monte Carlo error.

+
+
+

+3.10.3 Computational complexity +

+

Bayesian MI methods rely on the specification of prior distributions and the usage of Markov chain Monte Carlo (MCMC) methods. +All other methods based on multiple imputation or bootstrapping require no other tuning parameters than the specification of the number of imputations \(M\) or bootstrap samples \(B\) and rely on numerical optimization for fitting the MMRM imputation models via REML. Conditional mean imputation combined with the jackknife has no tuning parameters.

+

In our rbmi implementation, the fitting of the MMRM imputation model via REML is computationally most expensive. MCMC sampling using rstan (Stan Development Team (2020)) is typically relatively fast in our setting and requires only a small burn-in and burn-between of the chains. In addition, the number of random imputations for reliable inference using Rubin’s rules is often smaller than the number of resamples required for the jackknife or the bootstrap (see e.g. the discussions in I. R. White, Royston, and Wood (2011, sec. 7) for Bayesian MI and the Appendix of Wolbers et al. (2022) for the bootstrap). Thus, for many applications, we expect that conventional MI based on Bayesian posterior draws will be fastest, followed by conventional MI using approximate Bayesian posterior draws and conditional mean imputation combined with the jackknife. Conditional mean imputation combined with the bootstrap and bootstrapped MI methods will typically be most computationally demanding. Of note, all implemented methods are conceptually straightforward to parallelise and some parallelisation support is provided by rbmi.

+
+
+
+
+

+4 Mapping of statistical methods to rbmi functions +

+

For a full documentation of the rbmi package functionality we refer to the help pages of all functions and to the other package vignettes. Here we only give a brief overview of how the different steps of the imputation procedure are mapped to rbmi functions:

+
    +
  • The base imputation model fitting step is implemented in the function draws(). The chosen MI approach can be set using the argument method and should be one of the following: +
      +
    • Bayesian posterior parameter draws from the imputation model are obtained via the argument method = method_bayes().
      • +
    • Approximate Bayesian posterior parameter draws from the imputation model are obtained via argument method = method_approxbayes().
      • +
    • ML or REML parameter estimates of the imputation model parameters for the original dataset and all leave-one-subject-out datasets (as required for the jackknife) are obtained via argument method = method_condmean(type = "jackknife").
      • +
    • ML or REML parameter estimates of the imputation model parameters for the original dataset and bootstrapped datasets are obtained via argument method = method_condmean(type = "bootstrap").
      • +
    • Bootstrapped MI methods are obtained via argument method = method_bmlmi(B=B, D=D) where \(B\) refers to the number of bootstrap samples and \(D\) to the number of random imputations for each bootstrap sample.
      • +
    +
    • +
  • The imputation step using random imputation or deterministic conditional mean imputation, respectively, is implemented in function impute(). Imputation can be performed assuming the already implemented imputation strategies as presented in section 3.4. Additionally, user-defined imputation strategies are also supported.
    • +
  • The analysis step is implemented in function analyse() and applies the analysis model to all imputed datasets. By default, the analysis model (argument fun) is the ancova() function but alternative analysis functions can also be provided by the user. The analyse() function also allows for \(\delta\)-adjustments to the imputed datasets prior to the analysis via argument delta.
    • +
  • The inference step is implemented in function pool() which pools the results across imputed datasets. The Rubin and Bernard rule is applied in case of (approximate) Bayesian MI. For conditional mean imputation, jackknife and bootstrap (normal approximation or percentile) inference is supported. For BMLMI, the pooling and inference steps are performed via pool() which in this case implements the method described in Section 3.9.
    • +
+
+
+

+5 Comparison to other software implementations +

+

An established software implementation of reference-based imputation in SAS are the so-called “five macros” by James Roger (Roger (2021)). An alternative R implementation which is also currently under development is the R package RefBasedMI (McGrath and White (2021)).

+

rbmi has several features which are not supported by the other implementations:

+
    +

  1. In addition to the Bayesian MI approach implemented also in the other packages, our implementation provides three alternative MI approaches: approximate Bayesian MI, conditional mean imputation combined with resampling, and bootstrapped MI.

    2. +

  2. rbmi allows for the usage of data collected after an ICE. For example, suppose that we want to adopt a treatment policy strategy for the ICE “treatment discontinuation”. A possible implementation of this strategy is to use the observed outcome data for subjects who remain in the study after the ICE and to use reference-based imputation in case the subject drops out. In our implementation, this is implemented by excluding observed post ICE data from the imputation model which assumes MAR missingness but including them in the analysis model. To our knowledge, this is not directly supported by the other implementations.

    3. +

  3. RefBasedMI fits the imputation model to data from each treatment group separately which implies covariate-treatment group interactions for all covariates for the pooled data from both treatment groups. In contrast, Roger’s five macros assume a joint model including data from all the randomized groups and covariate-treatment interactions covariates are not allowed. We also chose to implement a joint model but use a flexible model for the linear predictor which may or may not include an interaction term between any covariate and the treatment group. In addition, our imputation model also allows for the inclusion of time-varying covariates.

    4. +

  4. In our implementation, the grouping of the subjects for the purpose of the imputation model (and the definition of the reference group) does not need to correspond to the assigned treatment groups. This provides additional flexibility for the imputation procedure. It is not clear to us whether this feature is supported by Roger’s five macros or RefBasedMI.

    5. +

  5. We believe that our R-based implementation is more modular than RefBasedMI which should facilitate further package enhancements.

    6. +
+

In contrast, the more general causal model introduced by I. White, Royes, and Best (2020) is available in the other implementations but is currently not supported by ours.

+
+
+

References +

+
+
+Barnard, John, and Donald B Rubin. 1999. “Miscellanea. Small-Sample Degrees of Freedom with Multiple Imputation.” Biometrika 86 (4): 948–55. +
+
+Bartlett, Jonathan W. 2023. “Reference-Based Multiple Imputation - What Is the Right Variance and How to Estimate It.” Statistics in Biopharmaceutical Research 15 (1): 178–86. +
+
+Bell, James, Thomas Drury, Tobias Mütze, Christian Bressen Pipper, Lorenzo Guizzaro, Marian Mitroiu, Khadija Rerhou Rantell, Marcel Wolbers, and David Wright. 2024. “Estimation Methods for Estimands Using the Treatment Policy Strategy; a Simulation Study Based on the PIONEER 1 Trial.” arXiv Preprint. https://arxiv.org/abs/2402.12850. +
+
+Carpenter, James R, James H Roger, and Michael G Kenward. 2013. “Analysis of Longitudinal Trials with Protocol Deviation: A Framework for Relevant, Accessible Assumptions, and Inference via Multiple Imputation.” Journal of Biopharmaceutical Statistics 23 (6): 1352–71. +
+
+Cro, Suzie, James R Carpenter, and Michael G Kenward. 2019. “Information-Anchored Sensitivity Analysis: Theory and Application.” Journal of the Royal Statistical Society: Series A (Statistics in Society) 182 (2): 623–45. +
+
+Cro, Suzie, Tim P Morris, Michael G Kenward, and James R Carpenter. 2020. “Sensitivity Analysis for Clinical Trials with Missing Continuous Outcome Data Using Controlled Multiple Imputation: A Practical Guide.” Statistics in Medicine 39 (21): 2815–42. +
+
+Darken, Patrick, Jack Nyberg, Shaila Ballal, and David Wright. 2020. “The Attributable Estimand: A New Approach to Account for Intercurrent Events.” Pharmaceutical Statistics 19 (5): 626–35. +
+
+Davison, Anthony C, and David V Hinkley. 1997. Bootstrap Methods and Their Application. Cambridge University Press. +
+
+Drury, Thomas, Juan J Abellan, Nicky Best, and Ian R White. 2024. “Estimation of Treatment Policy Estimands for Continuous Outcomes Using Off-Treatment Sequential Multiple Imputation.” Pharmaceutical Statistics. +
+
+Efron, Bradley. 1994. “Missing Data, Imputation, and the Bootstrap.” Journal of the American Statistical Association 89 (426): 463–75. +
+
+Efron, Bradley, and Robert J Tibshirani. 1994. An Introduction to the Bootstrap. CRC press. +
+
+Guizzaro, Lorenzo, Frank Pétavy, Robin Ristl, and Ciro Gallo. 2021. “The Use of a Variable Representing Compliance Improves Accuracy of Estimation of the Effect of Treatment Allocation Regardless of Discontinuation in Trials with Incomplete Follow-up.” Statistics in Biopharmaceutical Research 13 (1): 119–27. +
+
+Honaker, James, and Gary King. 2010. “What to Do about Missing Values in Time-Series Cross-Section Data.” American Journal of Political Science 54 (2): 561–81. +
+
+ICH E9 working group. 2019. “ICH E9 (R1): Addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials.” International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use. 2019. https://database.ich.org/sites/default/files/E9-R1_Step4_Guideline_2019_1203.pdf. +
+
+Little, Roderick JA, and Donald B Rubin. 2002. Statistical Analysis with Missing Data, Second Edition. John Wiley & Sons. +
+
+Lu, Kaifeng. 2021. “An Alternative Implementation of Reference-Based Controlled Imputation Procedures.” Statistics in Biopharmaceutical Research 13 (4): 483–91. +
+
+Mallinckrodt, CH, J Bell, G Liu, B Ratitch, M O’Kelly, I Lipkovich, P Singh, L Xu, and G Molenberghs. 2020. “Aligning Estimators with Estimands in Clinical Trials: Putting the ICH E9 (R1) Guidelines into Practice.” Therapeutic Innovation & Regulatory Science 54 (2): 353–64. +
+
+McGrath, Kevin, and Ian White. 2021. “RefBasedMI: Reference-Based Imputation for Longitudinal Clinical Trials with Protocol Deviation.” https://github.com/UCL/RefbasedMI. +
+
+Noci, Alessandro, Marcel Wolbers, Markus Abt, Corine Baayen, Hans Ulrich Burger, Man Jin, and Weining Zhao Robieson. 2023. “A Comparison of Estimand and Estimation Strategies for Clinical Trials in Early Parkinson’s Disease.” Statistics in Biopharmaceutical Research 15 (3): 491–501. +
+
+Patterson, H Desmond, and Robin Thompson. 1971. “Recovery of Inter-Block Information When Block Sizes Are Unequal.” Biometrika 58 (3): 545–54. +
+
+Polverejan, Elena, and Vladimir Dragalin. 2020. “Aligning Treatment Policy Estimands and Estimators—a Simulation Study in Alzheimer’s Disease.” Statistics in Biopharmaceutical Research 12 (2): 142–54. +
+
+Roger, James. 2021. “Reference-Based MI via Multivariate Normal RM (the ‘Five Macros’ and MIWithD).” https://www.lshtm.ac.uk/research/centres-projects-groups/missing-data#dia-missing-data. +
+
+Stan Development Team. 2020. “RStan: The R Interface to Stan.” https://mc-stan.org/. +
+
+von Hippel, Paul T, and Jonathan W Bartlett. 2021. “Maximum Likelihood Multiple Imputation: Faster Imputations and Consistent Standard Errors Without Posterior Draws.” Statistical Science 36 (3): 400–420. +
+
+White, Ian R, Patrick Royston, and Angela M Wood. 2011. “Multiple Imputation Using Chained Equations: Issues and Guidance for Practice.” Statistics in Medicine 30 (4): 377–99. +
+
+White, Ian, Joseph Royes, and Nicky Best. 2020. “A Causal Modelling Framework for Reference-Based Imputation and Tipping Point Analysis in Clinical Trials with Quantitative Outcome.” Journal of Biopharmaceutical Statistics 30 (2): 334–50. +
+
+Wolbers, Marcel, Alessandro Noci, Paul Delmar, Craig Gower-Page, Sean Yiu, and Jonathan W Bartlett. 2022. “Standard and Reference-Based Conditional Mean Imputation.” Pharmaceutical Statistics 21 (6): 1246–57. +
+
+
+
+
+ + + + +
+ + + + + + + diff --git a/v1.3.1/authors.html b/v1.3.1/authors.html new file mode 100644 index 000000000..c8be70fad --- /dev/null +++ b/v1.3.1/authors.html @@ -0,0 +1,120 @@ + +Authors and Citation • rbmi + Skip to contents + + +
+
+
+

Authors and Citation

+
+ +
+

Authors

+ +
  • +

    Craig Gower-Page. Author, maintainer. +

    +
    • +
  • +

    Alessandro Noci. Author. +

    +
    • +
  • +

    Marcel Wolbers. Contributor. +

    +
    • +
  • +

    Isaac Gravestock. Author. +

    +
    • +
  • +

    F. Hoffmann-La Roche AG. Copyright holder, funder. +

    +
    • +
+ +
+

Citation

+

Source: inst/CITATION

+ +

Gower-Page C, Noci A, Gravestock I (2024). +rbmi: Reference Based Multiple Imputation. +R package version 1.3.1, https://github.com/insightsengineering/rbmi, https://insightsengineering.github.io/rbmi/. +

+ 
@Manual{,
+  title = {rbmi: Reference Based Multiple Imputation},
+  author = {Craig Gower-Page and Alessandro Noci and Isaac Gravestock},
+  year = {2024},
+  note = {R package version 1.3.1, https://github.com/insightsengineering/rbmi},
+  url = {https://insightsengineering.github.io/rbmi/},
+}
+

Gower-Page C, Noci A, Wolbers M (2022). +“rbmi: A R package for standard and reference-based multiple imputation methods.” +Journal of Open Source Software, 7(74), 4251. +doi:10.21105/joss.04251, https://doi.org/10.21105/joss.04251. +

+ 
@Article{,
+  title = {rbmi: A R package for standard and reference-based multiple imputation methods},
+  author = {Craig Gower-Page and Alessandro Noci and Marcel Wolbers},
+  year = {2022},
+  publisher = {The Open Journal},
+  doi = {10.21105/joss.04251},
+  url = {https://doi.org/10.21105/joss.04251},
+  volume = {7},
+  number = {74},
+  pages = {4251},
+  journal = {Journal of Open Source Software},
+}
+
+ +
+ + +
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0,r(6469)),l=r(505),c=r(5884);e.DirectionVH=((r={})[1]="v",r[2]="h",r),e.CommonMoMixin=function(t){return o(e,n=t),e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1),this.protoBBox(t),this.node.attributes.get("symmetric")&&2!==this.stretch.dir&&(e=this.getCenterOffset(t),t.h+=e,t.d-=e),this.node.getProperty("mathaccent")&&(0===this.stretch.dir||0<=this.size)&&(t.w=0)},e.prototype.protoBBox=function(t){var e=0!==this.stretch.dir;e&&null===this.size&&this.getStretchedVariant([0]),e&&this.size<0||(n.prototype.computeBBox.call(this,t),this.copySkewIC(t))},e.prototype.getAccentOffset=function(){var t=a.BBox.empty();return this.protoBBox(t),-t.w/2},e.prototype.getCenterOffset=function(t){return(t=void 0===t?null:t)||(t=a.BBox.empty(),n.prototype.computeBBox.call(this,t)),(t.h+t.d)/2+this.font.params.axis_height-t.h},e.prototype.getVariant=function(){this.node.attributes.get("largeop")?this.variant=this.node.attributes.get("displaystyle")?"-largeop":"-smallop":this.node.attributes.getExplicit("mathvariant")||!1!==this.node.getProperty("pseudoscript")?n.prototype.getVariant.call(this):this.variant="-tex-variant"},e.prototype.canStretch=function(t){if(0!==this.stretch.dir)return this.stretch.dir===t;if(!this.node.attributes.get("stretchy"))return!1;var e=this.getText();if(1!==Array.from(e).length)return!1;e=this.font.getDelimiter(e.codePointAt(0));return this.stretch=e&&e.dir===t?e:c.NOSTRETCH,0!==this.stretch.dir},e.prototype.getStretchedVariant=function(t,e){var r,n;if(void 0===e&&(e=!1),0!==this.stretch.dir){var o=this.getWH(t),i=this.getSize("minsize",0),a=this.getSize("maxsize",1/0),s=this.node.getProperty("mathaccent"),o=Math.max(i,Math.min(a,o)),a=this.font.params.delimiterfactor/1e3,l=this.font.params.delimitershortfall,c=i||e?o:s?Math.min(o/a,o+l):Math.max(o*a,o-l),u=this.stretch,p=u.c||this.getText().codePointAt(0),h=0;if(u.sizes)try{for(var d=y(u.sizes),f=d.next();!f.done;f=d.next()){if(f.value>=c)return s&&h&&h--,this.variant=this.font.getSizeVariant(p,h),this.size=h,void(u.schar&&u.schar[h]&&(this.stretch=m(m({},this.stretch),{c:u.schar[h]})));h++}}catch(t){r={error:t}}finally{try{f&&!f.done&&(n=d.return)&&n.call(d)}finally{if(r)throw r.error}}u.stretch?(this.size=-1,this.invalidateBBox(),this.getStretchBBox(t,this.checkExtendedHeight(o,u),u)):(this.variant=this.font.getSizeVariant(p,h-1),this.size=h-1)}},e.prototype.getSize=function(t,e){var r=this.node.attributes;return e=r.isSet(t)?this.length2em(r.get(t),1,1):e},e.prototype.getWH=function(t){if(0===t.length)return 0;if(1===t.length)return t[0];var t=s(t,2),e=t[0],t=t[1],r=this.font.params.axis_height;return this.node.attributes.get("symmetric")?2*Math.max(e-r,t+r):e+t},e.prototype.getStretchBBox=function(t,e,r){r.hasOwnProperty("min")&&r.min>e&&(e=r.min);var n=s(r.HDW,3),o=n[0],i=n[1],n=n[2];1===this.stretch.dir?(o=(t=s(this.getBaseline(t,e,r),2))[0],i=t[1]):n=e,this.bbox.h=o,this.bbox.d=i,this.bbox.w=n},e.prototype.getBaseline=function(t,e,r){var n=2===t.length&&t[0]+t[1]===e,o=this.node.attributes.get("symmetric"),t=s(n?t:[e,0],2),e=t[0],t=t[1],i=s([e+t,0],2),a=i[0],i=i[1];return i=o?(o=this.font.params.axis_height,(a=n?2*Math.max(e-o,t+o):a)/2-o):n?t:(o=(e=s(r.HDW||[.75,.25],2))[0],(n=e[1])*(a/(o+n))),[a-i,i]},e.prototype.checkExtendedHeight=function(t,e){var r;return e.fullExt&&(r=(e=s(e.fullExt,2))[0],t=(e=e[1])+Math.ceil(Math.max(0,t-e)/r)*r),t},e.prototype.remapChars=function(t){var e=this.node.getProperty("primes");return e?(0,l.unicodeChars)(e):(1===t.length&&(e=this.node.coreParent().parent,e=this.isAccent&&!e.isKind("mrow")?"accent":"mo",(e=this.font.getRemappedChar(e,t[0]))&&(t=this.unicodeChars(e,this.variant))),t)},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonInferredMrowMixin=e.CommonMrowMixin=void 0,r(6469));e.CommonMrowMixin=function(t){return o(e,s=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),e.prototype.stretchChildren=function(){var t,e,r,n,o,i,a=[];try{for(var s=x(this.childNodes),l=s.next();!l.done;l=s.next())(S=l.value).canStretch(1)&&a.push(S)}catch(e){t={error:e}}finally{try{l&&!l.done&&(e=s.return)&&e.call(s)}finally{if(t)throw t.error}}var c=a.length,u=this.childNodes.length;if(c&&1p&&(p=g),(b*=v)>h&&(h=b))}}catch(t){r={error:t}}finally{try{m&&!m.done&&(n=f.return)&&n.call(f)}finally{if(r)throw r.error}}try{for(var S,O=x(a),M=O.next();!M.done;M=O.next())(S=M.value).coreMO().getStretchedVariant([p,h])}catch(t){o={error:t}}finally{try{M&&!M.done&&(i=O.return)&&i.call(O)}finally{if(o)throw o.error}}}},e;function e(){for(var e,t,r=[],n=0;nthis.surdH?(t.h+t.d-(this.surdH-2*e-r/2))/2:e+r/4]},e.prototype.getRootDimens=function(t,e){return[0,0,0,0]},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},s=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMtableMixin=void 0,r(6469)),l=r(505),u=r(7875);e.CommonMtableMixin=function(t){return i(e,o=t),Object.defineProperty(e.prototype,"tableRows",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.findContainer=function(){for(var t=this,e=t.parent;e&&(e.node.notParent||e.node.isKind("mrow"));)e=(t=e).parent;this.container=e,this.containerI=t.node.childPosition()},e.prototype.getPercentageWidth=function(){var t;this.hasLabels?this.bbox.pwidth=s.BBox.fullWidth:(t=this.node.attributes.get("width"),(0,l.isPercent)(t)&&(this.bbox.pwidth=t))},e.prototype.stretchRows=function(){for(var t=this.node.attributes.get("equalrows"),e=t?this.getEqualRowHeight():0,r=t?this.getTableData():{H:[0],D:[0]},n=r.H,o=r.D,i=this.tableRows,a=0;ao[r]&&(o[r]=c),u>i[r]&&(i[r]=u),sa[e]&&(a[e]=l),s},e.prototype.extendHD=function(t,e,r,n){n=(n-(e[t]+r[t]))/2;n<1e-5||(e[t]+=n,r[t]+=n)},e.prototype.recordPWidthCell=function(t,e){t.childNodes[0]&&t.childNodes[0].getBBox().pwidth&&this.pwidthCells.push([t,e])},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var e=this.getTableData(),r=e.H,e=e.D,r=(n=this.node.attributes.get("equalrows")?(n=this.getEqualRowHeight(),(0,u.sum)([].concat(this.rLines,this.rSpace))+n*this.numRows):(0,u.sum)(r.concat(e,this.rLines,this.rSpace)),n+=2*(this.fLine+this.fSpace[1]),this.getComputedWidths()),e=(0,u.sum)(r.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),r=this.node.attributes.get("width"),n=("auto"!==r&&(e=Math.max(this.length2em(r,0)+2*this.fLine,e)),p(this.getBBoxHD(n),2)),o=n[0],n=n[1],o=(t.h=o,t.d=n,t.w=e,p(this.getBBoxLR(),2)),n=o[0],e=o[1];t.L=n,t.R=e,(0,l.isPercent)(r)||this.setColumnPWidths()},e.prototype.setChildPWidths=function(t,e,r){var n=this.node.attributes.get("width");if(!(0,l.isPercent)(n))return!1;this.hasLabels||(this.bbox.pwidth="",this.container.bbox.pwidth="");var o=this.bbox,i=o.w,a=o.L,o=o.R,s=this.node.attributes.get("data-width-includes-label"),n=Math.max(i,this.length2em(n,Math.max(e,a+i+o)))-(s?a+o:0),e=this.node.attributes.get("equalcolumns")?Array(this.numCols).fill(this.percent(1/Math.max(1,this.numCols))):this.getColumnAttributes("columnwidth",0),s=(this.cWidths=this.getColumnWidthsFixed(e,n),this.getComputedWidths());return this.pWidth=(0,u.sum)(s.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),this.isTop&&(this.bbox.w=this.pWidth),this.setColumnPWidths(),this.pWidth!==i&&this.parent.invalidateBBox(),this.pWidth!==i},e.prototype.setColumnPWidths=function(){var t,e,r=this.cWidths;try{for(var n=_(this.pwidthCells),o=n.next();!o.done;o=n.next()){var i=p(o.value,2),a=i[0],s=i[1];a.setChildPWidths(!1,r[s])&&(a.invalidateBBox(),a.getBBox())}}catch(e){t={error:e}}finally{try{o&&!o.done&&(e=n.return)&&e.call(n)}finally{if(t)throw t.error}}},e.prototype.getBBoxHD=function(t){var e,r=p(this.getAlignmentRow(),2),n=r[0],r=r[1];if(null===r)return{top:[0,t],center:[e=t/2,e],bottom:[t,0],baseline:[e,e],axis:[e+(o=this.font.params.axis_height),e-o]}[n]||[e,e];var o=this.getVerticalPosition(r,n);return[o,t-o]},e.prototype.getBBoxLR=function(){var t,e,r,n;return this.hasLabels?(t=(n=this.node.attributes).get("side"),e=(r=p(this.getPadAlignShift(t),2))[0],r=r[1],(n=this.hasLabels&&!!n.get("data-width-includes-label"))&&this.frame&&this.fSpace[0]&&(e-=this.fSpace[0]),"center"!==r||n?"left"===t?[e,0]:[0,e]:[e,e]):[0,0]},e.prototype.getPadAlignShift=function(t){var e=this.getTableData().L+this.length2em(this.node.attributes.get("minlabelspacing")),r=p(null==this.styles?["",""]:[this.styles.get("padding-left"),this.styles.get("padding-right")],2),n=r[0],r=r[1],n=((n||r)&&(e=Math.max(e,this.length2em(n||"0"),this.length2em(r||"0"))),p(this.getAlignShift(),2)),r=n[0],n=n[1];return[e,r,n=r===t?"left"===t?Math.max(e,n)-e:Math.min(-e,n)+e:n]},e.prototype.getAlignShift=function(){return this.isTop?o.prototype.getAlignShift.call(this):[this.container.getChildAlign(this.containerI),0]},e.prototype.getWidth=function(){return this.pWidth||this.getBBox().w},e.prototype.getEqualRowHeight=function(){var t=this.getTableData(),e=t.H,r=t.D,t=Array.from(e.keys()).map(function(t){return e[t]+r[t]});return Math.max.apply(Math,t)},e.prototype.getComputedWidths=function(){var e=this,r=this.getTableData().W,t=Array.from(r.keys()).map(function(t){return("number"==typeof e.cWidths[t]?e.cWidths:r)[t]});return t=this.node.attributes.get("equalcolumns")?Array(t.length).fill((0,u.max)(t)):t},e.prototype.getColumnWidths=function(){var t=this.node.attributes.get("width");if(this.node.attributes.get("equalcolumns"))return this.getEqualColumns(t);var e=this.getColumnAttributes("columnwidth",0);return"auto"===t?this.getColumnWidthsAuto(e):(0,l.isPercent)(t)?this.getColumnWidthsPercent(e):this.getColumnWidthsFixed(e,this.length2em(t))},e.prototype.getEqualColumns=function(t){var e,r=Math.max(1,this.numCols);return t="auto"===t?(e=this.getTableData().W,(0,u.max)(e)):(0,l.isPercent)(t)?this.percent(1/r):(e=(0,u.sum)([].concat(this.cLines,this.cSpace))+2*this.fSpace[0],Math.max(0,this.length2em(t)-e)/r),Array(this.numCols).fill(t)},e.prototype.getColumnWidthsAuto=function(t){var e=this;return t.map(function(t){return"auto"===t||"fit"===t?null:(0,l.isPercent)(t)?t:e.length2em(t)})},e.prototype.getColumnWidthsPercent=function(r){var n=this,o=0<=r.indexOf("fit"),i=(o?this.getTableData():{W:null}).W;return Array.from(r.keys()).map(function(t){var e=r[t];return"fit"===e?null:"auto"===e?o?i[t]:null:(0,l.isPercent)(e)?e:n.length2em(e)})},e.prototype.getColumnWidthsFixed=function(r,t){var n=this,e=Array.from(r.keys()),o=e.filter(function(t){return"fit"===r[t]}),i=e.filter(function(t){return"auto"===r[t]}),i=o.length||i.length,a=(i?this.getTableData():{W:null}).W,s=t-(0,u.sum)([].concat(this.cLines,this.cSpace))-2*this.fSpace[0],l=s,c=(e.forEach(function(t){var e=r[t];l-="fit"===e||"auto"===e?a[t]:n.length2em(e,s)}),i&&0this.numRows?null:t-1]},e.prototype.getColumnAttributes=function(t,e){var r=this.numCols-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getRowAttributes=function(t,e){var r=this.numRows-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getAttributeArray=function(t){var e=this.node.attributes.get(t);return e?(0,l.split)(e):[this.node.attributes.getDefault(t)]},e.prototype.addEm=function(t,e){var r=this;return void 0===e&&(e=1),t?t.map(function(t){return r.em(t/e)}):null},e.prototype.convertLengths=function(t){var e=this;return t?t.map(function(t){return e.length2em(t)}):null},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")};Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMlabeledtrMixin=e.CommonMtrMixin=void 0,e.CommonMtrMixin=function(t){return o(e,r=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"numCells",{get:function(){return this.childNodes.length},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"labeled",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"tableCells",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.getChild=function(t){return this.childNodes[t]},e.prototype.getChildBBoxes=function(){return this.childNodes.map(function(t){return t.getBBox()})},e.prototype.stretchChildren=function(t){void 0===t&&(t=null);var e,r,n,o,i=[],a=this.labeled?this.childNodes.slice(1):this.childNodes;try{for(var s=M(a),l=s.next();!l.done;l=s.next())(_=l.value.childNodes[0]).canStretch(1)&&i.push(_)}catch(t){u={error:t}}finally{try{l&&!l.done&&(c=s.return)&&c.call(s)}finally{if(u)throw u.error}}var c=i.length,u=this.childNodes.length;if(c&&1=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},a=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonScriptbaseMixin=void 0,r(9007));e.CommonScriptbaseMixin=function(t){var o;return i(e,o=t),Object.defineProperty(e.prototype,"baseChild",{get:function(){return this.childNodes[this.node.base]},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"scriptChild",{get:function(){return this.childNodes[1]},enumerable:!1,configurable:!0}),e.prototype.getBaseCore=function(){for(var t=this.getSemanticBase()||this.childNodes[0];t&&(1===t.childNodes.length&&(t.node.isKind("mrow")||t.node.isKind("TeXAtom")&&t.node.texClass!==a.TEXCLASS.VCENTER||t.node.isKind("mstyle")||t.node.isKind("mpadded")||t.node.isKind("mphantom")||t.node.isKind("semantics"))||t.node.isKind("munderover")&&t.isMathAccent);)this.setBaseAccentsFor(t),t=t.childNodes[0];return t||(this.baseHasAccentOver=this.baseHasAccentUnder=!1),t||this.childNodes[0]},e.prototype.setBaseAccentsFor=function(t){t.node.isKind("munderover")&&(null===this.baseHasAccentOver&&(this.baseHasAccentOver=!!t.node.attributes.get("accent")),null===this.baseHasAccentUnder&&(this.baseHasAccentUnder=!!t.node.attributes.get("accentunder")))},e.prototype.getSemanticBase=function(){var t=this.node.attributes.getExplicit("data-semantic-fencepointer");return this.getBaseFence(this.baseChild,t)},e.prototype.getBaseFence=function(t,e){var r,n;if(!t||!t.node.attributes||!e)return null;if(t.node.attributes.getExplicit("data-semantic-id")===e)return t;try{for(var o=O(t.childNodes),i=o.next();!i.done;i=o.next()){var a=i.value,s=this.getBaseFence(a,e);if(s)return s}}catch(t){r={error:t}}finally{try{i&&!i.done&&(n=o.return)&&n.call(o)}finally{if(r)throw r.error}}return null},e.prototype.getBaseScale=function(){for(var t=this.baseCore,e=1;t&&t!==this;)e*=t.getOuterBBox().rscale,t=t.parent;return e},e.prototype.getBaseIc=function(){return this.baseCore.getOuterBBox().ic*this.baseScale},e.prototype.getAdjustedIc=function(){var t=this.baseCore.getOuterBBox();return(t.ic?1.05*t.ic+.05:0)*this.baseScale},e.prototype.isCharBase=function(){var t=this.baseCore;return(t.node.isKind("mo")&&null===t.size||t.node.isKind("mi")||t.node.isKind("mn"))&&1===t.bbox.rscale&&1===Array.from(t.getText()).length},e.prototype.checkLineAccents=function(){this.node.isKind("munderover")&&(this.node.isKind("mover")?this.isLineAbove=this.isLineAccent(this.scriptChild):this.node.isKind("munder")?this.isLineBelow=this.isLineAccent(this.scriptChild):(this.isLineAbove=this.isLineAccent(this.overChild),this.isLineBelow=this.isLineAccent(this.underChild)))},e.prototype.isLineAccent=function(t){t=t.coreMO().node;return t.isToken&&"―"===t.getText()},e.prototype.getBaseWidth=function(){var t=this.baseChild.getOuterBBox();return t.w*t.rscale-(this.baseRemoveIc?this.baseIc:0)+this.font.params.extra_ic},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var r=this.getBaseWidth(),n=y(this.getOffset(),2),o=n[0],n=n[1];t.append(this.baseChild.getOuterBBox()),t.combine(this.scriptChild.getOuterBBox(),r+o,n),t.w+=this.font.params.scriptspace,t.clean(),this.setChildPWidths(e)},e.prototype.getOffset=function(){return[0,0]},e.prototype.baseCharZero=function(t){var e=!!this.baseCore.node.attributes.get("largeop"),r=this.baseScale;return this.baseIsChar&&!e&&1===r?0:t},e.prototype.getV=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.length2em(this.node.attributes.get("subscriptshift"),r.sub1);return Math.max(this.baseCharZero(t.d*this.baseScale+r.sub_drop*e.rscale),n,e.h*e.rscale-.8*r.x_height)},e.prototype.getU=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.node.attributes.getList("displaystyle","superscriptshift"),o=this.node.getProperty("texprimestyle")?r.sup3:n.displaystyle?r.sup1:r.sup2,n=this.length2em(n.superscriptshift,o);return Math.max(this.baseCharZero(t.h*this.baseScale-r.sup_drop*e.rscale),n,e.d*e.rscale+.25*r.x_height)},e.prototype.hasMovableLimits=function(){var t=this.node.attributes.get("displaystyle"),e=this.baseChild.coreMO().node;return!t&&!!e.attributes.get("movablelimits")},e.prototype.getOverKU=function(t,e){var r=this.node.attributes.get("accent"),n=this.font.params,e=e.d*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentOver?o:0,o=this.isLineAbove?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing1,n.big_op_spacing3-Math.max(0,e)))-i;return[r,t.h*t.rscale+r+e]},e.prototype.getUnderKV=function(t,e){var r=this.node.attributes.get("accentunder"),n=this.font.params,e=e.h*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentUnder?o:0,o=this.isLineBelow?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing2,n.big_op_spacing4-e))-i;return[r,-(t.d*t.rscale+r+e)]},e.prototype.getDeltaW=function(e,t){void 0===t&&(t=[0,0,0]);var r,n,o,i,a=this.node.attributes.get("align"),s=e.map(function(t){return t.w*t.rscale}),l=(s[0]-=this.baseRemoveIc&&!this.baseCore.node.attributes.get("largeop")?this.baseIc:0,Math.max.apply(Math,g([],y(s),!1))),c=[],u=0;try{for(var p=O(s.keys()),h=p.next();!h.done;h=p.next()){var d=h.value;c[d]=("center"===a?(l-s[d])/2:"right"===a?l-s[d]:0)+t[d],c[d]=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,o,i=r.call(t),a=[];try{for(;(void 0===e||0=t.length?void 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MathJax is a JavaScript library that allows page"," authors to include mathematics within their web pages."," As a reader, you don't need to do anything to make that happen.

","

Browsers: MathJax works with all modern browsers including"," Edge, Firefox, Chrome, Safari, Opera, and most mobile browsers.

","

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Show Math As: These options allow you to view the formula's"," source markup (as MathML or in its original format).

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Copy to Clipboard: These options copy the formula's source markup,"," as MathML or in its original format, to the clipboard"," (in browsers that support that).

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","

Accessibility: MathJax can work with screen"," readers to make mathematics accessible to the visually impaired."," Turn on the explorer to enable generation of speech strings"," and the ability to investigate expressions interactively.

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Language: This menu lets you select the language used by MathJax"," for its menus and warning messages. (Not yet implemented in version 3.)

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","

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","

Preferences: MathJax uses your browser's localStorage database"," to save the preferences set via this menu locally in your browser. These"," are not used to track you, and are not transferred or used remotely by"," MathJax in any way.

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r.copyOriginal()}),this.submenu("Annotation","Annotation")]),this.rule(),this.submenu("Settings","Math Settings",[this.submenu("Renderer","Math Renderer",this.radioGroup("renderer",[["CHTML"],["SVG"]])),this.rule(),this.submenu("ZoomTrigger","Zoom Trigger",[this.command("ZoomNow","Zoom Once Now",function(){return r.zoom(null,"",r.menu.mathItem)}),this.rule(),this.radioGroup("zoom",[["Click"],["DoubleClick","Double-Click"],["NoZoom","No Zoom"]]),this.rule(),this.label("TriggerRequires","Trigger Requires:"),this.checkbox(v?"Option":"Alt",v?"Option":"Alt","alt"),this.checkbox("Command","Command","cmd",{hidden:!v}),this.checkbox("Control","Control","ctrl",{hiddne:v}),this.checkbox("Shift","Shift","shift")]),this.submenu("ZoomFactor","Zoom Factor",this.radioGroup("zscale",[["150%"],["175%"],["200%"],["250%"],["300%"],["400%"]])),this.rule(),this.command("Scale","Scale All Math...",function(){return r.scaleAllMath()}),this.rule(),this.checkbox("texHints","Add TeX hints to MathML","texHints"),this.checkbox("semantics","Add original as annotation","semantics"),this.rule(),this.command("Reset","Reset to defaults",function(){return r.resetDefaults()})]),this.submenu("Accessibility","Accessibility",[this.checkbox("Activate","Activate","explorer"),this.submenu("Speech","Speech",[this.checkbox("Speech","Speech Output","speech"),this.checkbox("Subtitles","Speech Subtitles","subtitles"),this.checkbox("Braille","Braille Output","braille"),this.checkbox("View Braille","Braille Subtitles","viewBraille"),this.rule(),this.submenu("A11yLanguage","Language"),this.rule(),this.submenu("Mathspeak","Mathspeak Rules",this.radioGroup("speechRules",[["mathspeak-default","Verbose"],["mathspeak-brief","Brief"],["mathspeak-sbrief","Superbrief"]])),this.submenu("Clearspeak","Clearspeak Rules",this.radioGroup("speechRules",[["clearspeak-default","Auto"]])),this.submenu("ChromeVox","ChromeVox 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r.help.post()})]}),this.menu);this.about.attachMenu(t),this.help.attachMenu(t),this.originalText.attachMenu(t),this.annotationText.attachMenu(t),this.mathmlCode.attachMenu(t),this.zoomBox.attachMenu(t),this.checkLoadableItems(),this.enableExplorerItems(this.settings.explorer),t.showAnnotation=this.annotationText,t.copyAnnotation=this.copyAnnotation.bind(this),t.annotationTypes=this.options.annotationTypes,y.CssStyles.addInfoStyles(this.document.document),y.CssStyles.addMenuStyles(this.document.document)},_.prototype.checkLoadableItems=function(){var t,e;if(b&&b._&&b.loader&&b.startup)!this.settings.collapsible||b._.a11y&&b._.a11y.complexity||this.loadA11y("complexity"),!this.settings.explorer||b._.a11y&&b._.a11y.explorer||this.loadA11y("explorer"),!this.settings.assistiveMml||b._.a11y&&b._.a11y["assistive-mml"]||this.loadA11y("assistive-mml");else{var r=this.menu;try{for(var n=u(Object.keys(this.jax)),o=n.next();!o.done;o=n.next()){var 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n=u(Object.keys(this.settings)),o=n.next();!o.done;o=n.next()){var i=o.value;this.settings[i]!==this.defaultSettings[i]&&(r[i]=this.settings[i])}}catch(t){e={error:t}}finally{try{o&&!o.done&&(t=n.return)&&t.call(n)}finally{if(e)throw e.error}}try{Object.keys(r).length?localStorage.setItem(_.MENU_STORAGE,JSON.stringify(r)):localStorage.removeItem(_.MENU_STORAGE)}catch(t){console.log("MathJax localStorage error: "+t.message)}},_.prototype.setA11y=function(t){b._.a11y&&b._.a11y.explorer&&b._.a11y.explorer_ts.setA11yOptions(this.document,t)},_.prototype.getA11y=function(t){if(b._.a11y&&b._.a11y.explorer)return(void 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t.constructors&&(t.useOutput(r,!0),t.output=t.getOutputJax(),n.jax[e]=t.output,n.setOutputJax(e))}))},_.prototype.setOutputJax=function(t){this.jax[t].setAdaptor(this.document.adaptor),this.document.outputJax=this.jax[t],this.rerender()},_.prototype.setTabOrder=function(t){this.menu.store.inTaborder(t)},_.prototype.setAssistiveMml=function(t){!(this.document.options.enableAssistiveMml=t)||b._.a11y&&b._.a11y["assistive-mml"]?this.rerender():this.loadA11y("assistive-mml")},_.prototype.setExplorer=function(t){this.enableExplorerItems(t),!(this.document.options.enableExplorer=t)||b._.a11y&&b._.a11y.explorer?this.rerender(this.settings.collapsible?c.STATE.RERENDER:c.STATE.COMPILED):this.loadA11y("explorer")},_.prototype.setCollapsible=function(t){!(this.document.options.enableComplexity=t)||b._.a11y&&b._.a11y.complexity?this.rerender(c.STATE.COMPILED):this.loadA11y("complexity")},_.prototype.scaleAllMath=function(){var t=(100*parseFloat(this.settings.scale)).toFixed(1).replace(/.0$/,""),t=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");t&&(t.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(t=parseFloat(t)/100)?this.menu.pool.lookup("scale").setValue(String(t)):alert("The scale should not be zero"):alert("The scale should be a percentage (e.g., 120%)"))},_.prototype.resetDefaults=function(){_.loading++;var e,t,r=this.menu.pool,n=this.defaultSettings;try{for(var o=u(Object.keys(this.settings)),i=o.next();!i.done;i=o.next()){var a,s=i.value,l=r.lookup(s);l?(l.setValue(n[s]),(a=l.items[0])&&a.executeCallbacks_()):this.settings[s]=n[s]}}catch(t){e={error:t}}finally{try{i&&!i.done&&(t=o.return)&&t.call(o)}finally{if(e)throw e.error}}_.loading--,this.rerender(c.STATE.COMPILED)},_.prototype.checkComponent=function(t){t=_.loadingPromises.get(t);t&&i.mathjax.retryAfter(t)},_.prototype.loadComponent=function(t,e){var r;_.loadingPromises.has(t)||(r=b.loader)&&(_.loading++,r=r.load(t).then(function(){_.loading--,_.loadingPromises.delete(t),e(),0===_.loading&&_._loadingPromise&&(_._loadingPromise=null,_._loadingOK())}).catch(function(t){_._loadingPromise?(_._loadingPromise=null,_._loadingFailed(t)):console.log(t)}),_.loadingPromises.set(t,r))},_.prototype.loadA11y=function(r){var n=this,o=!c.STATE.ENRICHED;this.loadComponent("a11y/"+r,function(){var t=b.startup,e=(i.mathjax.handlers.unregister(t.handler),t.handler=t.getHandler(),i.mathjax.handlers.register(t.handler),n.document);n.document=t.document=t.getDocument(),(n.document.menu=n).document.outputJax.reset(),n.transferMathList(e),n.document.processed=e.processed,_._loadingPromise||(n.document.outputJax.reset(),n.rerender("complexity"===r||o?c.STATE.COMPILED:c.STATE.TYPESET))})},_.prototype.transferMathList=function(t){var e,r,n=this.document.options.MathItem;try{for(var o=u(t.math),i=o.next();!i.done;i=o.next()){var a=i.value,s=new n;Object.assign(s,a),this.document.math.push(s)}}catch(t){e={error:t}}finally{try{i&&!i.done&&(r=o.return)&&r.call(o)}finally{if(e)throw e.error}}},_.prototype.formatSource=function(t){return t.trim().replace(/&/g,"&").replace(//g,">")},_.prototype.toMML=function(t){return this.MmlVisitor.visitTree(t.root,t,{texHints:this.settings.texHints,semantics:this.settings.semantics&&"MathML"!==t.inputJax.name})},_.prototype.zoom=function(t,e,r){t&&!this.isZoomEvent(t,e)||(this.menu.mathItem=r,t&&this.menu.post(t),this.zoomBox.post())},_.prototype.isZoomEvent=function(t,e){return this.settings.zoom===e&&(!this.settings.alt||t.altKey)&&(!this.settings.ctrl||t.ctrlKey)&&(!this.settings.cmd||t.metaKey)&&(!this.settings.shift||t.shiftKey)},_.prototype.rerender=function(t){void 0===t&&(t=c.STATE.TYPESET),this.rerenderStart=Math.min(t,this.rerenderStart),_.loading||(this.rerenderStart<=c.STATE.COMPILED&&this.document.reset({inputJax:[]}),this.document.rerender(this.rerenderStart),this.rerenderStart=c.STATE.LAST)},_.prototype.copyMathML=function(){this.copyToClipboard(this.toMML(this.menu.mathItem))},_.prototype.copyOriginal=function(){this.copyToClipboard(this.menu.mathItem.math.trim())},_.prototype.copyAnnotation=function(){this.copyToClipboard(this.menu.annotation.trim())},_.prototype.copyToClipboard=function(t){var e=document.createElement("textarea");e.value=t,e.setAttribute("readonly",""),e.style.cssText="height: 1px; width: 1px; padding: 1px; position: absolute; left: -10px",document.body.appendChild(e),e.select();try{document.execCommand("copy")}catch(t){alert("Can't copy to clipboard: "+t.message)}document.body.removeChild(e)},_.prototype.addMenu=function(e){var r=this,t=e.typesetRoot;t.addEventListener("contextmenu",function(){return 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t,e=0;t=this.contentNodes[e];e++)n=n.concat(t.querySelectorAll(r));return r(this)&&n.unshift(this),n}xml(o,i){function t(t,e){const r=e.map(function(t){return t.xml(o,i)}),n=o.createElementNS("",t);for(let t,e=0;t=r[e];e++)n.appendChild(t);return n}const e=o.createElementNS("",this.type);return i||this.xmlAttributes(e),e.textContent=this.textContent,0");return n.serializeXml(this.xml(e,t))}allAttributes(){const t=[];return t.push(["role",this.role]),"unknown"!==this.font&&t.push(["font",this.font]),Object.keys(this.annotation).length&&t.push(["annotation",this.xmlAnnotation()]),this.embellished&&t.push(["embellished",this.embellished]),this.fencePointer&&t.push(["fencepointer",this.fencePointer]),t.push(["id",this.id.toString()]),t}xmlAnnotation(){const e=[];for(const r in this.annotation)this.annotation[r].forEach(function(t){e.push(r+":"+t)});return e.join(";")}toJson(){const r={};r.type=this.type;var n=this.allAttributes();for(let t,e=0;t=n[e];e++)r[t[0]]=t[1].toString();return this.textContent&&(r.$t=this.textContent),this.childNodes.length&&(r.children=this.childNodes.map(function(t){return t.toJson()})),this.contentNodes.length&&(r.content=this.contentNodes.map(function(t){return t.toJson()})),r}updateContent(t,e){var e=e?t.replace(/^[ \f\n\r\t\v\u200b]*/,"").replace(/[ \f\n\r\t\v\u200b]*$/,""):t.trim();this.textContent!==(t=t&&!e?t:e)&&(e=(0,o.lookupMeaning)(t),this.textContent=t,this.role=e.role,this.type=e.type,this.font=e.font)}addMathmlNodes(r){for(let t,e=0;t=r[e];e++)-1===this.mathml.indexOf(t)&&this.mathml.push(t)}appendChild(t){this.childNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this}replaceChild(e,r){var t,n=this.childNodes.indexOf(e);-1!==n&&(e.parent=null,(r.parent=this).childNodes[n]=r,n=e.mathml.filter(function(t){return-1===r.mathml.indexOf(t)}),t=r.mathml.filter(function(t){return-1===e.mathml.indexOf(t)}),this.removeMathmlNodes(n),this.addMathmlNodes(t))}appendContentNode(t){t&&(this.contentNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this)}removeContentNode(t){t&&-1!==(t=this.contentNodes.indexOf(t))&&this.contentNodes.slice(t,1)}equals(n){if(!n)return!1;if(this.type!==n.type||this.role!==n.role||this.textContent!==n.textContent||this.childNodes.length!==n.childNodes.length||this.contentNodes.length!==n.contentNodes.length)return!1;for(let t,e,r=0;t=this.childNodes[r],e=n.childNodes[r];r++)if(!t.equals(e))return!1;for(let t,e,r=0;t=this.contentNodes[r],e=n.contentNodes[r];r++)if(!t.equals(e))return!1;return!0}displayTree(){console.info(this.displayTree_(0))}addAnnotation(t,e){e&&this.addAnnotation_(t,e)}getAnnotation(t){return this.annotation[t]||[]}hasAnnotation(t,e){const r=this.annotation[t];return!!r&&-1!==r.indexOf(e)}parseAnnotation(t){const r=t.split(";");for(let t=0,e=r.length;ti(t,"infixop")))return!1}return!0},n.isPrefixFunctionBoundary=function(t){return c(t)&&!s(t,"division")||i(t,"appl")||l(t)},n.isBigOpBoundary=function(t){return c(t)||l(t)},n.isIntegralDxBoundary=function(t,e){return!!e&&i(e,"identifier")&&r.lookupSecondary("d",t.textContent)},n.isIntegralDxBoundarySingle=function(t){var e;return!!i(t,"identifier")&&((e=t.textContent[0])&&t.textContent[1]&&r.lookupSecondary("d",e))},n.isGeneralFunctionBoundary=l,n.isEmbellished=function(t){return t.embellished||(r.isEmbellishedType(t.type)?t.type:null)},n.isOperator=c,n.isRelation=u,n.isPunctuation=p,n.isFence=h,n.isElligibleEmbellishedFence=function(t){return!(!t||!h(t))&&(!t.embellished||function t(e){return!e.embellished||!(i(e,"tensor")&&(!i(e.childNodes[1],"empty")||!i(e.childNodes[2],"empty"))&&(!i(e.childNodes[3],"empty")||!i(e.childNodes[4],"empty")))&&(!s(e,"close")||!i(e,"tensor"))&&(!s(e,"open")||!i(e,"subscript")&&!i(e,"superscript"))&&t(e.childNodes[0])}(t))},n.isTableOrMultiline=d,n.tableIsMatrixOrVector=function(t){return!!t&&f(t)&&d(t.childNodes[0])},n.isFencedElement=f,n.tableIsCases=function(t,e){return 0=r)){const o=n.childNodes[0].role;"unknown"!==o&&t.childNodes.every(function(t){t=t.childNodes[0];return!t||t.role===o&&(c.isType(t,"relation")||c.isType(t,"relseq"))})&&(t.role=o)}}static classifyTable(t){var e=y.computeColumns_(t);y.classifyByColumns_(t,e,"equality")||y.classifyByColumns_(t,e,"inequality",["equality"])||y.classifyByColumns_(t,e,"arrow")||y.detectCaleyTable(t)}static detectCaleyTable(t){if(!t.mathmlTree)return!1;const e=t.mathmlTree,r=e.getAttribute("columnlines"),n=e.getAttribute("rowlines");return!(!r||!n||!y.cayleySpacing(r)||!y.cayleySpacing(n)||(t.role="cayley",0))}static cayleySpacing(t){const e=t.split(" ");return("solid"===e[0]||"dashed"===e[0])&&e.slice(1).every(t=>"none"===t)}static proof(t,e,r){e=y.separateSemantics(e);return y.getInstance().proof(t,e,r)}static findSemantics(t,e,r){r=null==r?null:r,t=y.getSemantics(t);return!(!t||!t[e]||null!=r&&t[e]!==r)}static getSemantics(t){t=t.getAttribute("semantics");return t?y.separateSemantics(t):null}static removePrefix(t){const[,...e]=t.split("_");return e.join("_")}static separateSemantics(t){const r={};return t.split(";").forEach(function(t){var[t,e]=t.split(":");r[y.removePrefix(t)]=e}),r}static matchSpaces_(r,n){for(let t,e=0;t=n[e];e++){const n=r[e].mathmlTree,i=r[e+1].mathmlTree;var o;n&&i&&((o=n.nextSibling)&&o!==i&&(o=y.getSpacer_(o))&&(t.mathml.push(o),t.mathmlTree=o,t.role="space"))}}static getSpacer_(t){if("MSPACE"===m.tagName(t))return t;for(;u.hasEmptyTag(t)&&1===t.childNodes.length;)if(t=t.childNodes[0],"MSPACE"===m.tagName(t))return t;return null}static fenceToPunct_(t){var e=y.FENCE_TO_PUNCT_[t.role];if(e){for(;t.embellished;)t.embellished="punctuation",c.isRole(t,"subsup")||c.isRole(t,"underover")||(t.role=e),t=t.childNodes[0];t.type="punctuation",t.role=e}}static classifyFunction_(e,r){if("appl"===e.type||"bigop"===e.type||"integral"===e.type)return"";if(r[0]&&r[0].textContent===s.functionApplication()){y.getInstance().funcAppls[e.id]=r.shift();let t="simple function";return o.run("simple2prefix",e),"prefix function"!==e.role&&"limit function"!==e.role||(t=e.role),y.propagateFunctionRole_(e,t),"prefix"}return y.CLASSIFY_FUNCTION_[e.role]||(c.isSimpleFunctionHead(e)?"simple":"")}static propagateFunctionRole_(t,e){t&&"infixop"!==t.type&&(c.isRole(t,"subsup")||c.isRole(t,"underover")||(t.role=e),y.propagateFunctionRole_(t.childNodes[0],e))}static getFunctionOp_(r,n){if(n(r))return r;for(let t,e=0;t=r.childNodes[e];e++){const r=y.getFunctionOp_(t,n);if(r)return r}return null}static tableToMatrixOrVector_(t){const r=t.childNodes[0];c.isType(r,"multiline")?y.tableToVector_(t):y.tableToMatrix_(t),t.contentNodes.forEach(r.appendContentNode.bind(r));for(let t,e=0;t=r.childNodes[e];e++)y.assignRoleToRow_(t,y.getComponentRoles_(r));return r.parent=null,r}static tableToVector_(t){const e=t.childNodes[0];e.type="vector",1!==e.childNodes.length?y.binomialForm_(e):y.tableToSquare_(t)}static binomialForm_(t){c.isBinomial(t)&&(t.role="binomial",t.childNodes[0].role="binomial",t.childNodes[1].role="binomial")}static tableToMatrix_(t){const e=t.childNodes[0];e.type="matrix",e.childNodes&&0t.match(/[^\s]/)),r=e.map(s.lookupMeaning);if(r.every(function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type&&"comma"===t.role}))return t.role="integer",void("0"===e[0]&&t.addAnnotation("general","basenumber"));r.every(function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type})?t.role="float":t.role="othernumber"}}static exprFont_(t){var e;"unknown"===t.font&&(e=[...t.textContent].map(s.lookupMeaning).reduce(function(t,e){return t&&e.font&&"unknown"!==e.font&&e.font!==t?"unknown"===t?e.font:null:t},"unknown"))&&(t.font=e)}static purgeFences_(e){const r=e.rel,n=e.comp,o=[],i=[];for(;0y.isPureRelation_(t,r))||2===e.length&&(y.testColumns_(e,1,t=>y.isEndRelation_(t,r)||y.isPureRelation_(t,r))||y.testColumns_(e,0,t=>y.isEndRelation_(t,r,!0)||y.isPureRelation_(t,r))))&&(t.role=r,!0)}static isEndRelation_(t,e,r){r=r?t.childNodes.length-1:0;return c.isType(t,"relseq")&&c.isRole(t,e)&&c.isType(t.childNodes[r],"empty")}static isPureRelation_(t,e){return c.isType(t,"relation")&&c.isRole(t,e)}static computeColumns_(e){const n=[];for(let r,t=0;r=e.childNodes[t];t++)for(let t,e=0;t=r.childNodes[e];e++)n[e]?n[e].push(t):n[e]=[t];return n}static testColumns_(t,e,r){const n=t[e];return!!n&&n.some(function(t){return t.childNodes.length&&r(t.childNodes[0])})&&n.every(function(t){return!t.childNodes.length||r(t.childNodes[0])})}setNodeFactory(t){y.getInstance().factory_=t,o.updateFactory(y.getInstance().factory_)}getNodeFactory(){return y.getInstance().factory_}identifierNode(t,e,r){if("MathML-Unit"===r)t.type="identifier",t.role="unit";else if(!e&&1===t.textContent.length&&("integer"===t.role||"latinletter"===t.role||"greekletter"===t.role)&&"normal"===t.font)return t.font="italic",o.run("simpleNamedFunction",t);return"unknown"===t.type&&(t.type="identifier"),y.exprFont_(t),o.run("simpleNamedFunction",t)}implicitNode(t){if(t=y.getInstance().getMixedNumbers_(t),1===(t=y.getInstance().combineUnits_(t)).length)return t[0];t=y.getInstance().implicitNode_(t);return o.run("combine_juxtaposition",t)}text(t,e){return y.exprFont_(t),t.type="text","MS"===e?t.role="string":"MSPACE"!==e&&!t.textContent.match(/^\s*$/)||(t.role="space"),t}row(t){return 0===(t=t.filter(function(t){return!c.isType(t,"empty")})).length?y.getInstance().factory_.makeEmptyNode():(t=y.getInstance().getFencesInRow_(t),t=y.getInstance().tablesInRow(t),t=y.getInstance().getPunctuationInRow_(t),t=y.getInstance().getTextInRow_(t),t=y.getInstance().getFunctionsInRow_(t),y.getInstance().relationsInRow_(t))}limitNode(t,e){if(!e.length)return y.getInstance().factory_.makeEmptyNode();let r,n=e[0],o="unknown";if(!e[1])return n;if(c.isLimitBase(n)){var i=(r=y.MML_TO_LIMIT_[t]).length;if(o=r.type,e=e.slice(0,r.length+1),1===i&&c.isAccent(e[1])||2===i&&c.isAccent(e[1])&&c.isAccent(e[2]))return r=y.MML_TO_BOUNDS_[t],y.getInstance().accentNode_(n,e,r.type,r.length,r.accent);if(2===i){if(c.isAccent(e[1]))return n=y.getInstance().accentNode_(n,[n,e[1]],{MSUBSUP:"subscript",MUNDEROVER:"underscore"}[t],1,!0),e[2]?y.getInstance().makeLimitNode_(n,[n,e[2]],null,"limupper"):n;if(e[2]&&c.isAccent(e[2]))return n=y.getInstance().accentNode_(n,[n,e[2]],{MSUBSUP:"superscript",MUNDEROVER:"overscore"}[t],1,!0),y.getInstance().makeLimitNode_(n,[n,e[1]],null,"limlower");e[i]||(o="limlower")}return y.getInstance().makeLimitNode_(n,e,null,o)}return r=y.MML_TO_BOUNDS_[t],y.getInstance().accentNode_(n,e,r.type,r.length,r.accent)}tablesInRow(t){let r=u.partitionNodes(t,c.tableIsMatrixOrVector),n=[];for(let t,e=0;t=r.rel[e];e++)(n=n.concat(r.comp.shift())).push(y.tableToMatrixOrVector_(t));n=n.concat(r.comp.shift()),r=u.partitionNodes(n,c.isTableOrMultiline),n=[];for(let t,e=0;t=r.rel[e];e++){const o=r.comp.shift();c.tableIsCases(t,o)&&y.tableToCases_(t,o.pop()),(n=n.concat(o)).push(t)}return n.concat(r.comp.shift())}mfenced(e,r,t,n){if(t&&0{r.push(y.getInstance().factory_.makeContentNode(e())),r.push(t)}),n=r}return e&&r?y.getInstance().horizontalFencedNode_(y.getInstance().factory_.makeContentNode(e),y.getInstance().factory_.makeContentNode(r),n):(e&&n.unshift(y.getInstance().factory_.makeContentNode(e)),r&&n.push(y.getInstance().factory_.makeContentNode(r)),y.getInstance().row(n))}fractionLikeNode(t,e,r,n){let o;if(n||!u.isZeroLength(r))return o=y.getInstance().fractionNode_(t,e),n&&o.addAnnotation("general","bevelled"),o;{const r=y.getInstance().factory_.makeBranchNode("line",[t],[]),n=y.getInstance().factory_.makeBranchNode("line",[e],[]);return o=y.getInstance().factory_.makeBranchNode("multiline",[r,n],[]),y.binomialForm_(o),y.classifyMultiline(o),o}}tensor(t,e,r,n,o){const i=y.getInstance().factory_.makeBranchNode("tensor",[t,y.getInstance().scriptNode_(e,"leftsub"),y.getInstance().scriptNode_(r,"leftsuper"),y.getInstance().scriptNode_(n,"rightsub"),y.getInstance().scriptNode_(o,"rightsuper")],[]);return i.role=t.role,i.embellished=c.isEmbellished(t),i}pseudoTensor(t,e,r){var n=t=>!c.isType(t,"empty"),o=e.filter(n).length,n=r.filter(n).length;if(!o&&!n)return t;const i=o?n?"MSUBSUP":"MSUB":"MSUP",a=[t];return o&&a.push(y.getInstance().scriptNode_(e,"rightsub",!0)),n&&a.push(y.getInstance().scriptNode_(r,"rightsuper",!0)),y.getInstance().limitNode(i,a)}font(t){return y.MATHJAX_FONTS[t]||t}proof(t,e,r){if(e.inference||e.axiom||console.log("Noise"),e.axiom){const e=y.getInstance().cleanInference(t.childNodes),n=e.length?y.getInstance().factory_.makeBranchNode("inference",r(e),[]):y.getInstance().factory_.makeEmptyNode();return n.role="axiom",n.mathmlTree=t,n}const n=y.getInstance().inference(t,e,r);return e.proof&&(n.role="proof",n.childNodes[0].role="final"),n}inference(t,e,r){if(e.inferenceRule){const e=y.getInstance().getFormulas(t,[],r);return y.getInstance().factory_.makeBranchNode("inference",[e.conclusion,e.premises],[])}const n=e.labelledRule,o=m.toArray(t.childNodes),i=[],a=("left"!==n&&"both"!==n||i.push(y.getInstance().getLabel(t,o,r,"left")),"right"!==n&&"both"!==n||i.push(y.getInstance().getLabel(t,o,r,"right")),y.getInstance().getFormulas(t,o,r)),s=y.getInstance().factory_.makeBranchNode("inference",[a.conclusion,a.premises],i);return s.mathmlTree=t,s}getLabel(t,e,r,n){const o=y.getInstance().findNestedRow(e,"prooflabel",n),i=y.getInstance().factory_.makeBranchNode("rulelabel",r(m.toArray(o.childNodes)),[]);return i.role=n,i.mathmlTree=o,i}getFormulas(t,e,r){const n=e.length?y.getInstance().findNestedRow(e,"inferenceRule"):t,o="up"===y.getSemantics(n).inferenceRule,i=o?n.childNodes[1]:n.childNodes[0],a=o?n.childNodes[0]:n.childNodes[1],s=i.childNodes[0].childNodes[0],l=m.toArray(s.childNodes[0].childNodes),c=[];let u=1;for(const t of l)u%2&&c.push(t.childNodes[0]),u++;const p=r(c),h=r(m.toArray(a.childNodes[0].childNodes))[0],d=y.getInstance().factory_.makeBranchNode("premises",p,[]),f=(d.mathmlTree=s,y.getInstance().factory_.makeBranchNode("conclusion",[h],[]));return f.mathmlTree=a.childNodes[0].childNodes[0],{conclusion:f,premises:d}}findNestedRow(t,e,r){return y.getInstance().findNestedRow_(t,e,0,r)}cleanInference(t){return m.toArray(t).filter(function(t){return"MSPACE"!==m.tagName(t)})}operatorNode(t){return"unknown"===t.type&&(t.type="operator"),o.run("multioperator",t)}implicitNode_(t){const e=y.getInstance().factory_.makeMultipleContentNodes(t.length-1,s.invisibleTimes()),r=(y.matchSpaces_(t,e),y.getInstance().infixNode_(t,e[0]));return r.role="implicit",e.forEach(function(t){t.parent=r}),r.contentNodes=e,r}infixNode_(t,e){const r=y.getInstance().factory_.makeBranchNode("infixop",t,[e],u.getEmbellishedInner(e).textContent);return r.role=e.role,o.run("propagateSimpleFunction",r)}explicitMixed_(r){var n=u.partitionNodes(r,function(t){return t.textContent===s.invisiblePlus()});if(!n.rel.length)return r;let o=[];for(let t,e=0;t=n.rel[e];e++){const s=n.comp[e],i=n.comp[e+1],a=s.length-1;if(s[a]&&i[0]&&c.isType(s[a],"number")&&!c.isRole(s[a],"mixed")&&c.isType(i[0],"fraction")){const r=y.getInstance().factory_.makeBranchNode("number",[s[a],i[0]],[]);r.role="mixed",(o=o.concat(s.slice(0,a))).push(r),i.shift()}else(o=o.concat(s)).push(t)}return o.concat(n.comp[n.comp.length-1])}concatNode_(t,e,r){if(0===e.length)return t;const n=e.map(function(t){return u.getEmbellishedInner(t).textContent}).join(" "),o=y.getInstance().factory_.makeBranchNode(r,[t],e,n);return 1c.isRole(t,"subtraction"));let n=y.getInstance().concatNode_(t,r.comp.pop(),"prefixop");for(1===n.contentNodes.length&&"addition"===n.contentNodes[0].role&&"+"===n.contentNodes[0].textContent&&(n.role="positive");0c.isType(t,"text"));if(0===r.rel.length)return t;const n=[];let o=r.comp[0];0c.isRole(t,"open");if(0===t.length){const t=n.shift();for(;0{t=t.type;return"punctuation"===t||"text"===t||"operator"===t||"relation"===t},t=u.partitionNodes(r,function(t){if(!c.isPunctuation(t))return!1;if(c.isPunctuation(t)&&!c.isRole(t,"ellipsis"))return!0;t=r.indexOf(t);if(0===t)return!r[1]||!n(r[1]);var e=r[t-1];if(t===r.length-1)return!n(e);t=r[t+1];return!n(e)||!n(t)});if(0===t.rel.length)return r;const e=[];let o=t.comp.shift(),i=(0c.isRole(t,"dummy"))?r.role="text":t.every(t=>c.isRole(t,"space"))?r.role="space":r.role="sequence",r}dummyNode_(t){const e=y.getInstance().factory_.makeMultipleContentNodes(t.length-1,s.invisibleComma());return e.forEach(function(t){t.role="dummy"}),y.getInstance().punctuatedNode_(t,e)}accentRole_(t,e){if(!c.isAccent(t))return!1;var r=t.textContent,r=s.lookupSecondary("bar",r)||s.lookupSecondary("tilde",r)||t.role;return t.role="underscore"===e?"underaccent":"overaccent",t.addAnnotation("accent",r),!0}accentNode_(t,e,r,n,o){var i=(e=e.slice(0,n+1))[1],a=e[2];let s;if(!o&&a&&((s=y.getInstance().factory_.makeBranchNode("subscript",[t,i],[])).role="subsup",e=[s,a],r="superscript"),o){const n=y.getInstance().accentRole_(i,r);a&&(r=y.getInstance().accentRole_(a,"overscore")&&!n?(e=[s=y.getInstance().factory_.makeBranchNode("overscore",[t,a],[]),i],"underscore"):(e=[s=y.getInstance().factory_.makeBranchNode("underscore",[t,i],[]),a],"overscore"),s.role="underover")}return y.getInstance().makeLimitNode_(t,e,s,r)}makeLimitNode_(t,e,r,n){if("limupper"===n&&"limlower"===t.type)return t.childNodes.push(e[1]),(e[1].parent=t).type="limboth",t;if("limlower"===n&&"limupper"===t.type)return t.childNodes.splice(1,-1,e[1]),(e[1].parent=t).type="limboth",t;const o=y.getInstance().factory_.makeBranchNode(n,e,[]),i=c.isEmbellished(t);return r&&(r.embellished=i),o.embellished=i,o.role=t.role,o}getFunctionsInRow_(t,e){const r=e||[];if(0===t.length)return r;var e=t.shift(),n=y.classifyFunction_(e,t);if(!n)return r.push(e),y.getInstance().getFunctionsInRow_(t,r);t=y.getInstance().getFunctionsInRow_(t,[]),e=y.getInstance().getFunctionArgs_(e,t,n);return r.concat(e)}getFunctionArgs_(t,e,r){let n,o,i;switch(r){case"integral":{const r=y.getInstance().getIntegralArgs_(e);if(!r.intvar&&!r.integrand.length)return r.rest.unshift(t),r.rest;const n=y.getInstance().row(r.integrand);return i=y.getInstance().integralNode_(t,n,r.intvar),r.rest.unshift(i),r.rest}case"prefix":if(e[0]&&"fenced"===e[0].type){const r=e.shift();return c.isNeutralFence(r)||(r.role="leftright"),i=y.getInstance().functionNode_(t,r),e.unshift(i),e}if((n=u.sliceNodes(e,c.isPrefixFunctionBoundary)).head.length)o=y.getInstance().row(n.head),n.div&&n.tail.unshift(n.div);else{if(!n.div||!c.isType(n.div,"appl"))return e.unshift(t),e;o=n.div}return i=y.getInstance().functionNode_(t,o),n.tail.unshift(i),n.tail;case"bigop":return(n=u.sliceNodes(e,c.isBigOpBoundary)).head.length?(o=y.getInstance().row(n.head),i=y.getInstance().bigOpNode_(t,o),n.div&&n.tail.unshift(n.div),n.tail.unshift(i),n.tail):(e.unshift(t),e);default:{if(0===e.length)return[t];const r=e[0];return"fenced"===r.type&&!c.isNeutralFence(r)&&c.isSimpleFunctionScope(r)?(r.role="leftright",y.propagateFunctionRole_(t,"simple function"),i=y.getInstance().functionNode_(t,e.shift()),e.unshift(i)):e.unshift(t),e}}}getIntegralArgs_(t,e=[]){if(0===t.length)return{integrand:e,intvar:null,rest:t};const 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r=i.tagName(t);-1!==o.IGNORETAGS.indexOf(r)||-1!==o.EMPTYTAGS.indexOf(r)&&0===t.childNodes.length||n.push(t)}return n},o.isZeroLength=function(t){if(!t)return!1;if(-1!==["negativeveryverythinmathspace","negativeverythinmathspace","negativethinmathspace","negativemediummathspace","negativethickmathspace","negativeverythickmathspace","negativeveryverythickmathspace"].indexOf(t))return!0;t=t.match(/[0-9.]+/);return!!t&&0===parseFloat(t[0])},o.addAttributes=function(e,t){if(t.hasAttributes()){var r=t.attributes;for(let t=r.length-1;0<=t;t--){const n=r[t].name;n.match(/^ext/)&&(e.attributes[n]=r[t].value,e.nobreaking=!0),-1!==o.directSpeechKeys.indexOf(n)&&(e.attributes["ext-speech"]=r[t].value,e.nobreaking=!0),n.match(/texclass$/)&&(e.attributes.texclass=r[t].value),"href"===n&&(e.attributes.href=r[t].value,e.nobreaking=!0)}}},o.getEmbellishedInner=function t(e){return 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e+"/"+t}));return[["ancestor::*/following-sibling::*",r,e(i.join(" | "))].join(" and ")]},s.removeParens=function(t){if(!t.childNodes.length||!t.childNodes[0].childNodes.length||!t.childNodes[0].childNodes[0].childNodes.length)return"";const e=t.childNodes[0].childNodes[0].childNodes[0].textContent;return e.match(/^\(.+\)$/)?e.slice(1,-1):e};const S=new Map([[3,"CSFleftsuperscript"],[4,"CSFleftsubscript"],[2,"CSFbaseline"],[1,"CSFrightsubscript"],[0,"CSFrightsuperscript"]]),O=new Map([[4,2],[3,3],[2,1],[1,4],[0,5]]);s.generateTensorRules=function(i,a=!0){var e=["11111","11110","11101","11100","10111","10110","10101","10100","01111","01110","01101","01100"];for(let o,t=0;o=e[t];t++){let t="tensor"+o,[e,r,n]=function(t){const e=[];let r="",n="",o=parseInt(t,2);for(let t=0;t<5;t++){var i="children/*["+O.get(t)+"]";if(1&o){const e=S.get(t%5);r="[t] "+e+"Verbose; [n] "+i+";"+r,n="[t] "+e+"Brief; [n] "+i+";"+n}else 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1i.generateTensorRules(t,!1),CTFrelationIterator:a.relationIterator,CTFimplicitIterator:a.implicitIterator})}},7599:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.init=e.INIT_=void 0;const n=r(5425),o=r(9577),i=r(9284);e.INIT_=!1,e.init=function(){e.INIT_||((0,o.MathspeakRules)(),(0,n.ClearspeakRules)(),(0,i.PrefixRules)(),(0,i.OtherRules)(),(0,i.BrailleRules)(),e.INIT_=!0)}},7283:function(t,o,e){Object.defineProperty(o,"__esModule",{value:!0}),o.getStore=o.addStore=o.funcStore=void 0;const n=e(1676);o.funcStore=new Map,o.addStore=function(t,e,r){var n={};if(e){const t=o.funcStore.get(e)||{};Object.assign(n,t)}o.funcStore.set(t,Object.assign(n,r))},o.getStore=function(t,e,r){return o.funcStore.get([t,e,r].join("."))||o.funcStore.get([n.DynamicCstr.DEFAULT_VALUES[n.Axis.LOCALE],e,r].join("."))||o.funcStore.get([n.DynamicCstr.BASE_LOCALE,e,r].join("."))||{}}},7598:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.oneLeft=e.leftMostUnit=e.rightMostUnit=e.unitMultipliers=void 0;const o=r(7052),n=r(5274),i=r(4356),a=(e.unitMultipliers=function(t,e){const r=t;let n=0;return function(){var t=o.AuditoryDescription.create({text:s(r[n])&&l(r[n+1])?i.LOCALE.MESSAGES.unitTimes:""},{});return n++,[t]}},["superscript","subscript","overscore","underscore"]);function s(t){for(;t;){if("unit"===t.getAttribute("role"))return!0;var e=t.tagName,r=n.evalXPath("children/*",t);t=-1!==a.indexOf(e)?r[0]:r[r.length-1]}return!1}function l(t){for(;t;){if("unit"===t.getAttribute("role"))return!0;t=n.evalXPath("children/*",t)[0]}return!1}e.rightMostUnit=s,e.leftMostUnit=l,e.oneLeft=function(t){for(;t;){if("number"===t.tagName&&"1"===t.textContent)return[t];if("infixop"!==t.tagName||"multiplication"!==t.getAttribute("role")&&"implicit"!==t.getAttribute("role"))return[];t=n.evalXPath("children/*",t)[0]}return[]}},3284:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.AbstractWalker=void 0;const o=r(7052),i=r(8290),a=r(5740),n=r(4440),s=r(6828),l=r(8496),c=r(2298),u=r(4356),p=r(2105),h=r(5656),d=r(9552),f=r(9543),m=r(8504),y=r(7730),g=r(1214),b=r(179),v=r(1204),_=r(5274);class S{constructor(t,e,r,n){this.node=t,this.generator=e,this.highlighter=r,this.modifier=!1,this.keyMapping=new Map([[l.KeyCode.UP,this.up.bind(this)],[l.KeyCode.DOWN,this.down.bind(this)],[l.KeyCode.RIGHT,this.right.bind(this)],[l.KeyCode.LEFT,this.left.bind(this)],[l.KeyCode.TAB,this.repeat.bind(this)],[l.KeyCode.DASH,this.expand.bind(this)],[l.KeyCode.SPACE,this.depth.bind(this)],[l.KeyCode.HOME,this.home.bind(this)],[l.KeyCode.X,this.summary.bind(this)],[l.KeyCode.Z,this.detail.bind(this)],[l.KeyCode.V,this.virtualize.bind(this)],[l.KeyCode.P,this.previous.bind(this)],[l.KeyCode.U,this.undo.bind(this)],[l.KeyCode.LESS,this.previousRules.bind(this)],[l.KeyCode.GREATER,this.nextRules.bind(this)]]),this.cursors=[],this.xml_=null,this.rebuilt_=null,this.focus_=null,this.active_=!1,this.node.id?this.id=this.node.id:this.node.hasAttribute(S.SRE_ID_ATTR)?this.id=this.node.getAttribute(S.SRE_ID_ATTR):(this.node.setAttribute(S.SRE_ID_ATTR,S.ID_COUNTER.toString()),this.id=S.ID_COUNTER++),this.rootNode=v.getSemanticRoot(t),this.rootId=this.rootNode.getAttribute(c.Attribute.ID),this.xmlString_=n,this.moved=b.WalkerMoves.ENTER}getXml(){return this.xml_||(this.xml_=a.parseInput(this.xmlString_)),this.xml_}getRebuilt(){return this.rebuilt_||this.rebuildStree(),this.rebuilt_}isActive(){return this.active_}activate(){this.isActive()||(this.generator.start(),this.toggleActive_())}deactivate(){this.isActive()&&(b.WalkerState.setState(this.id,this.primaryId()),this.generator.end(),this.toggleActive_())}getFocus(t=!1){return this.focus_||(this.focus_=this.singletonFocus(this.rootId)),t&&this.updateFocus(),this.focus_}setFocus(t){this.focus_=t}getDepth(){return this.levels.depth()-1}isSpeech(){return this.generator.modality===c.Attribute.SPEECH}focusDomNodes(){return this.getFocus().getDomNodes()}focusSemanticNodes(){return this.getFocus().getSemanticNodes()}speech(){var r=this.focusDomNodes();if(!r.length)return"";const n=this.specialMove();if(null!==n)return n;switch(this.moved){case b.WalkerMoves.DEPTH:return this.depth_();case b.WalkerMoves.SUMMARY:return this.summary_();case b.WalkerMoves.DETAIL:return this.detail_();default:{const n=[],a=this.focusSemanticNodes();for(let t=0,e=r.length;tt.id.toString()),this.getRebuilt(),this.node))}rebuildStree(){this.rebuilt_=new g.RebuildStree(this.getXml()),this.rootId=this.rebuilt_.stree.root.id.toString(),this.generator.setRebuilt(this.rebuilt_),this.skeleton=h.SemanticSkeleton.fromTree(this.rebuilt_.stree),this.skeleton.populate(),this.focus_=this.singletonFocus(this.rootId),this.levels=this.initLevels(),f.connectMactions(this.node,this.getXml(),this.rebuilt_.xml)}previousLevel(){var t=this.getFocus().getDomPrimary();return t?v.getAttribute(t,c.Attribute.PARENT):this.getFocus().getSemanticPrimary().parent.id.toString()}nextLevel(){var t=this.getFocus().getDomPrimary();let e,r;if(t){e=v.splitAttribute(v.getAttribute(t,c.Attribute.CHILDREN)),r=v.splitAttribute(v.getAttribute(t,c.Attribute.CONTENT));const n=v.getAttribute(t,c.Attribute.TYPE),o=v.getAttribute(t,c.Attribute.ROLE);return this.combineContentChildren(n,o,r,e)}const n=t=>t.id.toString(),o=this.getRebuilt().nodeDict[this.primaryId()];return e=o.childNodes.map(n),r=o.contentNodes.map(n),0===e.length?[]:this.combineContentChildren(o.type,o.role,r,e)}singletonFocus(t){this.getRebuilt();var e=this.retrieveVisuals(t);return this.focusFromId(t,e)}retrieveVisuals(t){if(!this.skeleton)return[t];const e=parseInt(t,10),r=this.skeleton.subtreeNodes(e);if(!r.length)return[t];r.unshift(e);const n={},o=[];_.updateEvaluator(this.getXml());for(const t of r)n[t]||(o.push(t.toString()),n[t]=!0,this.subtreeIds(t,n));return o}subtreeIds(t,e){t=_.evalXPath(`//*[@data-semantic-id="${t}"]`,this.getXml());_.evalXPath("*//@data-semantic-id",t[0]).forEach(t=>e[parseInt(t.textContent,10)]=!0)}focusFromId(t,e){return y.Focus.factory(t,e,this.getRebuilt(),this.node)}summary(){return this.moved=this.isSpeech()?b.WalkerMoves.SUMMARY:b.WalkerMoves.REPEAT,this.getFocus().clone()}detail(){return this.moved=this.isSpeech()?b.WalkerMoves.DETAIL:b.WalkerMoves.REPEAT,this.getFocus().clone()}specialMove(){return null}virtualize(t){return this.cursors.push({focus:this.getFocus(),levels:this.levels,undo:t||!this.cursors.length}),this.levels=this.levels.clone(),this.getFocus().clone()}previous(){var t=this.cursors.pop();return t?(this.levels=t.levels,t.focus):this.getFocus()}undo(){let t;for(;(t=this.cursors.pop())&&!t.undo;);return t?(this.levels=t.levels,t.focus):this.getFocus()}update(t){this.generator.setOptions(t),(0,s.setup)(t).then(()=>d.generator("Tree").getSpeech(this.node,this.getXml()))}nextRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(n.DOMAIN_TO_STYLES[t.domain]=t.style,t.domain="mathspeak"===t.domain?"clearspeak":"mathspeak",t.style=n.DOMAIN_TO_STYLES[t.domain],this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}nextStyle(t,e){if("mathspeak"===t){const t=["default","brief","sbrief"],n=t.indexOf(e);return-1===n?e:n>=t.length-1?t[0]:t[n+1]}if("clearspeak"!==t)return e;{const t=m.ClearspeakPreferences.getLocalePreferences().en;if(!t)return"default";const o=m.ClearspeakPreferences.relevantPreferences(this.getFocus().getSemanticPrimary()),i=m.ClearspeakPreferences.findPreference(e,o),a=t[o].map(function(t){return t.split("_")[1]}),s=a.indexOf(i);if(-1===s)return e;var r=s>=a.length-1?a[0]:a[s+1];return m.ClearspeakPreferences.addPreference(e,o,r)}}previousRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(t.style=this.nextStyle(t.domain,t.style),this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}refocus(){let t,e=this.getFocus();for(;!e.getNodes().length;){t=this.levels.peek();var r=this.up();if(!r)break;this.setFocus(r),e=this.getFocus(!0)}this.levels.push(t),this.setFocus(e)}toggleActive_(){this.active_=!this.active_}mergePrefix_(t,e=[]){var r=this.isSpeech()?this.prefix_():"",r=(r&&t.unshift(r),this.isSpeech()?this.postfix_():"");return r&&t.push(r),i.finalize(i.merge(e.concat(t)))}prefix_(){var t=this.getFocus().getDomNodes(),e=this.getFocus().getSemanticNodes();return t[0]?v.getAttribute(t[0],c.Attribute.PREFIX):f.retrievePrefix(e[0])}postfix_(){var t=this.getFocus().getDomNodes();return t[0]?v.getAttribute(t[0],c.Attribute.POSTFIX):""}depth_(){var t=p.Grammar.getInstance().getParameter("depth"),e=(p.Grammar.getInstance().setParameter("depth",!0),this.getFocus().getDomPrimary()),e=this.expandable(e)?u.LOCALE.MESSAGES.navigate.EXPANDABLE:this.collapsible(e)?u.LOCALE.MESSAGES.navigate.COLLAPSIBLE:"",r=u.LOCALE.MESSAGES.navigate.LEVEL+" "+this.getDepth(),n=this.getFocus().getSemanticNodes(),n=f.retrievePrefix(n[0]),r=[new o.AuditoryDescription({text:r,personality:{}}),new o.AuditoryDescription({text:n,personality:{}}),new o.AuditoryDescription({text:e,personality:{}})];return p.Grammar.getInstance().setParameter("depth",t),i.finalize(i.markup(r))}actionable_(t){t=null==t?void 0:t.parentNode;return t&&this.highlighter.isMactionNode(t)?t:null}summary_(){var t=this.getFocus().getSemanticPrimary().id.toString(),t=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:a.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],t=f.retrieveSummary(t);return this.mergePrefix_([t])}detail_(){const t=this.getFocus().getSemanticPrimary().id.toString(),e=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:a.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],r=e.getAttribute("alternative");e.removeAttribute("alternative");var n=f.computeMarkup(e),n=this.mergePrefix_([n]);return e.setAttribute("alternative",r),n}}(e.AbstractWalker=S).ID_COUNTER=0,S.SRE_ID_ATTR="sre-explorer-id"},162:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.DummyWalker=void 0;class n extends r(3284).AbstractWalker{up(){return null}down(){return null}left(){return null}right(){return null}repeat(){return null}depth(){return null}home(){return null}getDepth(){return 0}initLevels(){return null}combineContentChildren(t,e,r,n){return[]}findFocusOnLevel(t){return null}}e.DummyWalker=n},7730:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.Focus=void 0;const p=r(1204);class h{constructor(t,e){this.nodes=t,this.primary=e,this.domNodes=[],this.domPrimary_=null,this.allNodes=[]}static factory(t,e,r,n){const o=t=>p.getBySemanticId(n,t),i=r.nodeDict,a=o(t),s=e.map(o),l=e.map(function(t){return i[t]}),c=new h(l,i[t]);return c.domNodes=s,c.domPrimary_=a,c.allNodes=h.generateAllVisibleNodes_(e,s,i,n),c}static generateAllVisibleNodes_(r,n,o,i){var a=t=>p.getBySemanticId(i,t);let s=[];for(let t=0,e=r.length;t=e.length?null:e[t]}depth(){return this.level_.length}clone(){const t=new r;return t.level_=this.level_.slice(0),t}toString(){let r="";for(let t,e=0;t=this.level_[e];e++)r+="\n"+t.map(function(t){return t.toString()});return r}}},1214:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.RebuildStree=void 0;const n=r(5740),c=r(2298),o=r(3588),i=r(6537),a=r(3308),s=r(5656),l=r(7075),u=r(4795),p=r(1204);class h{constructor(t){this.mathml=t,this.factory=new i.SemanticNodeFactory,this.nodeDict={},this.mmlRoot=p.getSemanticRoot(t),this.streeRoot=this.assembleTree(this.mmlRoot),this.stree=l.SemanticTree.fromNode(this.streeRoot,this.mathml),this.xml=this.stree.xml(),a.default.getInstance().setNodeFactory(this.factory)}static addAttributes(t,e,r){r&&1===e.childNodes.length&&e.childNodes[0].nodeType!==n.NodeType.TEXT_NODE&&u.addAttributes(t,e.childNodes[0]),u.addAttributes(t,e)}static textContent(t,e,r){!r&&e.textContent?t.textContent=e.textContent:1<(r=p.splitAttribute(p.getAttribute(e,c.Attribute.OPERATOR))).length&&(t.textContent=r[1])}static isPunctuated(t){return!s.SemanticSkeleton.simpleCollapseStructure(t)&&t[1]&&s.SemanticSkeleton.contentCollapseStructure(t[1])}getTree(){return this.stree}assembleTree(t){const e=this.makeNode(t),r=p.splitAttribute(p.getAttribute(t,c.Attribute.CHILDREN)),n=p.splitAttribute(p.getAttribute(t,c.Attribute.CONTENT));if(h.addAttributes(e,t,!(r.length||n.length)),0===n.length&&0===r.length)return h.textContent(e,t),e;if(0this.setParent(t,e)),e.childNodes=r.map(t=>this.setParent(t,e));t=p.getAttribute(t,c.Attribute.COLLAPSED);return t?this.postProcess(e,t):e}makeNode(t){const e=p.getAttribute(t,c.Attribute.TYPE),r=p.getAttribute(t,c.Attribute.ROLE),n=p.getAttribute(t,c.Attribute.FONT),o=p.getAttribute(t,c.Attribute.ANNOTATION)||"",i=p.getAttribute(t,c.Attribute.ID),a=p.getAttribute(t,c.Attribute.EMBELLISHED),s=p.getAttribute(t,c.Attribute.FENCEPOINTER),l=this.createNode(parseInt(i,10));return l.type=e,l.role=r,l.font=n||"unknown",l.parseAnnotation(o),s&&(l.fencePointer=s),a&&(l.embellished=a),l}makePunctuation(t){const e=this.createNode(t);return e.updateContent((0,o.invisibleComma)()),e.role="dummy",e}makePunctuated(t,e,r){const n=this.createNode(e[0]),o=(n.type="punctuated",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r,e.splice(1,1)[0].slice(1));n.contentNodes=o.map(this.makePunctuation.bind(this)),this.collapsedChildren_(e)}makeEmpty(t,e,r){const n=this.createNode(e);n.type="empty",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r}makeIndex(t,e,r){if(h.isPunctuated(e))return this.makePunctuated(t,e,r),void e[0];s.SemanticSkeleton.simpleCollapseStructure(e)&&!this.nodeDict[e.toString()]&&this.makeEmpty(t,e,r)}postProcess(t,e){const r=s.SemanticSkeleton.fromString(e).array;if("subsup"===t.type){const e=this.createNode(r[1][0]);return e.type="subscript",e.role="subsup",t.type="superscript",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.makeIndex(t,r[1][2],"rightsub"),this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t}if("subscript"===t.type)return this.makeIndex(t,r[2],"rightsub"),this.collapsedChildren_(r),t;if("superscript"===t.type)return this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t;if("tensor"===t.type)return this.makeIndex(t,r[2],"leftsub"),this.makeIndex(t,r[3],"leftsuper"),this.makeIndex(t,r[4],"rightsub"),this.makeIndex(t,r[5],"rightsuper"),this.collapsedChildren_(r),t;if("punctuated"===t.type){if(h.isPunctuated(r)){const e=r.splice(1,1)[0].slice(1);t.contentNodes=e.map(this.makePunctuation.bind(this))}return t}if("underover"!==t.type)return t;{const e=this.createNode(r[1][0]);return"overaccent"===t.childNodes[1].role?(e.type="overscore",t.type="underscore"):(e.type="underscore",t.type="overscore"),e.role="underover",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.collapsedChildren_(r),t}}createNode(t){var e=this.factory.makeNode(t);return this.nodeDict[t.toString()]=e}collapsedChildren_(t){const i=r=>{const n=this.nodeDict[r[0]];n.childNodes=[];for(let t=1,e=r.length;tt.getSemanticPrimary().id===e)}}e.SemanticWalker=i},9806:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SyntaxWalker=void 0;const o=r(707),n=r(3284),i=r(9797);class a extends n.AbstractWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.levels=null,this.restoreState()}initLevels(){const t=new i.Levels;return t.push([this.primaryId()]),t}up(){super.up();var t=this.previousLevel();return t?(this.levels.pop(),this.singletonFocus(t)):null}down(){super.down();var t=this.nextLevel();if(0===t.length)return null;var e=this.singletonFocus(t[0]);return e&&this.levels.push(t),e}combineContentChildren(t,e,r,n){switch(t){case"relseq":case"infixop":case"multirel":return(0,o.interleaveLists)(n,r);case"prefixop":return r.concat(n);case"postfixop":return n.concat(r);case"matrix":case"vector":case"fenced":return n.unshift(r[0]),n.push(r[1]),n;case"cases":return n.unshift(r[0]),n;case"punctuated":return"text"===e?(0,o.interleaveLists)(n,r):n;case"appl":return[n[0],r[0],n[1]];case"root":return[n[1],n[0]];default:return n}}left(){super.left();var t=this.levels.indexOf(this.primaryId());if(null===t)return null;t=this.levels.get(t-1);return t?this.singletonFocus(t):null}right(){super.right();var t=this.levels.indexOf(this.primaryId());if(null===t)return null;t=this.levels.get(t+1);return t?this.singletonFocus(t):null}findFocusOnLevel(t){return 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n.SyntaxWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.firstJump=null,this.key_=null,this.row_=0,this.currentTable_=null,this.keyMapping.set(o.KeyCode.ZERO,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.ONE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.TWO,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.THREE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.FOUR,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.FIVE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.SIX,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.SEVEN,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.EIGHT,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.NINE,this.jumpCell.bind(this))}move(t){this.key_=t;t=super.move(t);return this.modifier=!1,t}up(){return this.moved=a.WalkerMoves.UP,this.eligibleCell_()?this.verticalMove_(!1):super.up()}down(){return 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t}))){T=O,E=!1;break}A.set(O,N)}if(E)for(var P=function(t){var e=v.find((function(e){var i=A.get(e);if(i)return i.slice(0,t).every((function(t){return t}))}));if(e)return T=e,"break"},M=p?3:1;M>0&&"break"!==P(M);M--);e.placement!==T&&(e.modifiersData[n]._skip=!0,e.placement=T,e.reset=!0)}},requiresIfExists:["offset"],data:{_skip:!1}};function oi(t,e,i){return void 0===i&&(i={x:0,y:0}),{top:t.top-e.height-i.y,right:t.right-e.width+i.x,bottom:t.bottom-e.height+i.y,left:t.left-e.width-i.x}}function ri(t){return[zt,qt,Rt,Vt].some((function(e){return t[e]>=0}))}const ai={name:"hide",enabled:!0,phase:"main",requiresIfExists:["preventOverflow"],fn:function(t){var 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m?m(Object.assign({},e.rects,{placement:e.placement})):m,O="number"==typeof C?{mainAxis:C,altAxis:C}:Object.assign({mainAxis:0,altAxis:0},C),x=e.modifiersData.offset?e.modifiersData.offset[e.placement]:null,k={x:0,y:0};if(A){if(o){var L,S="y"===y?zt:Vt,D="y"===y?Rt:qt,$="y"===y?"height":"width",I=A[y],N=I+g[S],P=I-g[D],M=f?-T[$]/2:0,j=b===Xt?E[$]:T[$],F=b===Xt?-T[$]:-E[$],H=e.elements.arrow,W=f&&H?Ce(H):{width:0,height:0},B=e.modifiersData["arrow#persistent"]?e.modifiersData["arrow#persistent"].padding:{top:0,right:0,bottom:0,left:0},z=B[S],R=B[D],q=Ne(0,E[$],W[$]),V=v?E[$]/2-M-q-z-O.mainAxis:j-q-z-O.mainAxis,K=v?-E[$]/2+M+q+R+O.mainAxis:F+q+R+O.mainAxis,Q=e.elements.arrow&&$e(e.elements.arrow),X=Q?"y"===y?Q.clientTop||0:Q.clientLeft||0:0,Y=null!=(L=null==x?void 0:x[y])?L:0,U=I+K-Y,G=Ne(f?ye(N,I+V-Y-X):N,I,f?ve(P,U):P);A[y]=G,k[y]=G-I}if(a){var J,Z="x"===y?zt:Vt,tt="x"===y?Rt:qt,et=A[w],it="y"===w?"height":"width",nt=et+g[Z],st=et-g[tt],ot=-1!==[zt,Vt].indexOf(_),rt=null!=(J=null==x?void 0:x[w])?J:0,at=ot?nt:et-E[it]-T[it]-rt+O.altAxis,lt=ot?et+E[it]+T[it]-rt-O.altAxis:st,ct=f&&ot?function(t,e,i){var n=Ne(t,e,i);return n>i?i:n}(at,et,lt):Ne(f?at:nt,et,f?lt:st);A[w]=ct,k[w]=ct-et}e.modifiersData[n]=k}},requiresIfExists:["offset"]};function di(t,e,i){void 0===i&&(i=!1);var n,s,o=me(e),r=me(e)&&function(t){var e=t.getBoundingClientRect(),i=we(e.width)/t.offsetWidth||1,n=we(e.height)/t.offsetHeight||1;return 1!==i||1!==n}(e),a=Le(e),l=Te(t,r,i),c={scrollLeft:0,scrollTop:0},h={x:0,y:0};return(o||!o&&!i)&&(("body"!==ue(e)||Ue(a))&&(c=(n=e)!==fe(n)&&me(n)?{scrollLeft:(s=n).scrollLeft,scrollTop:s.scrollTop}:Xe(n)),me(e)?((h=Te(e,!0)).x+=e.clientLeft,h.y+=e.clientTop):a&&(h.x=Ye(a))),{x:l.left+c.scrollLeft-h.x,y:l.top+c.scrollTop-h.y,width:l.width,height:l.height}}function ui(t){var e=new Map,i=new Set,n=[];function s(t){i.add(t.name),[].concat(t.requires||[],t.requiresIfExists||[]).forEach((function(t){if(!i.has(t)){var n=e.get(t);n&&s(n)}})),n.push(t)}return t.forEach((function(t){e.set(t.name,t)})),t.forEach((function(t){i.has(t.name)||s(t)})),n}var fi={placement:"bottom",modifiers:[],strategy:"absolute"};function pi(){for(var t=arguments.length,e=new Array(t),i=0;iNumber.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(F.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(".dropdown-menu 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e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const 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W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"
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")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName("show")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),N.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ts),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Jn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ts)}_isShown(){return this.tip&&this.tip.classList.contains(es)}_createPopper(t){const e=g(this._config.placement,[this,t,this._element]),i=rs[e.toUpperCase()];return bi(this._element,t,this._getPopperConfig(i))}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_resolvePossibleFunction(t){return g(t,[this._element])}_getPopperConfig(t){const e={placement:t,modifiers:[{name:"flip",options:{fallbackPlacements:this._config.fallbackPlacements}},{name:"offset",options:{offset:this._getOffset()}},{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"arrow",options:{element:`.${this.constructor.NAME}-arrow`}},{name:"preSetPlacement",enabled:!0,phase:"beforeMain",fn:t=>{this._getTipElement().setAttribute("data-popper-placement",t.state.placement)}}]};return{...e,...g(this._config.popperConfig,[e])}}_setListeners(){const t=this._config.trigger.split(" ");for(const e of t)if("click"===e)N.on(this._element,this.constructor.eventName("click"),this._config.selector,(t=>{this._initializeOnDelegatedTarget(t).toggle()}));else if("manual"!==e){const t=e===ss?this.constructor.eventName("mouseenter"):this.constructor.eventName("focusin"),i=e===ss?this.constructor.eventName("mouseleave"):this.constructor.eventName("focusout");N.on(this._element,t,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusin"===t.type?os:ss]=!0,e._enter()})),N.on(this._element,i,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusout"===t.type?os:ss]=e._element.contains(t.relatedTarget),e._leave()}))}this._hideModalHandler=()=>{this._element&&this.hide()},N.on(this._element.closest(is),ns,this._hideModalHandler)}_fixTitle(){const t=this._element.getAttribute("title");t&&(this._element.getAttribute("aria-label")||this._element.textContent.trim()||this._element.setAttribute("aria-label",t),this._element.setAttribute("data-bs-original-title",t),this._element.removeAttribute("title"))}_enter(){this._isShown()||this._isHovered?this._isHovered=!0:(this._isHovered=!0,this._setTimeout((()=>{this._isHovered&&this.show()}),this._config.delay.show))}_leave(){this._isWithActiveTrigger()||(this._isHovered=!1,this._setTimeout((()=>{this._isHovered||this.hide()}),this._config.delay.hide))}_setTimeout(t,e){clearTimeout(this._timeout),this._timeout=setTimeout(t,e)}_isWithActiveTrigger(){return Object.values(this._activeTrigger).includes(!0)}_getConfig(t){const e=F.getDataAttributes(this._element);for(const t of Object.keys(e))Zn.has(t)&&delete e[t];return t={...e,..."object"==typeof t&&t?t:{}},t=this._mergeConfigObj(t),t=this._configAfterMerge(t),this._typeCheckConfig(t),t}_configAfterMerge(t){return t.container=!1===t.container?document.body:r(t.container),"number"==typeof t.delay&&(t.delay={show:t.delay,hide:t.delay}),"number"==typeof t.title&&(t.title=t.title.toString()),"number"==typeof t.content&&(t.content=t.content.toString()),t}_getDelegateConfig(){const t={};for(const[e,i]of Object.entries(this._config))this.constructor.Default[e]!==i&&(t[e]=i);return t.selector=!1,t.trigger="manual",t}_disposePopper(){this._popper&&(this._popper.destroy(),this._popper=null),this.tip&&(this.tip.remove(),this.tip=null)}static jQueryInterface(t){return this.each((function(){const e=cs.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}m(cs);const hs={...cs.Default,content:"",offset:[0,8],placement:"right",template:'',trigger:"click"},ds={...cs.DefaultType,content:"(null|string|element|function)"};class us extends cs{static get Default(){return hs}static get DefaultType(){return ds}static get 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e=this._observableSections.get(t.target.hash);if(e){t.preventDefault();const i=this._rootElement||window,n=e.offsetTop-this._element.offsetTop;if(i.scrollTo)return void i.scrollTo({top:n,behavior:"smooth"});i.scrollTop=n}})))}_getNewObserver(){const t={root:this._rootElement,threshold:this._config.threshold,rootMargin:this._config.rootMargin};return new IntersectionObserver((t=>this._observerCallback(t)),t)}_observerCallback(t){const e=t=>this._targetLinks.get(`#${t.target.id}`),i=t=>{this._previousScrollData.visibleEntryTop=t.target.offsetTop,this._process(e(t))},n=(this._rootElement||document.documentElement).scrollTop,s=n>=this._previousScrollData.parentScrollTop;this._previousScrollData.parentScrollTop=n;for(const o of t){if(!o.isIntersecting){this._activeTarget=null,this._clearActiveClass(e(o));continue}const t=o.target.offsetTop>=this._previousScrollData.visibleEntryTop;if(s&&t){if(i(o),!n)return}else s||t||i(o)}}_initializeTargetsAndObservables(){this._targetLinks=new Map,this._observableSections=new Map;const t=z.find(bs,this._config.target);for(const e of t){if(!e.hash||l(e))continue;const t=z.findOne(decodeURI(e.hash),this._element);a(t)&&(this._targetLinks.set(decodeURI(e.hash),e),this._observableSections.set(e.hash,t))}}_process(t){this._activeTarget!==t&&(this._clearActiveClass(this._config.target),this._activeTarget=t,t.classList.add(_s),this._activateParents(t),N.trigger(this._element,ps,{relatedTarget:t}))}_activateParents(t){if(t.classList.contains("dropdown-item"))z.findOne(".dropdown-toggle",t.closest(".dropdown")).classList.add(_s);else for(const e of z.parents(t,".nav, .list-group"))for(const t of z.prev(e,ys))t.classList.add(_s)}_clearActiveClass(t){t.classList.remove(_s);const e=z.find(`${bs}.${_s}`,t);for(const t of e)t.classList.remove(_s)}static jQueryInterface(t){return this.each((function(){const e=Es.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}N.on(window,gs,(()=>{for(const t of z.find('[data-bs-spy="scroll"]'))Es.getOrCreateInstance(t)})),m(Es);const Ts=".bs.tab",Cs=`hide${Ts}`,Os=`hidden${Ts}`,xs=`show${Ts}`,ks=`shown${Ts}`,Ls=`click${Ts}`,Ss=`keydown${Ts}`,Ds=`load${Ts}`,$s="ArrowLeft",Is="ArrowRight",Ns="ArrowUp",Ps="ArrowDown",Ms="Home",js="End",Fs="active",Hs="fade",Ws="show",Bs=":not(.dropdown-toggle)",zs='[data-bs-toggle="tab"], [data-bs-toggle="pill"], [data-bs-toggle="list"]',Rs=`.nav-link${Bs}, .list-group-item${Bs}, [role="tab"]${Bs}, ${zs}`,qs=`.${Fs}[data-bs-toggle="tab"], .${Fs}[data-bs-toggle="pill"], .${Fs}[data-bs-toggle="list"]`;class Vs extends W{constructor(t){super(t),this._parent=this._element.closest('.list-group, .nav, [role="tablist"]'),this._parent&&(this._setInitialAttributes(this._parent,this._getChildren()),N.on(this._element,Ss,(t=>this._keydown(t))))}static get NAME(){return"tab"}show(){const t=this._element;if(this._elemIsActive(t))return;const e=this._getActiveElem(),i=e?N.trigger(e,Cs,{relatedTarget:t}):null;N.trigger(t,xs,{relatedTarget:e}).defaultPrevented||i&&i.defaultPrevented||(this._deactivate(e,t),this._activate(t,e))}_activate(t,e){t&&(t.classList.add(Fs),this._activate(z.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.removeAttribute("tabindex"),t.setAttribute("aria-selected",!0),this._toggleDropDown(t,!0),N.trigger(t,ks,{relatedTarget:e})):t.classList.add(Ws)}),t,t.classList.contains(Hs)))}_deactivate(t,e){t&&(t.classList.remove(Fs),t.blur(),this._deactivate(z.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.setAttribute("aria-selected",!1),t.setAttribute("tabindex","-1"),this._toggleDropDown(t,!1),N.trigger(t,Os,{relatedTarget:e})):t.classList.remove(Ws)}),t,t.classList.contains(Hs)))}_keydown(t){if(![$s,Is,Ns,Ps,Ms,js].includes(t.key))return;t.stopPropagation(),t.preventDefault();const e=this._getChildren().filter((t=>!l(t)));let i;if([Ms,js].includes(t.key))i=e[t.key===Ms?0:e.length-1];else{const n=[Is,Ps].includes(t.key);i=b(e,t.target,n,!0)}i&&(i.focus({preventScroll:!0}),Vs.getOrCreateInstance(i).show())}_getChildren(){return z.find(Rs,this._parent)}_getActiveElem(){return this._getChildren().find((t=>this._elemIsActive(t)))||null}_setInitialAttributes(t,e){this._setAttributeIfNotExists(t,"role","tablist");for(const t of e)this._setInitialAttributesOnChild(t)}_setInitialAttributesOnChild(t){t=this._getInnerElement(t);const e=this._elemIsActive(t),i=this._getOuterElement(t);t.setAttribute("aria-selected",e),i!==t&&this._setAttributeIfNotExists(i,"role","presentation"),e||t.setAttribute("tabindex","-1"),this._setAttributeIfNotExists(t,"role","tab"),this._setInitialAttributesOnTargetPanel(t)}_setInitialAttributesOnTargetPanel(t){const 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"${t}"`);e[t]()}}))}}N.on(document,Ls,zs,(function(t){["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this)||Vs.getOrCreateInstance(this).show()})),N.on(window,Ds,(()=>{for(const t of z.find(qs))Vs.getOrCreateInstance(t)})),m(Vs);const Ks=".bs.toast",Qs=`mouseover${Ks}`,Xs=`mouseout${Ks}`,Ys=`focusin${Ks}`,Us=`focusout${Ks}`,Gs=`hide${Ks}`,Js=`hidden${Ks}`,Zs=`show${Ks}`,to=`shown${Ks}`,eo="hide",io="show",no="showing",so={animation:"boolean",autohide:"boolean",delay:"number"},oo={animation:!0,autohide:!0,delay:5e3};class ro extends W{constructor(t,e){super(t,e),this._timeout=null,this._hasMouseInteraction=!1,this._hasKeyboardInteraction=!1,this._setListeners()}static get Default(){return oo}static get DefaultType(){return so}static get 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* --------------------------------------------------------------------------\n * Bootstrap dom/data.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n/**\n * Constants\n */\n\nconst elementMap = new Map()\n\nexport default {\n set(element, key, instance) {\n if (!elementMap.has(element)) {\n elementMap.set(element, new Map())\n }\n\n const instanceMap = elementMap.get(element)\n\n // make it clear we only want one instance per element\n // can be removed later when multiple key/instances are fine to be used\n if (!instanceMap.has(key) && instanceMap.size !== 0) {\n // eslint-disable-next-line no-console\n console.error(`Bootstrap doesn't allow more than one instance per element. Bound instance: ${Array.from(instanceMap.keys())[0]}.`)\n return\n }\n\n instanceMap.set(key, instance)\n },\n\n get(element, key) {\n if (elementMap.has(element)) {\n return elementMap.get(element).get(key) || null\n }\n\n return null\n },\n\n remove(element, key) {\n if (!elementMap.has(element)) {\n return\n }\n\n const instanceMap = elementMap.get(element)\n\n instanceMap.delete(key)\n\n // free up element references if there are no instances left for an element\n if (instanceMap.size === 0) {\n elementMap.delete(element)\n }\n }\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/index.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst MAX_UID = 1_000_000\nconst MILLISECONDS_MULTIPLIER = 1000\nconst TRANSITION_END = 'transitionend'\n\n/**\n * Properly escape IDs selectors to handle weird IDs\n * @param {string} selector\n * @returns {string}\n */\nconst parseSelector = selector => {\n if (selector && window.CSS && window.CSS.escape) {\n // document.querySelector needs escaping to handle IDs (html5+) containing for instance /\n selector = selector.replace(/#([^\\s\"#']+)/g, (match, id) => `#${CSS.escape(id)}`)\n }\n\n return selector\n}\n\n// Shout-out Angus Croll (https://goo.gl/pxwQGp)\nconst toType = object => {\n if (object === null || object === undefined) {\n return `${object}`\n }\n\n return Object.prototype.toString.call(object).match(/\\s([a-z]+)/i)[1].toLowerCase()\n}\n\n/**\n * Public Util API\n */\n\nconst getUID = prefix => {\n do {\n prefix += Math.floor(Math.random() * MAX_UID)\n } while (document.getElementById(prefix))\n\n return prefix\n}\n\nconst getTransitionDurationFromElement = element => {\n if (!element) {\n return 0\n }\n\n // Get transition-duration of the element\n let { transitionDuration, transitionDelay } = window.getComputedStyle(element)\n\n const floatTransitionDuration = Number.parseFloat(transitionDuration)\n const floatTransitionDelay = Number.parseFloat(transitionDelay)\n\n // Return 0 if element or transition duration is not found\n if (!floatTransitionDuration && !floatTransitionDelay) {\n return 0\n }\n\n // If multiple durations are defined, take the first\n transitionDuration = transitionDuration.split(',')[0]\n transitionDelay = transitionDelay.split(',')[0]\n\n return (Number.parseFloat(transitionDuration) + Number.parseFloat(transitionDelay)) * MILLISECONDS_MULTIPLIER\n}\n\nconst triggerTransitionEnd = element => {\n element.dispatchEvent(new Event(TRANSITION_END))\n}\n\nconst isElement = object => {\n if (!object || typeof object !== 'object') {\n return false\n }\n\n if (typeof object.jquery !== 'undefined') {\n object = object[0]\n }\n\n return typeof object.nodeType !== 'undefined'\n}\n\nconst getElement = object => {\n // it's a jQuery object or a node element\n if (isElement(object)) {\n return object.jquery ? object[0] : object\n }\n\n if (typeof object === 'string' && object.length > 0) {\n return document.querySelector(parseSelector(object))\n }\n\n return null\n}\n\nconst isVisible = element => {\n if (!isElement(element) || element.getClientRects().length === 0) {\n return false\n }\n\n const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible'\n // Handle `details` element as its content may falsie appear visible when it is closed\n const closedDetails = element.closest('details:not([open])')\n\n if (!closedDetails) {\n return elementIsVisible\n }\n\n if (closedDetails !== element) {\n const summary = element.closest('summary')\n if (summary && summary.parentNode !== closedDetails) {\n return false\n }\n\n if (summary === null) {\n return false\n }\n }\n\n return elementIsVisible\n}\n\nconst isDisabled = element => {\n if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n return true\n }\n\n if (element.classList.contains('disabled')) {\n return true\n }\n\n if (typeof element.disabled !== 'undefined') {\n return element.disabled\n }\n\n return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false'\n}\n\nconst findShadowRoot = element => {\n if (!document.documentElement.attachShadow) {\n return null\n }\n\n // Can find the shadow root otherwise it'll return the document\n if (typeof element.getRootNode === 'function') {\n const root = element.getRootNode()\n return root instanceof ShadowRoot ? root : null\n }\n\n if (element instanceof ShadowRoot) {\n return element\n }\n\n // when we don't find a shadow root\n if (!element.parentNode) {\n return null\n }\n\n return findShadowRoot(element.parentNode)\n}\n\nconst noop = () => {}\n\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\nconst reflow = element => {\n element.offsetHeight // eslint-disable-line no-unused-expressions\n}\n\nconst getjQuery = () => {\n if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n return window.jQuery\n }\n\n return null\n}\n\nconst DOMContentLoadedCallbacks = []\n\nconst onDOMContentLoaded = callback => {\n if (document.readyState === 'loading') {\n // add listener on the first call when the document is in loading state\n if (!DOMContentLoadedCallbacks.length) {\n document.addEventListener('DOMContentLoaded', () => {\n for (const callback of DOMContentLoadedCallbacks) {\n callback()\n }\n })\n }\n\n DOMContentLoadedCallbacks.push(callback)\n } else {\n callback()\n }\n}\n\nconst isRTL = () => document.documentElement.dir === 'rtl'\n\nconst defineJQueryPlugin = plugin => {\n onDOMContentLoaded(() => {\n const $ = getjQuery()\n /* istanbul ignore if */\n if ($) {\n const name = plugin.NAME\n const JQUERY_NO_CONFLICT = $.fn[name]\n $.fn[name] = plugin.jQueryInterface\n $.fn[name].Constructor = plugin\n $.fn[name].noConflict = () => {\n $.fn[name] = JQUERY_NO_CONFLICT\n return plugin.jQueryInterface\n }\n }\n })\n}\n\nconst execute = (possibleCallback, args = [], defaultValue = possibleCallback) => {\n return typeof possibleCallback === 'function' ? possibleCallback(...args) : defaultValue\n}\n\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n if (!waitForTransition) {\n execute(callback)\n return\n }\n\n const durationPadding = 5\n const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding\n\n let called = false\n\n const handler = ({ target }) => {\n if (target !== transitionElement) {\n return\n }\n\n called = true\n transitionElement.removeEventListener(TRANSITION_END, handler)\n execute(callback)\n }\n\n transitionElement.addEventListener(TRANSITION_END, handler)\n setTimeout(() => {\n if (!called) {\n triggerTransitionEnd(transitionElement)\n }\n }, emulatedDuration)\n}\n\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list The list of elements\n * @param activeElement The active element\n * @param shouldGetNext Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n const listLength = list.length\n let index = list.indexOf(activeElement)\n\n // if the element does not exist in the list return an element\n // depending on the direction and if cycle is allowed\n if (index === -1) {\n return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0]\n }\n\n index += shouldGetNext ? 1 : -1\n\n if (isCycleAllowed) {\n index = (index + listLength) % listLength\n }\n\n return list[Math.max(0, Math.min(index, listLength - 1))]\n}\n\nexport {\n defineJQueryPlugin,\n execute,\n executeAfterTransition,\n findShadowRoot,\n getElement,\n getjQuery,\n getNextActiveElement,\n getTransitionDurationFromElement,\n getUID,\n isDisabled,\n isElement,\n isRTL,\n isVisible,\n noop,\n onDOMContentLoaded,\n parseSelector,\n reflow,\n triggerTransitionEnd,\n toType\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { getjQuery } from '../util/index.js'\n\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/\nconst stripNameRegex = /\\..*/\nconst stripUidRegex = /::\\d+$/\nconst eventRegistry = {} // Events storage\nlet uidEvent = 1\nconst customEvents = {\n mouseenter: 'mouseover',\n mouseleave: 'mouseout'\n}\n\nconst nativeEvents = new Set([\n 'click',\n 'dblclick',\n 'mouseup',\n 'mousedown',\n 'contextmenu',\n 'mousewheel',\n 'DOMMouseScroll',\n 'mouseover',\n 'mouseout',\n 'mousemove',\n 'selectstart',\n 'selectend',\n 'keydown',\n 'keypress',\n 'keyup',\n 'orientationchange',\n 'touchstart',\n 'touchmove',\n 'touchend',\n 'touchcancel',\n 'pointerdown',\n 'pointermove',\n 'pointerup',\n 'pointerleave',\n 'pointercancel',\n 'gesturestart',\n 'gesturechange',\n 'gestureend',\n 'focus',\n 'blur',\n 'change',\n 'reset',\n 'select',\n 'submit',\n 'focusin',\n 'focusout',\n 'load',\n 'unload',\n 'beforeunload',\n 'resize',\n 'move',\n 'DOMContentLoaded',\n 'readystatechange',\n 'error',\n 'abort',\n 'scroll'\n])\n\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n return (uid && `${uid}::${uidEvent++}`) || element.uidEvent || uidEvent++\n}\n\nfunction getElementEvents(element) {\n const uid = makeEventUid(element)\n\n element.uidEvent = uid\n eventRegistry[uid] = eventRegistry[uid] || {}\n\n return eventRegistry[uid]\n}\n\nfunction bootstrapHandler(element, fn) {\n return function handler(event) {\n hydrateObj(event, { delegateTarget: element })\n\n if (handler.oneOff) {\n EventHandler.off(element, event.type, fn)\n }\n\n return fn.apply(element, [event])\n }\n}\n\nfunction bootstrapDelegationHandler(element, selector, fn) {\n return function handler(event) {\n const domElements = element.querySelectorAll(selector)\n\n for (let { target } = event; target && target !== this; target = target.parentNode) {\n for (const domElement of domElements) {\n if (domElement !== target) {\n continue\n }\n\n hydrateObj(event, { delegateTarget: target })\n\n if (handler.oneOff) {\n EventHandler.off(element, event.type, selector, fn)\n }\n\n return fn.apply(target, [event])\n }\n }\n }\n}\n\nfunction findHandler(events, callable, delegationSelector = null) {\n return Object.values(events)\n .find(event => event.callable === callable && event.delegationSelector === delegationSelector)\n}\n\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n const isDelegated = typeof handler === 'string'\n // TODO: tooltip passes `false` instead of selector, so we need to check\n const callable = isDelegated ? delegationFunction : (handler || delegationFunction)\n let typeEvent = getTypeEvent(originalTypeEvent)\n\n if (!nativeEvents.has(typeEvent)) {\n typeEvent = originalTypeEvent\n }\n\n return [isDelegated, callable, typeEvent]\n}\n\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return\n }\n\n let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n\n // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n if (originalTypeEvent in customEvents) {\n const wrapFunction = fn => {\n return function (event) {\n if (!event.relatedTarget || (event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget))) {\n return fn.call(this, event)\n }\n }\n }\n\n callable = wrapFunction(callable)\n }\n\n const events = getElementEvents(element)\n const handlers = events[typeEvent] || (events[typeEvent] = {})\n const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null)\n\n if (previousFunction) {\n previousFunction.oneOff = previousFunction.oneOff && oneOff\n\n return\n }\n\n const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''))\n const fn = isDelegated ?\n bootstrapDelegationHandler(element, handler, callable) :\n bootstrapHandler(element, callable)\n\n fn.delegationSelector = isDelegated ? handler : null\n fn.callable = callable\n fn.oneOff = oneOff\n fn.uidEvent = uid\n handlers[uid] = fn\n\n element.addEventListener(typeEvent, fn, isDelegated)\n}\n\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n const fn = findHandler(events[typeEvent], handler, delegationSelector)\n\n if (!fn) {\n return\n }\n\n element.removeEventListener(typeEvent, fn, Boolean(delegationSelector))\n delete events[typeEvent][fn.uidEvent]\n}\n\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n const storeElementEvent = events[typeEvent] || {}\n\n for (const [handlerKey, event] of Object.entries(storeElementEvent)) {\n if (handlerKey.includes(namespace)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n }\n }\n}\n\nfunction getTypeEvent(event) {\n // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n event = event.replace(stripNameRegex, '')\n return customEvents[event] || event\n}\n\nconst EventHandler = {\n on(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, false)\n },\n\n one(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, true)\n },\n\n off(element, originalTypeEvent, handler, delegationFunction) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return\n }\n\n const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n const inNamespace = typeEvent !== originalTypeEvent\n const events = getElementEvents(element)\n const storeElementEvent = events[typeEvent] || {}\n const isNamespace = originalTypeEvent.startsWith('.')\n\n if (typeof callable !== 'undefined') {\n // Simplest case: handler is passed, remove that listener ONLY.\n if (!Object.keys(storeElementEvent).length) {\n return\n }\n\n removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null)\n return\n }\n\n if (isNamespace) {\n for (const elementEvent of Object.keys(events)) {\n removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1))\n }\n }\n\n for (const [keyHandlers, event] of Object.entries(storeElementEvent)) {\n const handlerKey = keyHandlers.replace(stripUidRegex, '')\n\n if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n }\n }\n },\n\n trigger(element, event, args) {\n if (typeof event !== 'string' || !element) {\n return null\n }\n\n const $ = getjQuery()\n const typeEvent = getTypeEvent(event)\n const inNamespace = event !== typeEvent\n\n let jQueryEvent = null\n let bubbles = true\n let nativeDispatch = true\n let defaultPrevented = false\n\n if (inNamespace && $) {\n jQueryEvent = $.Event(event, args)\n\n $(element).trigger(jQueryEvent)\n bubbles = !jQueryEvent.isPropagationStopped()\n nativeDispatch = !jQueryEvent.isImmediatePropagationStopped()\n defaultPrevented = jQueryEvent.isDefaultPrevented()\n }\n\n const evt = hydrateObj(new Event(event, { bubbles, cancelable: true }), args)\n\n if (defaultPrevented) {\n evt.preventDefault()\n }\n\n if (nativeDispatch) {\n element.dispatchEvent(evt)\n }\n\n if (evt.defaultPrevented && jQueryEvent) {\n jQueryEvent.preventDefault()\n }\n\n return evt\n }\n}\n\nfunction hydrateObj(obj, meta = {}) {\n for (const [key, value] of Object.entries(meta)) {\n try {\n obj[key] = value\n } catch {\n Object.defineProperty(obj, key, {\n configurable: true,\n get() {\n return value\n }\n })\n }\n }\n\n return obj\n}\n\nexport default EventHandler\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nfunction normalizeData(value) {\n if (value === 'true') {\n return true\n }\n\n if (value === 'false') {\n return false\n }\n\n if (value === Number(value).toString()) {\n return Number(value)\n }\n\n if (value === '' || value === 'null') {\n return null\n }\n\n if (typeof value !== 'string') {\n return value\n }\n\n try {\n return JSON.parse(decodeURIComponent(value))\n } catch {\n return value\n }\n}\n\nfunction normalizeDataKey(key) {\n return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`)\n}\n\nconst Manipulator = {\n setDataAttribute(element, key, value) {\n element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value)\n },\n\n removeDataAttribute(element, key) {\n element.removeAttribute(`data-bs-${normalizeDataKey(key)}`)\n },\n\n getDataAttributes(element) {\n if (!element) {\n return {}\n }\n\n const attributes = {}\n const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'))\n\n for (const key of bsKeys) {\n let pureKey = key.replace(/^bs/, '')\n pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length)\n attributes[pureKey] = normalizeData(element.dataset[key])\n }\n\n return attributes\n },\n\n getDataAttribute(element, key) {\n return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`))\n }\n}\n\nexport default Manipulator\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport { isElement, toType } from './index.js'\n\n/**\n * Class definition\n */\n\nclass Config {\n // Getters\n static get Default() {\n return {}\n }\n\n static get DefaultType() {\n return {}\n }\n\n static get NAME() {\n throw new Error('You have to implement the static method \"NAME\", for each component!')\n }\n\n _getConfig(config) {\n config = this._mergeConfigObj(config)\n config = this._configAfterMerge(config)\n this._typeCheckConfig(config)\n return config\n }\n\n _configAfterMerge(config) {\n return config\n }\n\n _mergeConfigObj(config, element) {\n const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {} // try to parse\n\n return {\n ...this.constructor.Default,\n ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n ...(typeof config === 'object' ? config : {})\n }\n }\n\n _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n for (const [property, expectedTypes] of Object.entries(configTypes)) {\n const value = config[property]\n const valueType = isElement(value) ? 'element' : toType(value)\n\n if (!new RegExp(expectedTypes).test(valueType)) {\n throw new TypeError(\n `${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`\n )\n }\n }\n }\n}\n\nexport default Config\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Data from './dom/data.js'\nimport EventHandler from './dom/event-handler.js'\nimport Config from './util/config.js'\nimport { executeAfterTransition, getElement } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst VERSION = '5.3.1'\n\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n constructor(element, config) {\n super()\n\n element = getElement(element)\n if (!element) {\n return\n }\n\n this._element = element\n this._config = this._getConfig(config)\n\n Data.set(this._element, this.constructor.DATA_KEY, this)\n }\n\n // Public\n dispose() {\n Data.remove(this._element, this.constructor.DATA_KEY)\n EventHandler.off(this._element, this.constructor.EVENT_KEY)\n\n for (const propertyName of Object.getOwnPropertyNames(this)) {\n this[propertyName] = null\n }\n }\n\n _queueCallback(callback, element, isAnimated = true) {\n executeAfterTransition(callback, element, isAnimated)\n }\n\n _getConfig(config) {\n config = this._mergeConfigObj(config, this._element)\n config = this._configAfterMerge(config)\n this._typeCheckConfig(config)\n return config\n }\n\n // Static\n static getInstance(element) {\n return Data.get(getElement(element), this.DATA_KEY)\n }\n\n static getOrCreateInstance(element, config = {}) {\n return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null)\n }\n\n static get VERSION() {\n return VERSION\n }\n\n static get DATA_KEY() {\n return `bs.${this.NAME}`\n }\n\n static get EVENT_KEY() {\n return `.${this.DATA_KEY}`\n }\n\n static eventName(name) {\n return `${name}${this.EVENT_KEY}`\n }\n}\n\nexport default BaseComponent\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { isDisabled, isVisible, parseSelector } from '../util/index.js'\n\nconst getSelector = element => {\n let selector = element.getAttribute('data-bs-target')\n\n if (!selector || selector === '#') {\n let hrefAttribute = element.getAttribute('href')\n\n // The only valid content that could double as a selector are IDs or classes,\n // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n // `document.querySelector` will rightfully complain it is invalid.\n // See https://github.com/twbs/bootstrap/issues/32273\n if (!hrefAttribute || (!hrefAttribute.includes('#') && !hrefAttribute.startsWith('.'))) {\n return null\n }\n\n // Just in case some CMS puts out a full URL with the anchor appended\n if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n hrefAttribute = `#${hrefAttribute.split('#')[1]}`\n }\n\n selector = hrefAttribute && hrefAttribute !== '#' ? hrefAttribute.trim() : null\n }\n\n return parseSelector(selector)\n}\n\nconst SelectorEngine = {\n find(selector, element = document.documentElement) {\n return [].concat(...Element.prototype.querySelectorAll.call(element, selector))\n },\n\n findOne(selector, element = document.documentElement) {\n return Element.prototype.querySelector.call(element, selector)\n },\n\n children(element, selector) {\n return [].concat(...element.children).filter(child => child.matches(selector))\n },\n\n parents(element, selector) {\n const parents = []\n let ancestor = element.parentNode.closest(selector)\n\n while (ancestor) {\n parents.push(ancestor)\n ancestor = ancestor.parentNode.closest(selector)\n }\n\n return parents\n },\n\n prev(element, selector) {\n let previous = element.previousElementSibling\n\n while (previous) {\n if (previous.matches(selector)) {\n return [previous]\n }\n\n previous = previous.previousElementSibling\n }\n\n return []\n },\n // TODO: this is now unused; remove later along with prev()\n next(element, selector) {\n let next = element.nextElementSibling\n\n while (next) {\n if (next.matches(selector)) {\n return [next]\n }\n\n next = next.nextElementSibling\n }\n\n return []\n },\n\n focusableChildren(element) {\n const focusables = [\n 'a',\n 'button',\n 'input',\n 'textarea',\n 'select',\n 'details',\n '[tabindex]',\n '[contenteditable=\"true\"]'\n ].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',')\n\n return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el))\n },\n\n getSelectorFromElement(element) {\n const selector = getSelector(element)\n\n if (selector) {\n return SelectorEngine.findOne(selector) ? selector : null\n }\n\n return null\n },\n\n getElementFromSelector(element) {\n const selector = getSelector(element)\n\n return selector ? SelectorEngine.findOne(selector) : null\n },\n\n getMultipleElementsFromSelector(element) {\n const selector = getSelector(element)\n\n return selector ? SelectorEngine.find(selector) : []\n }\n}\n\nexport default SelectorEngine\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isDisabled } from './index.js'\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n const clickEvent = `click.dismiss${component.EVENT_KEY}`\n const name = component.NAME\n\n EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault()\n }\n\n if (isDisabled(this)) {\n return\n }\n\n const target = SelectorEngine.getElementFromSelector(this) || this.closest(`.${name}`)\n const instance = component.getOrCreateInstance(target)\n\n // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n instance[method]()\n })\n}\n\nexport {\n enableDismissTrigger\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'alert'\nconst DATA_KEY = 'bs.alert'\nconst EVENT_KEY = `.${DATA_KEY}`\n\nconst EVENT_CLOSE = `close${EVENT_KEY}`\nconst EVENT_CLOSED = `closed${EVENT_KEY}`\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\n\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME\n }\n\n // Public\n close() {\n const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE)\n\n if (closeEvent.defaultPrevented) {\n return\n }\n\n this._element.classList.remove(CLASS_NAME_SHOW)\n\n const isAnimated = this._element.classList.contains(CLASS_NAME_FADE)\n this._queueCallback(() => this._destroyElement(), this._element, isAnimated)\n }\n\n // Private\n _destroyElement() {\n this._element.remove()\n EventHandler.trigger(this._element, EVENT_CLOSED)\n this.dispose()\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Alert.getOrCreateInstance(this)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config](this)\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Alert, 'close')\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert)\n\nexport default Alert\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'button'\nconst DATA_KEY = 'bs.button'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst CLASS_NAME_ACTIVE = 'active'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"button\"]'\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle() {\n // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE))\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Button.getOrCreateInstance(this)\n\n if (config === 'toggle') {\n data[config]()\n }\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, event => {\n event.preventDefault()\n\n const button = event.target.closest(SELECTOR_DATA_TOGGLE)\n const data = Button.getOrCreateInstance(button)\n\n data.toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button)\n\nexport default Button\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'swipe'\nconst EVENT_KEY = '.bs.swipe'\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY}`\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY}`\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY}`\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY}`\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY}`\nconst POINTER_TYPE_TOUCH = 'touch'\nconst POINTER_TYPE_PEN = 'pen'\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event'\nconst SWIPE_THRESHOLD = 40\n\nconst Default = {\n endCallback: null,\n leftCallback: null,\n rightCallback: null\n}\n\nconst DefaultType = {\n endCallback: '(function|null)',\n leftCallback: '(function|null)',\n rightCallback: '(function|null)'\n}\n\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n constructor(element, config) {\n super()\n this._element = element\n\n if (!element || !Swipe.isSupported()) {\n return\n }\n\n this._config = this._getConfig(config)\n this._deltaX = 0\n this._supportPointerEvents = Boolean(window.PointerEvent)\n this._initEvents()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n dispose() {\n EventHandler.off(this._element, EVENT_KEY)\n }\n\n // Private\n _start(event) {\n if (!this._supportPointerEvents) {\n this._deltaX = event.touches[0].clientX\n\n return\n }\n\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX\n }\n }\n\n _end(event) {\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX - this._deltaX\n }\n\n this._handleSwipe()\n execute(this._config.endCallback)\n }\n\n _move(event) {\n this._deltaX = event.touches && event.touches.length > 1 ?\n 0 :\n event.touches[0].clientX - this._deltaX\n }\n\n _handleSwipe() {\n const absDeltaX = Math.abs(this._deltaX)\n\n if (absDeltaX <= SWIPE_THRESHOLD) {\n return\n }\n\n const direction = absDeltaX / this._deltaX\n\n this._deltaX = 0\n\n if (!direction) {\n return\n }\n\n execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback)\n }\n\n _initEvents() {\n if (this._supportPointerEvents) {\n EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event))\n EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event))\n\n this._element.classList.add(CLASS_NAME_POINTER_EVENT)\n } else {\n EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event))\n EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event))\n EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event))\n }\n }\n\n _eventIsPointerPenTouch(event) {\n return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH)\n }\n\n // Static\n static isSupported() {\n return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0\n }\n}\n\nexport default Swipe\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n defineJQueryPlugin,\n getNextActiveElement,\n isRTL,\n isVisible,\n reflow,\n triggerTransitionEnd\n} from './util/index.js'\nimport Swipe from './util/swipe.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'carousel'\nconst DATA_KEY = 'bs.carousel'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ARROW_LEFT_KEY = 'ArrowLeft'\nconst ARROW_RIGHT_KEY = 'ArrowRight'\nconst TOUCHEVENT_COMPAT_WAIT = 500 // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next'\nconst ORDER_PREV = 'prev'\nconst DIRECTION_LEFT = 'left'\nconst DIRECTION_RIGHT = 'right'\n\nconst EVENT_SLIDE = `slide${EVENT_KEY}`\nconst EVENT_SLID = `slid${EVENT_KEY}`\nconst EVENT_KEYDOWN = `keydown${EVENT_KEY}`\nconst EVENT_MOUSEENTER = `mouseenter${EVENT_KEY}`\nconst EVENT_MOUSELEAVE = `mouseleave${EVENT_KEY}`\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_CAROUSEL = 'carousel'\nconst CLASS_NAME_ACTIVE = 'active'\nconst CLASS_NAME_SLIDE = 'slide'\nconst CLASS_NAME_END = 'carousel-item-end'\nconst CLASS_NAME_START = 'carousel-item-start'\nconst CLASS_NAME_NEXT = 'carousel-item-next'\nconst CLASS_NAME_PREV = 'carousel-item-prev'\n\nconst SELECTOR_ACTIVE = '.active'\nconst SELECTOR_ITEM = '.carousel-item'\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM\nconst SELECTOR_ITEM_IMG = '.carousel-item img'\nconst SELECTOR_INDICATORS = '.carousel-indicators'\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]'\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]'\n\nconst KEY_TO_DIRECTION = {\n [ARROW_LEFT_KEY]: DIRECTION_RIGHT,\n [ARROW_RIGHT_KEY]: DIRECTION_LEFT\n}\n\nconst Default = {\n interval: 5000,\n keyboard: true,\n pause: 'hover',\n ride: false,\n touch: true,\n wrap: true\n}\n\nconst DefaultType = {\n interval: '(number|boolean)', // TODO:v6 remove boolean support\n keyboard: 'boolean',\n pause: '(string|boolean)',\n ride: '(boolean|string)',\n touch: 'boolean',\n wrap: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._interval = null\n this._activeElement = null\n this._isSliding = false\n this.touchTimeout = null\n this._swipeHelper = null\n\n this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element)\n this._addEventListeners()\n\n if (this._config.ride === CLASS_NAME_CAROUSEL) {\n this.cycle()\n }\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n next() {\n this._slide(ORDER_NEXT)\n }\n\n nextWhenVisible() {\n // FIXME TODO use `document.visibilityState`\n // Don't call next when the page isn't visible\n // or the carousel or its parent isn't visible\n if (!document.hidden && isVisible(this._element)) {\n this.next()\n }\n }\n\n prev() {\n this._slide(ORDER_PREV)\n }\n\n pause() {\n if (this._isSliding) {\n triggerTransitionEnd(this._element)\n }\n\n this._clearInterval()\n }\n\n cycle() {\n this._clearInterval()\n this._updateInterval()\n\n this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval)\n }\n\n _maybeEnableCycle() {\n if (!this._config.ride) {\n return\n }\n\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.cycle())\n return\n }\n\n this.cycle()\n }\n\n to(index) {\n const items = this._getItems()\n if (index > items.length - 1 || index < 0) {\n return\n }\n\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.to(index))\n return\n }\n\n const activeIndex = this._getItemIndex(this._getActive())\n if (activeIndex === index) {\n return\n }\n\n const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV\n\n this._slide(order, items[index])\n }\n\n dispose() {\n if (this._swipeHelper) {\n this._swipeHelper.dispose()\n }\n\n super.dispose()\n }\n\n // Private\n _configAfterMerge(config) {\n config.defaultInterval = config.interval\n return config\n }\n\n _addEventListeners() {\n if (this._config.keyboard) {\n EventHandler.on(this._element, EVENT_KEYDOWN, event => this._keydown(event))\n }\n\n if (this._config.pause === 'hover') {\n EventHandler.on(this._element, EVENT_MOUSEENTER, () => this.pause())\n EventHandler.on(this._element, EVENT_MOUSELEAVE, () => this._maybeEnableCycle())\n }\n\n if (this._config.touch && Swipe.isSupported()) {\n this._addTouchEventListeners()\n }\n }\n\n _addTouchEventListeners() {\n for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault())\n }\n\n const endCallBack = () => {\n if (this._config.pause !== 'hover') {\n return\n }\n\n // If it's a touch-enabled device, mouseenter/leave are fired as\n // part of the mouse compatibility events on first tap - the carousel\n // would stop cycling until user tapped out of it;\n // here, we listen for touchend, explicitly pause the carousel\n // (as if it's the second time we tap on it, mouseenter compat event\n // is NOT fired) and after a timeout (to allow for mouse compatibility\n // events to fire) we explicitly restart cycling\n\n this.pause()\n if (this.touchTimeout) {\n clearTimeout(this.touchTimeout)\n }\n\n this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval)\n }\n\n const swipeConfig = {\n leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n endCallback: endCallBack\n }\n\n this._swipeHelper = new Swipe(this._element, swipeConfig)\n }\n\n _keydown(event) {\n if (/input|textarea/i.test(event.target.tagName)) {\n return\n }\n\n const direction = KEY_TO_DIRECTION[event.key]\n if (direction) {\n event.preventDefault()\n this._slide(this._directionToOrder(direction))\n }\n }\n\n _getItemIndex(element) {\n return this._getItems().indexOf(element)\n }\n\n _setActiveIndicatorElement(index) {\n if (!this._indicatorsElement) {\n return\n }\n\n const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement)\n\n activeIndicator.classList.remove(CLASS_NAME_ACTIVE)\n activeIndicator.removeAttribute('aria-current')\n\n const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement)\n\n if (newActiveIndicator) {\n newActiveIndicator.classList.add(CLASS_NAME_ACTIVE)\n newActiveIndicator.setAttribute('aria-current', 'true')\n }\n }\n\n _updateInterval() {\n const element = this._activeElement || this._getActive()\n\n if (!element) {\n return\n }\n\n const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10)\n\n this._config.interval = elementInterval || this._config.defaultInterval\n }\n\n _slide(order, element = null) {\n if (this._isSliding) {\n return\n }\n\n const activeElement = this._getActive()\n const isNext = order === ORDER_NEXT\n const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap)\n\n if (nextElement === activeElement) {\n return\n }\n\n const nextElementIndex = this._getItemIndex(nextElement)\n\n const triggerEvent = eventName => {\n return EventHandler.trigger(this._element, eventName, {\n relatedTarget: nextElement,\n direction: this._orderToDirection(order),\n from: this._getItemIndex(activeElement),\n to: nextElementIndex\n })\n }\n\n const slideEvent = triggerEvent(EVENT_SLIDE)\n\n if (slideEvent.defaultPrevented) {\n return\n }\n\n if (!activeElement || !nextElement) {\n // Some weirdness is happening, so we bail\n // TODO: change tests that use empty divs to avoid this check\n return\n }\n\n const isCycling = Boolean(this._interval)\n this.pause()\n\n this._isSliding = true\n\n this._setActiveIndicatorElement(nextElementIndex)\n this._activeElement = nextElement\n\n const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END\n const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV\n\n nextElement.classList.add(orderClassName)\n\n reflow(nextElement)\n\n activeElement.classList.add(directionalClassName)\n nextElement.classList.add(directionalClassName)\n\n const completeCallBack = () => {\n nextElement.classList.remove(directionalClassName, orderClassName)\n nextElement.classList.add(CLASS_NAME_ACTIVE)\n\n activeElement.classList.remove(CLASS_NAME_ACTIVE, orderClassName, directionalClassName)\n\n this._isSliding = false\n\n triggerEvent(EVENT_SLID)\n }\n\n this._queueCallback(completeCallBack, activeElement, this._isAnimated())\n\n if (isCycling) {\n this.cycle()\n }\n }\n\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_SLIDE)\n }\n\n _getActive() {\n return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element)\n }\n\n _getItems() {\n return SelectorEngine.find(SELECTOR_ITEM, this._element)\n }\n\n _clearInterval() {\n if (this._interval) {\n clearInterval(this._interval)\n this._interval = null\n }\n }\n\n _directionToOrder(direction) {\n if (isRTL()) {\n return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT\n }\n\n return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV\n }\n\n _orderToDirection(order) {\n if (isRTL()) {\n return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT\n }\n\n return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Carousel.getOrCreateInstance(this, config)\n\n if (typeof config === 'number') {\n data.to(config)\n return\n }\n\n if (typeof config === 'string') {\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n }\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_SLIDE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this)\n\n if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n return\n }\n\n event.preventDefault()\n\n const carousel = Carousel.getOrCreateInstance(target)\n const slideIndex = this.getAttribute('data-bs-slide-to')\n\n if (slideIndex) {\n carousel.to(slideIndex)\n carousel._maybeEnableCycle()\n return\n }\n\n if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n carousel.next()\n carousel._maybeEnableCycle()\n return\n }\n\n carousel.prev()\n carousel._maybeEnableCycle()\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE)\n\n for (const carousel of carousels) {\n Carousel.getOrCreateInstance(carousel)\n }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel)\n\nexport default Carousel\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n defineJQueryPlugin,\n getElement,\n reflow\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'collapse'\nconst DATA_KEY = 'bs.collapse'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_COLLAPSE = 'collapse'\nconst CLASS_NAME_COLLAPSING = 'collapsing'\nconst CLASS_NAME_COLLAPSED = 'collapsed'\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal'\n\nconst WIDTH = 'width'\nconst HEIGHT = 'height'\n\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"collapse\"]'\n\nconst Default = {\n parent: null,\n toggle: true\n}\n\nconst DefaultType = {\n parent: '(null|element)',\n toggle: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._isTransitioning = false\n this._triggerArray = []\n\n const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE)\n\n for (const elem of toggleList) {\n const selector = SelectorEngine.getSelectorFromElement(elem)\n const filterElement = SelectorEngine.find(selector)\n .filter(foundElement => foundElement === this._element)\n\n if (selector !== null && filterElement.length) {\n this._triggerArray.push(elem)\n }\n }\n\n this._initializeChildren()\n\n if (!this._config.parent) {\n this._addAriaAndCollapsedClass(this._triggerArray, this._isShown())\n }\n\n if (this._config.toggle) {\n this.toggle()\n }\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle() {\n if (this._isShown()) {\n this.hide()\n } else {\n this.show()\n }\n }\n\n show() {\n if (this._isTransitioning || this._isShown()) {\n return\n }\n\n let activeChildren = []\n\n // find active children\n if (this._config.parent) {\n activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES)\n .filter(element => element !== this._element)\n .map(element => Collapse.getOrCreateInstance(element, { toggle: false }))\n }\n\n if (activeChildren.length && activeChildren[0]._isTransitioning) {\n return\n }\n\n const startEvent = EventHandler.trigger(this._element, EVENT_SHOW)\n if (startEvent.defaultPrevented) {\n return\n }\n\n for (const activeInstance of activeChildren) {\n activeInstance.hide()\n }\n\n const dimension = this._getDimension()\n\n this._element.classList.remove(CLASS_NAME_COLLAPSE)\n this._element.classList.add(CLASS_NAME_COLLAPSING)\n\n this._element.style[dimension] = 0\n\n this._addAriaAndCollapsedClass(this._triggerArray, true)\n this._isTransitioning = true\n\n const complete = () => {\n this._isTransitioning = false\n\n this._element.classList.remove(CLASS_NAME_COLLAPSING)\n this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n this._element.style[dimension] = ''\n\n EventHandler.trigger(this._element, EVENT_SHOWN)\n }\n\n const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1)\n const scrollSize = `scroll${capitalizedDimension}`\n\n this._queueCallback(complete, this._element, true)\n this._element.style[dimension] = `${this._element[scrollSize]}px`\n }\n\n hide() {\n if (this._isTransitioning || !this._isShown()) {\n return\n }\n\n const startEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n if (startEvent.defaultPrevented) {\n return\n }\n\n const dimension = this._getDimension()\n\n this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`\n\n reflow(this._element)\n\n this._element.classList.add(CLASS_NAME_COLLAPSING)\n this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n for (const trigger of this._triggerArray) {\n const element = SelectorEngine.getElementFromSelector(trigger)\n\n if (element && !this._isShown(element)) {\n this._addAriaAndCollapsedClass([trigger], false)\n }\n }\n\n this._isTransitioning = true\n\n const complete = () => {\n this._isTransitioning = false\n this._element.classList.remove(CLASS_NAME_COLLAPSING)\n this._element.classList.add(CLASS_NAME_COLLAPSE)\n EventHandler.trigger(this._element, EVENT_HIDDEN)\n }\n\n this._element.style[dimension] = ''\n\n this._queueCallback(complete, this._element, true)\n }\n\n _isShown(element = this._element) {\n return element.classList.contains(CLASS_NAME_SHOW)\n }\n\n // Private\n _configAfterMerge(config) {\n config.toggle = Boolean(config.toggle) // Coerce string values\n config.parent = getElement(config.parent)\n return config\n }\n\n _getDimension() {\n return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT\n }\n\n _initializeChildren() {\n if (!this._config.parent) {\n return\n }\n\n const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE)\n\n for (const element of children) {\n const selected = SelectorEngine.getElementFromSelector(element)\n\n if (selected) {\n this._addAriaAndCollapsedClass([element], this._isShown(selected))\n }\n }\n }\n\n _getFirstLevelChildren(selector) {\n const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent)\n // remove children if greater depth\n return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element))\n }\n\n _addAriaAndCollapsedClass(triggerArray, isOpen) {\n if (!triggerArray.length) {\n return\n }\n\n for (const element of triggerArray) {\n element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen)\n element.setAttribute('aria-expanded', isOpen)\n }\n }\n\n // Static\n static jQueryInterface(config) {\n const _config = {}\n if (typeof config === 'string' && /show|hide/.test(config)) {\n _config.toggle = false\n }\n\n return this.each(function () {\n const data = Collapse.getOrCreateInstance(this, _config)\n\n if (typeof config === 'string') {\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n }\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n // preventDefault only for elements (which change the URL) not inside the collapsible element\n if (event.target.tagName === 'A' || (event.delegateTarget && event.delegateTarget.tagName === 'A')) {\n event.preventDefault()\n }\n\n for (const element of SelectorEngine.getMultipleElementsFromSelector(this)) {\n Collapse.getOrCreateInstance(element, { toggle: false }).toggle()\n }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse)\n\nexport default Collapse\n","export var top = 'top';\nexport var bottom = 'bottom';\nexport var right = 'right';\nexport var left = 'left';\nexport var auto = 'auto';\nexport var basePlacements = [top, bottom, right, left];\nexport var start = 'start';\nexport var end = 'end';\nexport var clippingParents = 'clippingParents';\nexport var viewport = 'viewport';\nexport var popper = 'popper';\nexport var reference = 'reference';\nexport var variationPlacements = /*#__PURE__*/basePlacements.reduce(function (acc, placement) {\n return acc.concat([placement + \"-\" + start, placement + \"-\" + end]);\n}, []);\nexport var placements = /*#__PURE__*/[].concat(basePlacements, [auto]).reduce(function (acc, placement) {\n return acc.concat([placement, placement + \"-\" + start, placement + \"-\" + end]);\n}, []); // modifiers that need to read the DOM\n\nexport var beforeRead = 'beforeRead';\nexport var read = 'read';\nexport var afterRead = 'afterRead'; // pure-logic modifiers\n\nexport var beforeMain = 'beforeMain';\nexport var main = 'main';\nexport var afterMain = 'afterMain'; // modifier with the purpose to write to the DOM (or write into a framework state)\n\nexport var beforeWrite = 'beforeWrite';\nexport var write = 'write';\nexport var afterWrite = 'afterWrite';\nexport var modifierPhases = [beforeRead, read, afterRead, beforeMain, main, afterMain, beforeWrite, write, afterWrite];","export default function getNodeName(element) {\n return element ? (element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n if (node == null) {\n return window;\n }\n\n if (node.toString() !== '[object Window]') {\n var ownerDocument = node.ownerDocument;\n return ownerDocument ? ownerDocument.defaultView || window : window;\n }\n\n return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n var OwnElement = getWindow(node).Element;\n return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n var OwnElement = getWindow(node).HTMLElement;\n return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n // IE 11 has no ShadowRoot\n if (typeof ShadowRoot === 'undefined') {\n return false;\n }\n\n var OwnElement = getWindow(node).ShadowRoot;\n return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n var state = _ref.state;\n Object.keys(state.elements).forEach(function (name) {\n var style = state.styles[name] || {};\n var attributes = state.attributes[name] || {};\n var element = state.elements[name]; // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n } // Flow doesn't support to extend this property, but it's the most\n // effective way to apply styles to an HTMLElement\n // $FlowFixMe[cannot-write]\n\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (name) {\n var value = attributes[name];\n\n if (value === false) {\n element.removeAttribute(name);\n } else {\n element.setAttribute(name, value === true ? '' : value);\n }\n });\n });\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state;\n var initialStyles = {\n popper: {\n position: state.options.strategy,\n left: '0',\n top: '0',\n margin: '0'\n },\n arrow: {\n position: 'absolute'\n },\n reference: {}\n };\n Object.assign(state.elements.popper.style, initialStyles.popper);\n state.styles = initialStyles;\n\n if (state.elements.arrow) {\n Object.assign(state.elements.arrow.style, initialStyles.arrow);\n }\n\n return function () {\n Object.keys(state.elements).forEach(function (name) {\n var element = state.elements[name];\n var attributes = state.attributes[name] || {};\n var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n var style = styleProperties.reduce(function (style, property) {\n style[property] = '';\n return style;\n }, {}); // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n }\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (attribute) {\n element.removeAttribute(attribute);\n });\n });\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'applyStyles',\n enabled: true,\n phase: 'write',\n fn: applyStyles,\n effect: effect,\n requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n var uaData = navigator.userAgentData;\n\n if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n return uaData.brands.map(function (item) {\n return item.brand + \"/\" + item.version;\n }).join(' ');\n }\n\n return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n if (includeScale === void 0) {\n includeScale = false;\n }\n\n if (isFixedStrategy === void 0) {\n isFixedStrategy = false;\n }\n\n var clientRect = element.getBoundingClientRect();\n var scaleX = 1;\n var scaleY = 1;\n\n if (includeScale && isHTMLElement(element)) {\n scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n }\n\n var _ref = isElement(element) ? getWindow(element) : window,\n visualViewport = _ref.visualViewport;\n\n var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n var width = clientRect.width / scaleX;\n var height = clientRect.height / scaleY;\n return {\n width: width,\n height: height,\n top: y,\n right: x + width,\n bottom: y + height,\n left: x,\n x: x,\n y: y\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n var width = element.offsetWidth;\n var height = element.offsetHeight;\n\n if (Math.abs(clientRect.width - width) <= 1) {\n width = clientRect.width;\n }\n\n if (Math.abs(clientRect.height - height) <= 1) {\n height = clientRect.height;\n }\n\n return {\n x: element.offsetLeft,\n y: element.offsetTop,\n width: width,\n height: height\n };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n if (parent.contains(child)) {\n return true;\n } // then fallback to custom implementation with Shadow DOM support\n else if (rootNode && isShadowRoot(rootNode)) {\n var next = child;\n\n do {\n if (next && parent.isSameNode(next)) {\n return true;\n } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n next = next.parentNode || next.host;\n } while (next);\n } // Give up, the result is false\n\n\n return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n if (getNodeName(element) === 'html') {\n return element;\n }\n\n return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n // $FlowFixMe[incompatible-return]\n // $FlowFixMe[prop-missing]\n element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n element.parentNode || ( // DOM Element detected\n isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n getDocumentElement(element) // fallback\n\n );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n getComputedStyle(element).position === 'fixed') {\n return null;\n }\n\n return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n var isFirefox = /firefox/i.test(getUAString());\n var isIE = /Trident/i.test(getUAString());\n\n if (isIE && isHTMLElement(element)) {\n // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n var elementCss = getComputedStyle(element);\n\n if (elementCss.position === 'fixed') {\n return null;\n }\n }\n\n var currentNode = getParentNode(element);\n\n if (isShadowRoot(currentNode)) {\n currentNode = currentNode.host;\n }\n\n while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n // create a containing block.\n // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n return currentNode;\n } else {\n currentNode = currentNode.parentNode;\n }\n }\n\n return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n var window = getWindow(element);\n var offsetParent = getTrueOffsetParent(element);\n\n while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n offsetParent = getTrueOffsetParent(offsetParent);\n }\n\n if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n return window;\n }\n\n return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n var v = within(min, value, max);\n return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n return {\n top: 0,\n right: 0,\n bottom: 0,\n left: 0\n };\n}","export default function expandToHashMap(value, keys) {\n return keys.reduce(function (hashMap, key) {\n hashMap[key] = value;\n return hashMap;\n }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n placement: state.placement\n })) : padding;\n return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n var _state$modifiersData$;\n\n var state = _ref.state,\n name = _ref.name,\n options = _ref.options;\n var arrowElement = state.elements.arrow;\n var popperOffsets = state.modifiersData.popperOffsets;\n var basePlacement = getBasePlacement(state.placement);\n var axis = getMainAxisFromPlacement(basePlacement);\n var isVertical = [left, right].indexOf(basePlacement) >= 0;\n var len = isVertical ? 'height' : 'width';\n\n if (!arrowElement || !popperOffsets) {\n return;\n }\n\n var paddingObject = toPaddingObject(options.padding, state);\n var arrowRect = getLayoutRect(arrowElement);\n var minProp = axis === 'y' ? top : left;\n var maxProp = axis === 'y' ? bottom : right;\n var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n var arrowOffsetParent = getOffsetParent(arrowElement);\n var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n // outside of the popper bounds\n\n var min = paddingObject[minProp];\n var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n var axisProp = axis;\n state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state,\n options = _ref2.options;\n var _options$element = options.element,\n arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n if (arrowElement == null) {\n return;\n } // CSS selector\n\n\n if (typeof arrowElement === 'string') {\n arrowElement = state.elements.popper.querySelector(arrowElement);\n\n if (!arrowElement) {\n return;\n }\n }\n\n if (!contains(state.elements.popper, arrowElement)) {\n return;\n }\n\n state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'arrow',\n enabled: true,\n phase: 'main',\n fn: arrow,\n effect: effect,\n requires: ['popperOffsets'],\n requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n top: 'auto',\n right: 'auto',\n bottom: 'auto',\n left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n var x = _ref.x,\n y = _ref.y;\n var dpr = win.devicePixelRatio || 1;\n return {\n x: round(x * dpr) / dpr || 0,\n y: round(y * dpr) / dpr || 0\n };\n}\n\nexport function mapToStyles(_ref2) {\n var _Object$assign2;\n\n var popper = _ref2.popper,\n popperRect = _ref2.popperRect,\n placement = _ref2.placement,\n variation = _ref2.variation,\n offsets = _ref2.offsets,\n position = _ref2.position,\n gpuAcceleration = _ref2.gpuAcceleration,\n adaptive = _ref2.adaptive,\n roundOffsets = _ref2.roundOffsets,\n isFixed = _ref2.isFixed;\n var _offsets$x = offsets.x,\n x = _offsets$x === void 0 ? 0 : _offsets$x,\n _offsets$y = offsets.y,\n y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n x: x,\n y: y\n }) : {\n x: x,\n y: y\n };\n\n x = _ref3.x;\n y = _ref3.y;\n var hasX = offsets.hasOwnProperty('x');\n var hasY = offsets.hasOwnProperty('y');\n var sideX = left;\n var sideY = top;\n var win = window;\n\n if (adaptive) {\n var offsetParent = getOffsetParent(popper);\n var heightProp = 'clientHeight';\n var widthProp = 'clientWidth';\n\n if (offsetParent === getWindow(popper)) {\n offsetParent = getDocumentElement(popper);\n\n if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n heightProp = 'scrollHeight';\n widthProp = 'scrollWidth';\n }\n } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n offsetParent = offsetParent;\n\n if (placement === top || (placement === left || placement === right) && variation === end) {\n sideY = bottom;\n var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n offsetParent[heightProp];\n y -= offsetY - popperRect.height;\n y *= gpuAcceleration ? 1 : -1;\n }\n\n if (placement === left || (placement === top || placement === bottom) && variation === end) {\n sideX = right;\n var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n offsetParent[widthProp];\n x -= offsetX - popperRect.width;\n x *= gpuAcceleration ? 1 : -1;\n }\n }\n\n var commonStyles = Object.assign({\n position: position\n }, adaptive && unsetSides);\n\n var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n x: x,\n y: y\n }, getWindow(popper)) : {\n x: x,\n y: y\n };\n\n x = _ref4.x;\n y = _ref4.y;\n\n if (gpuAcceleration) {\n var _Object$assign;\n\n return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n }\n\n return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n var state = _ref5.state,\n options = _ref5.options;\n var _options$gpuAccelerat = options.gpuAcceleration,\n gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n _options$adaptive = options.adaptive,\n adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n _options$roundOffsets = options.roundOffsets,\n roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n var commonStyles = {\n placement: getBasePlacement(state.placement),\n variation: getVariation(state.placement),\n popper: state.elements.popper,\n popperRect: state.rects.popper,\n gpuAcceleration: gpuAcceleration,\n isFixed: state.options.strategy === 'fixed'\n };\n\n if (state.modifiersData.popperOffsets != null) {\n state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.popperOffsets,\n position: state.options.strategy,\n adaptive: adaptive,\n roundOffsets: roundOffsets\n })));\n }\n\n if (state.modifiersData.arrow != null) {\n state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.arrow,\n position: 'absolute',\n adaptive: false,\n roundOffsets: roundOffsets\n })));\n }\n\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-placement': state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'computeStyles',\n enabled: true,\n phase: 'beforeWrite',\n fn: computeStyles,\n data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n passive: true\n};\n\nfunction effect(_ref) {\n var state = _ref.state,\n instance = _ref.instance,\n options = _ref.options;\n var _options$scroll = options.scroll,\n scroll = _options$scroll === void 0 ? true : _options$scroll,\n _options$resize = options.resize,\n resize = _options$resize === void 0 ? true : _options$resize;\n var window = getWindow(state.elements.popper);\n var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.addEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.addEventListener('resize', instance.update, passive);\n }\n\n return function () {\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.removeEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.removeEventListener('resize', instance.update, passive);\n }\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'eventListeners',\n enabled: true,\n phase: 'write',\n fn: function fn() {},\n effect: effect,\n data: {}\n};","var hash = {\n left: 'right',\n right: 'left',\n bottom: 'top',\n top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n return placement.replace(/left|right|bottom|top/g, function (matched) {\n return hash[matched];\n });\n}","var hash = {\n start: 'end',\n end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n return placement.replace(/start|end/g, function (matched) {\n return hash[matched];\n });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n var win = getWindow(node);\n var scrollLeft = win.pageXOffset;\n var scrollTop = win.pageYOffset;\n return {\n scrollLeft: scrollLeft,\n scrollTop: scrollTop\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n // If has a CSS width greater than the viewport, then this will be\n // incorrect for RTL.\n // Popper 1 is broken in this case and never had a bug report so let's assume\n // it's not an issue. I don't think anyone ever specifies width on \n // anyway.\n // Browsers where the left scrollbar doesn't cause an issue report `0` for\n // this (e.g. Edge 2019, IE11, Safari)\n return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n // Firefox wants us to check `-x` and `-y` variations as well\n var _getComputedStyle = getComputedStyle(element),\n overflow = _getComputedStyle.overflow,\n overflowX = _getComputedStyle.overflowX,\n overflowY = _getComputedStyle.overflowY;\n\n return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return node.ownerDocument.body;\n }\n\n if (isHTMLElement(node) && isScrollParent(node)) {\n return node;\n }\n\n return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n var _element$ownerDocumen;\n\n if (list === void 0) {\n list = [];\n }\n\n var scrollParent = getScrollParent(element);\n var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n var win = getWindow(scrollParent);\n var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n var updatedList = list.concat(target);\n return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n return Object.assign({}, rect, {\n left: rect.x,\n top: rect.y,\n right: rect.x + rect.width,\n bottom: rect.y + rect.height\n });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n rect.top = rect.top + element.clientTop;\n rect.left = rect.left + element.clientLeft;\n rect.bottom = rect.top + element.clientHeight;\n rect.right = rect.left + element.clientWidth;\n rect.width = element.clientWidth;\n rect.height = element.clientHeight;\n rect.x = rect.left;\n rect.y = rect.top;\n return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n var clippingParents = listScrollParents(getParentNode(element));\n var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n if (!isElement(clipperElement)) {\n return [];\n } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n return clippingParents.filter(function (clippingParent) {\n return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n var firstClippingParent = clippingParents[0];\n var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n accRect.top = max(rect.top, accRect.top);\n accRect.right = min(rect.right, accRect.right);\n accRect.bottom = min(rect.bottom, accRect.bottom);\n accRect.left = max(rect.left, accRect.left);\n return accRect;\n }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n clippingRect.width = clippingRect.right - clippingRect.left;\n clippingRect.height = clippingRect.bottom - clippingRect.top;\n clippingRect.x = clippingRect.left;\n clippingRect.y = clippingRect.top;\n return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n var win = getWindow(element);\n var html = getDocumentElement(element);\n var visualViewport = win.visualViewport;\n var width = html.clientWidth;\n var height = html.clientHeight;\n var x = 0;\n var y = 0;\n\n if (visualViewport) {\n width = visualViewport.width;\n height = visualViewport.height;\n var layoutViewport = isLayoutViewport();\n\n if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n x = visualViewport.offsetLeft;\n y = visualViewport.offsetTop;\n }\n }\n\n return {\n width: width,\n height: height,\n x: x + getWindowScrollBarX(element),\n y: y\n };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `` and `` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n var _element$ownerDocumen;\n\n var html = getDocumentElement(element);\n var winScroll = getWindowScroll(element);\n var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n var y = -winScroll.scrollTop;\n\n if (getComputedStyle(body || html).direction === 'rtl') {\n x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n }\n\n return {\n width: width,\n height: height,\n x: x,\n y: y\n };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n var reference = _ref.reference,\n element = _ref.element,\n placement = _ref.placement;\n var basePlacement = placement ? getBasePlacement(placement) : null;\n var variation = placement ? getVariation(placement) : null;\n var commonX = reference.x + reference.width / 2 - element.width / 2;\n var commonY = reference.y + reference.height / 2 - element.height / 2;\n var offsets;\n\n switch (basePlacement) {\n case top:\n offsets = {\n x: commonX,\n y: reference.y - element.height\n };\n break;\n\n case bottom:\n offsets = {\n x: commonX,\n y: reference.y + reference.height\n };\n break;\n\n case right:\n offsets = {\n x: reference.x + reference.width,\n y: commonY\n };\n break;\n\n case left:\n offsets = {\n x: reference.x - element.width,\n y: commonY\n };\n break;\n\n default:\n offsets = {\n x: reference.x,\n y: reference.y\n };\n }\n\n var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n if (mainAxis != null) {\n var len = mainAxis === 'y' ? 'height' : 'width';\n\n switch (variation) {\n case start:\n offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n break;\n\n case end:\n offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n break;\n\n default:\n }\n }\n\n return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n _options$placement = _options.placement,\n placement = _options$placement === void 0 ? state.placement : _options$placement,\n _options$strategy = _options.strategy,\n strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n _options$boundary = _options.boundary,\n boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n _options$rootBoundary = _options.rootBoundary,\n rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n _options$elementConte = _options.elementContext,\n elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n _options$altBoundary = _options.altBoundary,\n altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n _options$padding = _options.padding,\n padding = _options$padding === void 0 ? 0 : _options$padding;\n var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n var altContext = elementContext === popper ? reference : popper;\n var popperRect = state.rects.popper;\n var element = state.elements[altBoundary ? altContext : elementContext];\n var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n var referenceClientRect = getBoundingClientRect(state.elements.reference);\n var popperOffsets = computeOffsets({\n reference: referenceClientRect,\n element: popperRect,\n strategy: 'absolute',\n placement: placement\n });\n var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n // 0 or negative = within the clipping rect\n\n var overflowOffsets = {\n top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n };\n var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n if (elementContext === popper && offsetData) {\n var offset = offsetData[placement];\n Object.keys(overflowOffsets).forEach(function (key) {\n var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n overflowOffsets[key] += offset[axis] * multiply;\n });\n }\n\n return overflowOffsets;\n}","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n placement = _options.placement,\n boundary = _options.boundary,\n rootBoundary = _options.rootBoundary,\n padding = _options.padding,\n flipVariations = _options.flipVariations,\n _options$allowedAutoP = _options.allowedAutoPlacements,\n allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n var variation = getVariation(placement);\n var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n return getVariation(placement) === variation;\n }) : basePlacements;\n var allowedPlacements = placements.filter(function (placement) {\n return allowedAutoPlacements.indexOf(placement) >= 0;\n });\n\n if (allowedPlacements.length === 0) {\n allowedPlacements = placements;\n } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n var overflows = allowedPlacements.reduce(function (acc, placement) {\n acc[placement] = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding\n })[getBasePlacement(placement)];\n return acc;\n }, {});\n return Object.keys(overflows).sort(function (a, b) {\n return overflows[a] - overflows[b];\n });\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n if (getBasePlacement(placement) === auto) {\n return [];\n }\n\n var oppositePlacement = getOppositePlacement(placement);\n return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n\n if (state.modifiersData[name]._skip) {\n return;\n }\n\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n specifiedFallbackPlacements = options.fallbackPlacements,\n padding = options.padding,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n _options$flipVariatio = options.flipVariations,\n flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n allowedAutoPlacements = options.allowedAutoPlacements;\n var preferredPlacement = state.options.placement;\n var basePlacement = getBasePlacement(preferredPlacement);\n var isBasePlacement = basePlacement === preferredPlacement;\n var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n flipVariations: flipVariations,\n allowedAutoPlacements: allowedAutoPlacements\n }) : placement);\n }, []);\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var checksMap = new Map();\n var makeFallbackChecks = true;\n var firstFittingPlacement = placements[0];\n\n for (var i = 0; i < placements.length; i++) {\n var placement = placements[i];\n\n var _basePlacement = getBasePlacement(placement);\n\n var isStartVariation = getVariation(placement) === start;\n var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n var len = isVertical ? 'width' : 'height';\n var overflow = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n altBoundary: altBoundary,\n padding: padding\n });\n var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n if (referenceRect[len] > popperRect[len]) {\n mainVariationSide = getOppositePlacement(mainVariationSide);\n }\n\n var altVariationSide = getOppositePlacement(mainVariationSide);\n var checks = [];\n\n if (checkMainAxis) {\n checks.push(overflow[_basePlacement] <= 0);\n }\n\n if (checkAltAxis) {\n checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n }\n\n if (checks.every(function (check) {\n return check;\n })) {\n firstFittingPlacement = placement;\n makeFallbackChecks = false;\n break;\n }\n\n checksMap.set(placement, checks);\n }\n\n if (makeFallbackChecks) {\n // `2` may be desired in some cases – research later\n var numberOfChecks = flipVariations ? 3 : 1;\n\n var _loop = function _loop(_i) {\n var fittingPlacement = placements.find(function (placement) {\n var checks = checksMap.get(placement);\n\n if (checks) {\n return checks.slice(0, _i).every(function (check) {\n return check;\n });\n }\n });\n\n if (fittingPlacement) {\n firstFittingPlacement = fittingPlacement;\n return \"break\";\n }\n };\n\n for (var _i = numberOfChecks; _i > 0; _i--) {\n var _ret = _loop(_i);\n\n if (_ret === \"break\") break;\n }\n }\n\n if (state.placement !== firstFittingPlacement) {\n state.modifiersData[name]._skip = true;\n state.placement = firstFittingPlacement;\n state.reset = true;\n }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'flip',\n enabled: true,\n phase: 'main',\n fn: flip,\n requiresIfExists: ['offset'],\n data: {\n _skip: false\n }\n};","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n if (preventedOffsets === void 0) {\n preventedOffsets = {\n x: 0,\n y: 0\n };\n }\n\n return {\n top: overflow.top - rect.height - preventedOffsets.y,\n right: overflow.right - rect.width + preventedOffsets.x,\n bottom: overflow.bottom - rect.height + preventedOffsets.y,\n left: overflow.left - rect.width - preventedOffsets.x\n };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n return [top, right, bottom, left].some(function (side) {\n return overflow[side] >= 0;\n });\n}\n\nfunction hide(_ref) {\n var state = _ref.state,\n name = _ref.name;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var preventedOffsets = state.modifiersData.preventOverflow;\n var referenceOverflow = detectOverflow(state, {\n elementContext: 'reference'\n });\n var popperAltOverflow = detectOverflow(state, {\n altBoundary: true\n });\n var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n state.modifiersData[name] = {\n referenceClippingOffsets: referenceClippingOffsets,\n popperEscapeOffsets: popperEscapeOffsets,\n isReferenceHidden: isReferenceHidden,\n hasPopperEscaped: hasPopperEscaped\n };\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-reference-hidden': isReferenceHidden,\n 'data-popper-escaped': hasPopperEscaped\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'hide',\n enabled: true,\n phase: 'main',\n requiresIfExists: ['preventOverflow'],\n fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n var basePlacement = getBasePlacement(placement);\n var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n placement: placement\n })) : offset,\n skidding = _ref[0],\n distance = _ref[1];\n\n skidding = skidding || 0;\n distance = (distance || 0) * invertDistance;\n return [left, right].indexOf(basePlacement) >= 0 ? {\n x: distance,\n y: skidding\n } : {\n x: skidding,\n y: distance\n };\n}\n\nfunction offset(_ref2) {\n var state = _ref2.state,\n options = _ref2.options,\n name = _ref2.name;\n var _options$offset = options.offset,\n offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n var data = placements.reduce(function (acc, placement) {\n acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n return acc;\n }, {});\n var _data$state$placement = data[state.placement],\n x = _data$state$placement.x,\n y = _data$state$placement.y;\n\n if (state.modifiersData.popperOffsets != null) {\n state.modifiersData.popperOffsets.x += x;\n state.modifiersData.popperOffsets.y += y;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'offset',\n enabled: true,\n phase: 'main',\n requires: ['popperOffsets'],\n fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n var state = _ref.state,\n name = _ref.name;\n // Offsets are the actual position the popper needs to have to be\n // properly positioned near its reference element\n // This is the most basic placement, and will be adjusted by\n // the modifiers in the next step\n state.modifiersData[name] = computeOffsets({\n reference: state.rects.reference,\n element: state.rects.popper,\n strategy: 'absolute',\n placement: state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'popperOffsets',\n enabled: true,\n phase: 'read',\n fn: popperOffsets,\n data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n padding = options.padding,\n _options$tether = options.tether,\n tether = _options$tether === void 0 ? true : _options$tether,\n _options$tetherOffset = options.tetherOffset,\n tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n var overflow = detectOverflow(state, {\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n altBoundary: altBoundary\n });\n var basePlacement = getBasePlacement(state.placement);\n var variation = getVariation(state.placement);\n var isBasePlacement = !variation;\n var mainAxis = getMainAxisFromPlacement(basePlacement);\n var altAxis = getAltAxis(mainAxis);\n var popperOffsets = state.modifiersData.popperOffsets;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n placement: state.placement\n })) : tetherOffset;\n var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n mainAxis: tetherOffsetValue,\n altAxis: tetherOffsetValue\n } : Object.assign({\n mainAxis: 0,\n altAxis: 0\n }, tetherOffsetValue);\n var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n var data = {\n x: 0,\n y: 0\n };\n\n if (!popperOffsets) {\n return;\n }\n\n if (checkMainAxis) {\n var _offsetModifierState$;\n\n var mainSide = mainAxis === 'y' ? top : left;\n var altSide = mainAxis === 'y' ? bottom : right;\n var len = mainAxis === 'y' ? 'height' : 'width';\n var offset = popperOffsets[mainAxis];\n var min = offset + overflow[mainSide];\n var max = offset - overflow[altSide];\n var additive = tether ? -popperRect[len] / 2 : 0;\n var minLen = variation === start ? referenceRect[len] : popperRect[len];\n var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n // outside the reference bounds\n\n var arrowElement = state.elements.arrow;\n var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n width: 0,\n height: 0\n };\n var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n var arrowPaddingMin = arrowPaddingObject[mainSide];\n var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n // to include its full size in the calculation. If the reference is small\n // and near the edge of a boundary, the popper can overflow even if the\n // reference is not overflowing as well (e.g. virtual elements with no\n // width or height)\n\n var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n var tetherMax = offset + maxOffset - offsetModifierValue;\n var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n popperOffsets[mainAxis] = preventedOffset;\n data[mainAxis] = preventedOffset - offset;\n }\n\n if (checkAltAxis) {\n var _offsetModifierState$2;\n\n var _mainSide = mainAxis === 'x' ? top : left;\n\n var _altSide = mainAxis === 'x' ? bottom : right;\n\n var _offset = popperOffsets[altAxis];\n\n var _len = altAxis === 'y' ? 'height' : 'width';\n\n var _min = _offset + overflow[_mainSide];\n\n var _max = _offset - overflow[_altSide];\n\n var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n popperOffsets[altAxis] = _preventedOffset;\n data[altAxis] = _preventedOffset - _offset;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'preventOverflow',\n enabled: true,\n phase: 'main',\n fn: preventOverflow,\n requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n var rect = element.getBoundingClientRect();\n var scaleX = round(rect.width) / element.offsetWidth || 1;\n var scaleY = round(rect.height) / element.offsetHeight || 1;\n return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n if (isFixed === void 0) {\n isFixed = false;\n }\n\n var isOffsetParentAnElement = isHTMLElement(offsetParent);\n var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n var documentElement = getDocumentElement(offsetParent);\n var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n var scroll = {\n scrollLeft: 0,\n scrollTop: 0\n };\n var offsets = {\n x: 0,\n y: 0\n };\n\n if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n isScrollParent(documentElement)) {\n scroll = getNodeScroll(offsetParent);\n }\n\n if (isHTMLElement(offsetParent)) {\n offsets = getBoundingClientRect(offsetParent, true);\n offsets.x += offsetParent.clientLeft;\n offsets.y += offsetParent.clientTop;\n } else if (documentElement) {\n offsets.x = getWindowScrollBarX(documentElement);\n }\n }\n\n return {\n x: rect.left + scroll.scrollLeft - offsets.x,\n y: rect.top + scroll.scrollTop - offsets.y,\n width: rect.width,\n height: rect.height\n };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n if (node === getWindow(node) || !isHTMLElement(node)) {\n return getWindowScroll(node);\n } else {\n return getHTMLElementScroll(node);\n }\n}","export default function getHTMLElementScroll(element) {\n return {\n scrollLeft: element.scrollLeft,\n scrollTop: element.scrollTop\n };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n var map = new Map();\n var visited = new Set();\n var result = [];\n modifiers.forEach(function (modifier) {\n map.set(modifier.name, modifier);\n }); // On visiting object, check for its dependencies and visit them recursively\n\n function sort(modifier) {\n visited.add(modifier.name);\n var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n requires.forEach(function (dep) {\n if (!visited.has(dep)) {\n var depModifier = map.get(dep);\n\n if (depModifier) {\n sort(depModifier);\n }\n }\n });\n result.push(modifier);\n }\n\n modifiers.forEach(function (modifier) {\n if (!visited.has(modifier.name)) {\n // check for visited object\n sort(modifier);\n }\n });\n return result;\n}\n\nexport default function orderModifiers(modifiers) {\n // order based on dependencies\n var orderedModifiers = order(modifiers); // order based on phase\n\n return modifierPhases.reduce(function (acc, phase) {\n return acc.concat(orderedModifiers.filter(function (modifier) {\n return modifier.phase === phase;\n }));\n }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nvar DEFAULT_OPTIONS = {\n placement: 'bottom',\n modifiers: [],\n strategy: 'absolute'\n};\n\nfunction areValidElements() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n return !args.some(function (element) {\n return !(element && typeof element.getBoundingClientRect === 'function');\n });\n}\n\nexport function popperGenerator(generatorOptions) {\n if (generatorOptions === void 0) {\n generatorOptions = {};\n }\n\n var _generatorOptions = generatorOptions,\n _generatorOptions$def = _generatorOptions.defaultModifiers,\n defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n _generatorOptions$def2 = _generatorOptions.defaultOptions,\n defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n return function createPopper(reference, popper, options) {\n if (options === void 0) {\n options = defaultOptions;\n }\n\n var state = {\n placement: 'bottom',\n orderedModifiers: [],\n options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n modifiersData: {},\n elements: {\n reference: reference,\n popper: popper\n },\n attributes: {},\n styles: {}\n };\n var effectCleanupFns = [];\n var isDestroyed = false;\n var instance = {\n state: state,\n setOptions: function setOptions(setOptionsAction) {\n var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n cleanupModifierEffects();\n state.options = Object.assign({}, defaultOptions, state.options, options);\n state.scrollParents = {\n reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n popper: listScrollParents(popper)\n }; // Orders the modifiers based on their dependencies and `phase`\n // properties\n\n var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n state.orderedModifiers = orderedModifiers.filter(function (m) {\n return m.enabled;\n });\n runModifierEffects();\n return instance.update();\n },\n // Sync update – it will always be executed, even if not necessary. This\n // is useful for low frequency updates where sync behavior simplifies the\n // logic.\n // For high frequency updates (e.g. `resize` and `scroll` events), always\n // prefer the async Popper#update method\n forceUpdate: function forceUpdate() {\n if (isDestroyed) {\n return;\n }\n\n var _state$elements = state.elements,\n reference = _state$elements.reference,\n popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n // anymore\n\n if (!areValidElements(reference, popper)) {\n return;\n } // Store the reference and popper rects to be read by modifiers\n\n\n state.rects = {\n reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n popper: getLayoutRect(popper)\n }; // Modifiers have the ability to reset the current update cycle. The\n // most common use case for this is the `flip` modifier changing the\n // placement, which then needs to re-run all the modifiers, because the\n // logic was previously ran for the previous placement and is therefore\n // stale/incorrect\n\n state.reset = false;\n state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n // is filled with the initial data specified by the modifier. This means\n // it doesn't persist and is fresh on each update.\n // To ensure persistent data, use `${name}#persistent`\n\n state.orderedModifiers.forEach(function (modifier) {\n return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n });\n\n for (var index = 0; index < state.orderedModifiers.length; index++) {\n if (state.reset === true) {\n state.reset = false;\n index = -1;\n continue;\n }\n\n var _state$orderedModifie = state.orderedModifiers[index],\n fn = _state$orderedModifie.fn,\n _state$orderedModifie2 = _state$orderedModifie.options,\n _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n name = _state$orderedModifie.name;\n\n if (typeof fn === 'function') {\n state = fn({\n state: state,\n options: _options,\n name: name,\n instance: instance\n }) || state;\n }\n }\n },\n // Async and optimistically optimized update – it will not be executed if\n // not necessary (debounced to run at most once-per-tick)\n update: debounce(function () {\n return new Promise(function (resolve) {\n instance.forceUpdate();\n resolve(state);\n });\n }),\n destroy: function destroy() {\n cleanupModifierEffects();\n isDestroyed = true;\n }\n };\n\n if (!areValidElements(reference, popper)) {\n return instance;\n }\n\n instance.setOptions(options).then(function (state) {\n if (!isDestroyed && options.onFirstUpdate) {\n options.onFirstUpdate(state);\n }\n }); // Modifiers have the ability to execute arbitrary code before the first\n // update cycle runs. They will be executed in the same order as the update\n // cycle. This is useful when a modifier adds some persistent data that\n // other modifiers need to use, but the modifier is run after the dependent\n // one.\n\n function runModifierEffects() {\n state.orderedModifiers.forEach(function (_ref) {\n var name = _ref.name,\n _ref$options = _ref.options,\n options = _ref$options === void 0 ? {} : _ref$options,\n effect = _ref.effect;\n\n if (typeof effect === 'function') {\n var cleanupFn = effect({\n state: state,\n name: name,\n instance: instance,\n options: options\n });\n\n var noopFn = function noopFn() {};\n\n effectCleanupFns.push(cleanupFn || noopFn);\n }\n });\n }\n\n function cleanupModifierEffects() {\n effectCleanupFns.forEach(function (fn) {\n return fn();\n });\n effectCleanupFns = [];\n }\n\n return instance;\n };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n var pending;\n return function () {\n if (!pending) {\n pending = new Promise(function (resolve) {\n Promise.resolve().then(function () {\n pending = undefined;\n resolve(fn());\n });\n });\n }\n\n return pending;\n };\n}","export default function mergeByName(modifiers) {\n var merged = modifiers.reduce(function (merged, current) {\n var existing = merged[current.name];\n merged[current.name] = existing ? Object.assign({}, existing, current, {\n options: Object.assign({}, existing.options, current.options),\n data: Object.assign({}, existing.data, current.data)\n }) : current;\n return merged;\n }, {}); // IE11 does not support Object.values\n\n return Object.keys(merged).map(function (key) {\n return merged[key];\n });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","/**\n * --------------------------------------------------------------------------\n * Bootstrap dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n defineJQueryPlugin,\n execute,\n getElement,\n getNextActiveElement,\n isDisabled,\n isElement,\n isRTL,\n isVisible,\n noop\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'dropdown'\nconst DATA_KEY = 'bs.dropdown'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ESCAPE_KEY = 'Escape'\nconst TAB_KEY = 'Tab'\nconst ARROW_UP_KEY = 'ArrowUp'\nconst ARROW_DOWN_KEY = 'ArrowDown'\nconst RIGHT_MOUSE_BUTTON = 2 // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_DROPUP = 'dropup'\nconst CLASS_NAME_DROPEND = 'dropend'\nconst CLASS_NAME_DROPSTART = 'dropstart'\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center'\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center'\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)'\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE}.${CLASS_NAME_SHOW}`\nconst SELECTOR_MENU = '.dropdown-menu'\nconst SELECTOR_NAVBAR = '.navbar'\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav'\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)'\n\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start'\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end'\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start'\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end'\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start'\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start'\nconst PLACEMENT_TOPCENTER = 'top'\nconst PLACEMENT_BOTTOMCENTER = 'bottom'\n\nconst Default = {\n autoClose: true,\n boundary: 'clippingParents',\n display: 'dynamic',\n offset: [0, 2],\n popperConfig: null,\n reference: 'toggle'\n}\n\nconst DefaultType = {\n autoClose: '(boolean|string)',\n boundary: '(string|element)',\n display: 'string',\n offset: '(array|string|function)',\n popperConfig: '(null|object|function)',\n reference: '(string|element|object)'\n}\n\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._popper = null\n this._parent = this._element.parentNode // dropdown wrapper\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] ||\n SelectorEngine.prev(this._element, SELECTOR_MENU)[0] ||\n SelectorEngine.findOne(SELECTOR_MENU, this._parent)\n this._inNavbar = this._detectNavbar()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle() {\n return this._isShown() ? this.hide() : this.show()\n }\n\n show() {\n if (isDisabled(this._element) || this._isShown()) {\n return\n }\n\n const relatedTarget = {\n relatedTarget: this._element\n }\n\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, relatedTarget)\n\n if (showEvent.defaultPrevented) {\n return\n }\n\n this._createPopper()\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop)\n }\n }\n\n this._element.focus()\n this._element.setAttribute('aria-expanded', true)\n\n this._menu.classList.add(CLASS_NAME_SHOW)\n this._element.classList.add(CLASS_NAME_SHOW)\n EventHandler.trigger(this._element, EVENT_SHOWN, relatedTarget)\n }\n\n hide() {\n if (isDisabled(this._element) || !this._isShown()) {\n return\n }\n\n const relatedTarget = {\n relatedTarget: this._element\n }\n\n this._completeHide(relatedTarget)\n }\n\n dispose() {\n if (this._popper) {\n this._popper.destroy()\n }\n\n super.dispose()\n }\n\n update() {\n this._inNavbar = this._detectNavbar()\n if (this._popper) {\n this._popper.update()\n }\n }\n\n // Private\n _completeHide(relatedTarget) {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE, relatedTarget)\n if (hideEvent.defaultPrevented) {\n return\n }\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop)\n }\n }\n\n if (this._popper) {\n this._popper.destroy()\n }\n\n this._menu.classList.remove(CLASS_NAME_SHOW)\n this._element.classList.remove(CLASS_NAME_SHOW)\n this._element.setAttribute('aria-expanded', 'false')\n Manipulator.removeDataAttribute(this._menu, 'popper')\n EventHandler.trigger(this._element, EVENT_HIDDEN, relatedTarget)\n }\n\n _getConfig(config) {\n config = super._getConfig(config)\n\n if (typeof config.reference === 'object' && !isElement(config.reference) &&\n typeof config.reference.getBoundingClientRect !== 'function'\n ) {\n // Popper virtual elements require a getBoundingClientRect method\n throw new TypeError(`${NAME.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`)\n }\n\n return config\n }\n\n _createPopper() {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)')\n }\n\n let referenceElement = this._element\n\n if (this._config.reference === 'parent') {\n referenceElement = this._parent\n } else if (isElement(this._config.reference)) {\n referenceElement = getElement(this._config.reference)\n } else if (typeof this._config.reference === 'object') {\n referenceElement = this._config.reference\n }\n\n const popperConfig = this._getPopperConfig()\n this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig)\n }\n\n _isShown() {\n return this._menu.classList.contains(CLASS_NAME_SHOW)\n }\n\n _getPlacement() {\n const parentDropdown = this._parent\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n return PLACEMENT_RIGHT\n }\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n return PLACEMENT_LEFT\n }\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n return PLACEMENT_TOPCENTER\n }\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n return PLACEMENT_BOTTOMCENTER\n }\n\n // We need to trim the value because custom properties can also include spaces\n const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end'\n\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP\n }\n\n return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM\n }\n\n _detectNavbar() {\n return this._element.closest(SELECTOR_NAVBAR) !== null\n }\n\n _getOffset() {\n const { offset } = this._config\n\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10))\n }\n\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element)\n }\n\n return offset\n }\n\n _getPopperConfig() {\n const defaultBsPopperConfig = {\n placement: this._getPlacement(),\n modifiers: [{\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n },\n {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n }]\n }\n\n // Disable Popper if we have a static display or Dropdown is in Navbar\n if (this._inNavbar || this._config.display === 'static') {\n Manipulator.setDataAttribute(this._menu, 'popper', 'static') // TODO: v6 remove\n defaultBsPopperConfig.modifiers = [{\n name: 'applyStyles',\n enabled: false\n }]\n }\n\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n }\n }\n\n _selectMenuItem({ key, target }) {\n const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element))\n\n if (!items.length) {\n return\n }\n\n // if target isn't included in items (e.g. when expanding the dropdown)\n // allow cycling to get the last item in case key equals ARROW_UP_KEY\n getNextActiveElement(items, target, key === ARROW_DOWN_KEY, !items.includes(target)).focus()\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Dropdown.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n })\n }\n\n static clearMenus(event) {\n if (event.button === RIGHT_MOUSE_BUTTON || (event.type === 'keyup' && event.key !== TAB_KEY)) {\n return\n }\n\n const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN)\n\n for (const toggle of openToggles) {\n const context = Dropdown.getInstance(toggle)\n if (!context || context._config.autoClose === false) {\n continue\n }\n\n const composedPath = event.composedPath()\n const isMenuTarget = composedPath.includes(context._menu)\n if (\n composedPath.includes(context._element) ||\n (context._config.autoClose === 'inside' && !isMenuTarget) ||\n (context._config.autoClose === 'outside' && isMenuTarget)\n ) {\n continue\n }\n\n // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n if (context._menu.contains(event.target) && ((event.type === 'keyup' && event.key === TAB_KEY) || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n continue\n }\n\n const relatedTarget = { relatedTarget: context._element }\n\n if (event.type === 'click') {\n relatedTarget.clickEvent = event\n }\n\n context._completeHide(relatedTarget)\n }\n }\n\n static dataApiKeydownHandler(event) {\n // If not an UP | DOWN | ESCAPE key => not a dropdown command\n // If input/textarea && if key is other than ESCAPE => not a dropdown command\n\n const isInput = /input|textarea/i.test(event.target.tagName)\n const isEscapeEvent = event.key === ESCAPE_KEY\n const isUpOrDownEvent = [ARROW_UP_KEY, ARROW_DOWN_KEY].includes(event.key)\n\n if (!isUpOrDownEvent && !isEscapeEvent) {\n return\n }\n\n if (isInput && !isEscapeEvent) {\n return\n }\n\n event.preventDefault()\n\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE) ?\n this :\n (SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE)[0] ||\n SelectorEngine.next(this, SELECTOR_DATA_TOGGLE)[0] ||\n SelectorEngine.findOne(SELECTOR_DATA_TOGGLE, event.delegateTarget.parentNode))\n\n const instance = Dropdown.getOrCreateInstance(getToggleButton)\n\n if (isUpOrDownEvent) {\n event.stopPropagation()\n instance.show()\n instance._selectMenuItem(event)\n return\n }\n\n if (instance._isShown()) { // else is escape and we check if it is shown\n event.stopPropagation()\n instance.hide()\n getToggleButton.focus()\n }\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_CLICK_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n event.preventDefault()\n Dropdown.getOrCreateInstance(this).toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown)\n\nexport default Dropdown\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute, executeAfterTransition, getElement, reflow } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'backdrop'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME}`\n\nconst Default = {\n className: 'modal-backdrop',\n clickCallback: null,\n isAnimated: false,\n isVisible: true, // if false, we use the backdrop helper without adding any element to the dom\n rootElement: 'body' // give the choice to place backdrop under different elements\n}\n\nconst DefaultType = {\n className: 'string',\n clickCallback: '(function|null)',\n isAnimated: 'boolean',\n isVisible: 'boolean',\n rootElement: '(element|string)'\n}\n\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n constructor(config) {\n super()\n this._config = this._getConfig(config)\n this._isAppended = false\n this._element = null\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n show(callback) {\n if (!this._config.isVisible) {\n execute(callback)\n return\n }\n\n this._append()\n\n const element = this._getElement()\n if (this._config.isAnimated) {\n reflow(element)\n }\n\n element.classList.add(CLASS_NAME_SHOW)\n\n this._emulateAnimation(() => {\n execute(callback)\n })\n }\n\n hide(callback) {\n if (!this._config.isVisible) {\n execute(callback)\n return\n }\n\n this._getElement().classList.remove(CLASS_NAME_SHOW)\n\n this._emulateAnimation(() => {\n this.dispose()\n execute(callback)\n })\n }\n\n dispose() {\n if (!this._isAppended) {\n return\n }\n\n EventHandler.off(this._element, EVENT_MOUSEDOWN)\n\n this._element.remove()\n this._isAppended = false\n }\n\n // Private\n _getElement() {\n if (!this._element) {\n const backdrop = document.createElement('div')\n backdrop.className = this._config.className\n if (this._config.isAnimated) {\n backdrop.classList.add(CLASS_NAME_FADE)\n }\n\n this._element = backdrop\n }\n\n return this._element\n }\n\n _configAfterMerge(config) {\n // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n config.rootElement = getElement(config.rootElement)\n return config\n }\n\n _append() {\n if (this._isAppended) {\n return\n }\n\n const element = this._getElement()\n this._config.rootElement.append(element)\n\n EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n execute(this._config.clickCallback)\n })\n\n this._isAppended = true\n }\n\n _emulateAnimation(callback) {\n executeAfterTransition(callback, this._getElement(), this._config.isAnimated)\n }\n}\n\nexport default Backdrop\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'focustrap'\nconst DATA_KEY = 'bs.focustrap'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst EVENT_FOCUSIN = `focusin${EVENT_KEY}`\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY}`\n\nconst TAB_KEY = 'Tab'\nconst TAB_NAV_FORWARD = 'forward'\nconst TAB_NAV_BACKWARD = 'backward'\n\nconst Default = {\n autofocus: true,\n trapElement: null // The element to trap focus inside of\n}\n\nconst DefaultType = {\n autofocus: 'boolean',\n trapElement: 'element'\n}\n\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n constructor(config) {\n super()\n this._config = this._getConfig(config)\n this._isActive = false\n this._lastTabNavDirection = null\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n activate() {\n if (this._isActive) {\n return\n }\n\n if (this._config.autofocus) {\n this._config.trapElement.focus()\n }\n\n EventHandler.off(document, EVENT_KEY) // guard against infinite focus loop\n EventHandler.on(document, EVENT_FOCUSIN, event => this._handleFocusin(event))\n EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event))\n\n this._isActive = true\n }\n\n deactivate() {\n if (!this._isActive) {\n return\n }\n\n this._isActive = false\n EventHandler.off(document, EVENT_KEY)\n }\n\n // Private\n _handleFocusin(event) {\n const { trapElement } = this._config\n\n if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n return\n }\n\n const elements = SelectorEngine.focusableChildren(trapElement)\n\n if (elements.length === 0) {\n trapElement.focus()\n } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n elements[elements.length - 1].focus()\n } else {\n elements[0].focus()\n }\n }\n\n _handleKeydown(event) {\n if (event.key !== TAB_KEY) {\n return\n }\n\n this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD\n }\n}\n\nexport default FocusTrap\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top'\nconst SELECTOR_STICKY_CONTENT = '.sticky-top'\nconst PROPERTY_PADDING = 'padding-right'\nconst PROPERTY_MARGIN = 'margin-right'\n\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n constructor() {\n this._element = document.body\n }\n\n // Public\n getWidth() {\n // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n const documentWidth = document.documentElement.clientWidth\n return Math.abs(window.innerWidth - documentWidth)\n }\n\n hide() {\n const width = this.getWidth()\n this._disableOverFlow()\n // give padding to element to balance the hidden scrollbar width\n this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width)\n }\n\n reset() {\n this._resetElementAttributes(this._element, 'overflow')\n this._resetElementAttributes(this._element, PROPERTY_PADDING)\n this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING)\n this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN)\n }\n\n isOverflowing() {\n return this.getWidth() > 0\n }\n\n // Private\n _disableOverFlow() {\n this._saveInitialAttribute(this._element, 'overflow')\n this._element.style.overflow = 'hidden'\n }\n\n _setElementAttributes(selector, styleProperty, callback) {\n const scrollbarWidth = this.getWidth()\n const manipulationCallBack = element => {\n if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n return\n }\n\n this._saveInitialAttribute(element, styleProperty)\n const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty)\n element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`)\n }\n\n this._applyManipulationCallback(selector, manipulationCallBack)\n }\n\n _saveInitialAttribute(element, styleProperty) {\n const actualValue = element.style.getPropertyValue(styleProperty)\n if (actualValue) {\n Manipulator.setDataAttribute(element, styleProperty, actualValue)\n }\n }\n\n _resetElementAttributes(selector, styleProperty) {\n const manipulationCallBack = element => {\n const value = Manipulator.getDataAttribute(element, styleProperty)\n // We only want to remove the property if the value is `null`; the value can also be zero\n if (value === null) {\n element.style.removeProperty(styleProperty)\n return\n }\n\n Manipulator.removeDataAttribute(element, styleProperty)\n element.style.setProperty(styleProperty, value)\n }\n\n this._applyManipulationCallback(selector, manipulationCallBack)\n }\n\n _applyManipulationCallback(selector, callBack) {\n if (isElement(selector)) {\n callBack(selector)\n return\n }\n\n for (const sel of SelectorEngine.find(selector, this._element)) {\n callBack(sel)\n }\n }\n}\n\nexport default ScrollBarHelper\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport { defineJQueryPlugin, isRTL, isVisible, reflow } from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'modal'\nconst DATA_KEY = 'bs.modal'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst ESCAPE_KEY = 'Escape'\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY}`\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_OPEN = 'modal-open'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_STATIC = 'modal-static'\n\nconst OPEN_SELECTOR = '.modal.show'\nconst SELECTOR_DIALOG = '.modal-dialog'\nconst SELECTOR_MODAL_BODY = '.modal-body'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"modal\"]'\n\nconst Default = {\n backdrop: true,\n focus: true,\n keyboard: true\n}\n\nconst DefaultType = {\n backdrop: '(boolean|string)',\n focus: 'boolean',\n keyboard: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element)\n this._backdrop = this._initializeBackDrop()\n this._focustrap = this._initializeFocusTrap()\n this._isShown = false\n this._isTransitioning = false\n this._scrollBar = new ScrollBarHelper()\n\n this._addEventListeners()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget)\n }\n\n show(relatedTarget) {\n if (this._isShown || this._isTransitioning) {\n return\n }\n\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, {\n relatedTarget\n })\n\n if (showEvent.defaultPrevented) {\n return\n }\n\n this._isShown = true\n this._isTransitioning = true\n\n this._scrollBar.hide()\n\n document.body.classList.add(CLASS_NAME_OPEN)\n\n this._adjustDialog()\n\n this._backdrop.show(() => this._showElement(relatedTarget))\n }\n\n hide() {\n if (!this._isShown || this._isTransitioning) {\n return\n }\n\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n if (hideEvent.defaultPrevented) {\n return\n }\n\n this._isShown = false\n this._isTransitioning = true\n this._focustrap.deactivate()\n\n this._element.classList.remove(CLASS_NAME_SHOW)\n\n this._queueCallback(() => this._hideModal(), this._element, this._isAnimated())\n }\n\n dispose() {\n EventHandler.off(window, EVENT_KEY)\n EventHandler.off(this._dialog, EVENT_KEY)\n\n this._backdrop.dispose()\n this._focustrap.deactivate()\n\n super.dispose()\n }\n\n handleUpdate() {\n this._adjustDialog()\n }\n\n // Private\n _initializeBackDrop() {\n return new Backdrop({\n isVisible: Boolean(this._config.backdrop), // 'static' option will be translated to true, and booleans will keep their value,\n isAnimated: this._isAnimated()\n })\n }\n\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n })\n }\n\n _showElement(relatedTarget) {\n // try to append dynamic modal\n if (!document.body.contains(this._element)) {\n document.body.append(this._element)\n }\n\n this._element.style.display = 'block'\n this._element.removeAttribute('aria-hidden')\n this._element.setAttribute('aria-modal', true)\n this._element.setAttribute('role', 'dialog')\n this._element.scrollTop = 0\n\n const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog)\n if (modalBody) {\n modalBody.scrollTop = 0\n }\n\n reflow(this._element)\n\n this._element.classList.add(CLASS_NAME_SHOW)\n\n const transitionComplete = () => {\n if (this._config.focus) {\n this._focustrap.activate()\n }\n\n this._isTransitioning = false\n EventHandler.trigger(this._element, EVENT_SHOWN, {\n relatedTarget\n })\n }\n\n this._queueCallback(transitionComplete, this._dialog, this._isAnimated())\n }\n\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n if (event.key !== ESCAPE_KEY) {\n return\n }\n\n if (this._config.keyboard) {\n this.hide()\n return\n }\n\n this._triggerBackdropTransition()\n })\n\n EventHandler.on(window, EVENT_RESIZE, () => {\n if (this._isShown && !this._isTransitioning) {\n this._adjustDialog()\n }\n })\n\n EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n if (this._element !== event.target || this._element !== event2.target) {\n return\n }\n\n if (this._config.backdrop === 'static') {\n this._triggerBackdropTransition()\n return\n }\n\n if (this._config.backdrop) {\n this.hide()\n }\n })\n })\n }\n\n _hideModal() {\n this._element.style.display = 'none'\n this._element.setAttribute('aria-hidden', true)\n this._element.removeAttribute('aria-modal')\n this._element.removeAttribute('role')\n this._isTransitioning = false\n\n this._backdrop.hide(() => {\n document.body.classList.remove(CLASS_NAME_OPEN)\n this._resetAdjustments()\n this._scrollBar.reset()\n EventHandler.trigger(this._element, EVENT_HIDDEN)\n })\n }\n\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_FADE)\n }\n\n _triggerBackdropTransition() {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n if (hideEvent.defaultPrevented) {\n return\n }\n\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n const initialOverflowY = this._element.style.overflowY\n // return if the following background transition hasn't yet completed\n if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n return\n }\n\n if (!isModalOverflowing) {\n this._element.style.overflowY = 'hidden'\n }\n\n this._element.classList.add(CLASS_NAME_STATIC)\n this._queueCallback(() => {\n this._element.classList.remove(CLASS_NAME_STATIC)\n this._queueCallback(() => {\n this._element.style.overflowY = initialOverflowY\n }, this._dialog)\n }, this._dialog)\n\n this._element.focus()\n }\n\n /**\n * The following methods are used to handle overflowing modals\n */\n\n _adjustDialog() {\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n const scrollbarWidth = this._scrollBar.getWidth()\n const isBodyOverflowing = scrollbarWidth > 0\n\n if (isBodyOverflowing && !isModalOverflowing) {\n const property = isRTL() ? 'paddingLeft' : 'paddingRight'\n this._element.style[property] = `${scrollbarWidth}px`\n }\n\n if (!isBodyOverflowing && isModalOverflowing) {\n const property = isRTL() ? 'paddingRight' : 'paddingLeft'\n this._element.style[property] = `${scrollbarWidth}px`\n }\n }\n\n _resetAdjustments() {\n this._element.style.paddingLeft = ''\n this._element.style.paddingRight = ''\n }\n\n // Static\n static jQueryInterface(config, relatedTarget) {\n return this.each(function () {\n const data = Modal.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config](relatedTarget)\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this)\n\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault()\n }\n\n EventHandler.one(target, EVENT_SHOW, showEvent => {\n if (showEvent.defaultPrevented) {\n // only register focus restorer if modal will actually get shown\n return\n }\n\n EventHandler.one(target, EVENT_HIDDEN, () => {\n if (isVisible(this)) {\n this.focus()\n }\n })\n })\n\n // avoid conflict when clicking modal toggler while another one is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n if (alreadyOpen) {\n Modal.getInstance(alreadyOpen).hide()\n }\n\n const data = Modal.getOrCreateInstance(target)\n\n data.toggle(this)\n})\n\nenableDismissTrigger(Modal)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal)\n\nexport default Modal\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport {\n defineJQueryPlugin,\n isDisabled,\n isVisible\n} from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'offcanvas'\nconst DATA_KEY = 'bs.offcanvas'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst ESCAPE_KEY = 'Escape'\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_SHOWING = 'showing'\nconst CLASS_NAME_HIDING = 'hiding'\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop'\nconst OPEN_SELECTOR = '.offcanvas.show'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"offcanvas\"]'\n\nconst Default = {\n backdrop: true,\n keyboard: true,\n scroll: false\n}\n\nconst DefaultType = {\n backdrop: '(boolean|string)',\n keyboard: 'boolean',\n scroll: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n this._isShown = false\n this._backdrop = this._initializeBackDrop()\n this._focustrap = this._initializeFocusTrap()\n this._addEventListeners()\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget)\n }\n\n show(relatedTarget) {\n if (this._isShown) {\n return\n }\n\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, { relatedTarget })\n\n if (showEvent.defaultPrevented) {\n return\n }\n\n this._isShown = true\n this._backdrop.show()\n\n if (!this._config.scroll) {\n new ScrollBarHelper().hide()\n }\n\n this._element.setAttribute('aria-modal', true)\n this._element.setAttribute('role', 'dialog')\n this._element.classList.add(CLASS_NAME_SHOWING)\n\n const completeCallBack = () => {\n if (!this._config.scroll || this._config.backdrop) {\n this._focustrap.activate()\n }\n\n this._element.classList.add(CLASS_NAME_SHOW)\n this._element.classList.remove(CLASS_NAME_SHOWING)\n EventHandler.trigger(this._element, EVENT_SHOWN, { relatedTarget })\n }\n\n this._queueCallback(completeCallBack, this._element, true)\n }\n\n hide() {\n if (!this._isShown) {\n return\n }\n\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n if (hideEvent.defaultPrevented) {\n return\n }\n\n this._focustrap.deactivate()\n this._element.blur()\n this._isShown = false\n this._element.classList.add(CLASS_NAME_HIDING)\n this._backdrop.hide()\n\n const completeCallback = () => {\n this._element.classList.remove(CLASS_NAME_SHOW, CLASS_NAME_HIDING)\n this._element.removeAttribute('aria-modal')\n this._element.removeAttribute('role')\n\n if (!this._config.scroll) {\n new ScrollBarHelper().reset()\n }\n\n EventHandler.trigger(this._element, EVENT_HIDDEN)\n }\n\n this._queueCallback(completeCallback, this._element, true)\n }\n\n dispose() {\n this._backdrop.dispose()\n this._focustrap.deactivate()\n super.dispose()\n }\n\n // Private\n _initializeBackDrop() {\n const clickCallback = () => {\n if (this._config.backdrop === 'static') {\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n return\n }\n\n this.hide()\n }\n\n // 'static' option will be translated to true, and booleans will keep their value\n const isVisible = Boolean(this._config.backdrop)\n\n return new Backdrop({\n className: CLASS_NAME_BACKDROP,\n isVisible,\n isAnimated: true,\n rootElement: this._element.parentNode,\n clickCallback: isVisible ? clickCallback : null\n })\n }\n\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n })\n }\n\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n if (event.key !== ESCAPE_KEY) {\n return\n }\n\n if (this._config.keyboard) {\n this.hide()\n return\n }\n\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n })\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Offcanvas.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config](this)\n })\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this)\n\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault()\n }\n\n if (isDisabled(this)) {\n return\n }\n\n EventHandler.one(target, EVENT_HIDDEN, () => {\n // focus on trigger when it is closed\n if (isVisible(this)) {\n this.focus()\n }\n })\n\n // avoid conflict when clicking a toggler of an offcanvas, while another is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n if (alreadyOpen && alreadyOpen !== target) {\n Offcanvas.getInstance(alreadyOpen).hide()\n }\n\n const data = Offcanvas.getOrCreateInstance(target)\n data.toggle(this)\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n Offcanvas.getOrCreateInstance(selector).show()\n }\n})\n\nEventHandler.on(window, EVENT_RESIZE, () => {\n for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n if (getComputedStyle(element).position !== 'fixed') {\n Offcanvas.getOrCreateInstance(element).hide()\n }\n }\n})\n\nenableDismissTrigger(Offcanvas)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas)\n\nexport default Offcanvas\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n// js-docs-start allow-list\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i\n\nexport const DefaultAllowlist = {\n // Global attributes allowed on any supplied element below.\n '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n a: ['target', 'href', 'title', 'rel'],\n area: [],\n b: [],\n br: [],\n col: [],\n code: [],\n div: [],\n em: [],\n hr: [],\n h1: [],\n h2: [],\n h3: [],\n h4: [],\n h5: [],\n h6: [],\n i: [],\n img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n li: [],\n ol: [],\n p: [],\n pre: [],\n s: [],\n small: [],\n span: [],\n sub: [],\n sup: [],\n strong: [],\n u: [],\n ul: []\n}\n// js-docs-end allow-list\n\nconst uriAttributes = new Set([\n 'background',\n 'cite',\n 'href',\n 'itemtype',\n 'longdesc',\n 'poster',\n 'src',\n 'xlink:href'\n])\n\n/**\n * A pattern that recognizes URLs that are safe wrt. XSS in URL navigation\n * contexts.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/15.2.8/packages/core/src/sanitization/url_sanitizer.ts#L38\n */\n// eslint-disable-next-line unicorn/better-regex\nconst SAFE_URL_PATTERN = /^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i\n\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n const attributeName = attribute.nodeName.toLowerCase()\n\n if (allowedAttributeList.includes(attributeName)) {\n if (uriAttributes.has(attributeName)) {\n return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue))\n }\n\n return true\n }\n\n // Check if a regular expression validates the attribute.\n return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp)\n .some(regex => regex.test(attributeName))\n}\n\nexport function sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n if (!unsafeHtml.length) {\n return unsafeHtml\n }\n\n if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n return sanitizeFunction(unsafeHtml)\n }\n\n const domParser = new window.DOMParser()\n const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html')\n const elements = [].concat(...createdDocument.body.querySelectorAll('*'))\n\n for (const element of elements) {\n const elementName = element.nodeName.toLowerCase()\n\n if (!Object.keys(allowList).includes(elementName)) {\n element.remove()\n continue\n }\n\n const attributeList = [].concat(...element.attributes)\n const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || [])\n\n for (const attribute of attributeList) {\n if (!allowedAttribute(attribute, allowedAttributes)) {\n element.removeAttribute(attribute.nodeName)\n }\n }\n }\n\n return createdDocument.body.innerHTML\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\nimport { DefaultAllowlist, sanitizeHtml } from './sanitizer.js'\nimport { execute, getElement, isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'TemplateFactory'\n\nconst Default = {\n allowList: DefaultAllowlist,\n content: {}, // { selector : text , selector2 : text2 , }\n extraClass: '',\n html: false,\n sanitize: true,\n sanitizeFn: null,\n template: '
'\n}\n\nconst DefaultType = {\n allowList: 'object',\n content: 'object',\n extraClass: '(string|function)',\n html: 'boolean',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n template: 'string'\n}\n\nconst DefaultContentType = {\n entry: '(string|element|function|null)',\n selector: '(string|element)'\n}\n\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n constructor(config) {\n super()\n this._config = this._getConfig(config)\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n getContent() {\n return Object.values(this._config.content)\n .map(config => this._resolvePossibleFunction(config))\n .filter(Boolean)\n }\n\n hasContent() {\n return this.getContent().length > 0\n }\n\n changeContent(content) {\n this._checkContent(content)\n this._config.content = { ...this._config.content, ...content }\n return this\n }\n\n toHtml() {\n const templateWrapper = document.createElement('div')\n templateWrapper.innerHTML = this._maybeSanitize(this._config.template)\n\n for (const [selector, text] of Object.entries(this._config.content)) {\n this._setContent(templateWrapper, text, selector)\n }\n\n const template = templateWrapper.children[0]\n const extraClass = this._resolvePossibleFunction(this._config.extraClass)\n\n if (extraClass) {\n template.classList.add(...extraClass.split(' '))\n }\n\n return template\n }\n\n // Private\n _typeCheckConfig(config) {\n super._typeCheckConfig(config)\n this._checkContent(config.content)\n }\n\n _checkContent(arg) {\n for (const [selector, content] of Object.entries(arg)) {\n super._typeCheckConfig({ selector, entry: content }, DefaultContentType)\n }\n }\n\n _setContent(template, content, selector) {\n const templateElement = SelectorEngine.findOne(selector, template)\n\n if (!templateElement) {\n return\n }\n\n content = this._resolvePossibleFunction(content)\n\n if (!content) {\n templateElement.remove()\n return\n }\n\n if (isElement(content)) {\n this._putElementInTemplate(getElement(content), templateElement)\n return\n }\n\n if (this._config.html) {\n templateElement.innerHTML = this._maybeSanitize(content)\n return\n }\n\n templateElement.textContent = content\n }\n\n _maybeSanitize(arg) {\n return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg\n }\n\n _resolvePossibleFunction(arg) {\n return execute(arg, [this])\n }\n\n _putElementInTemplate(element, templateElement) {\n if (this._config.html) {\n templateElement.innerHTML = ''\n templateElement.append(element)\n return\n }\n\n templateElement.textContent = element.textContent\n }\n}\n\nexport default TemplateFactory\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport { defineJQueryPlugin, execute, findShadowRoot, getElement, getUID, isRTL, noop } from './util/index.js'\nimport { DefaultAllowlist } from './util/sanitizer.js'\nimport TemplateFactory from './util/template-factory.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'tooltip'\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn'])\n\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_MODAL = 'modal'\nconst CLASS_NAME_SHOW = 'show'\n\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner'\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`\n\nconst EVENT_MODAL_HIDE = 'hide.bs.modal'\n\nconst TRIGGER_HOVER = 'hover'\nconst TRIGGER_FOCUS = 'focus'\nconst TRIGGER_CLICK = 'click'\nconst TRIGGER_MANUAL = 'manual'\n\nconst EVENT_HIDE = 'hide'\nconst EVENT_HIDDEN = 'hidden'\nconst EVENT_SHOW = 'show'\nconst EVENT_SHOWN = 'shown'\nconst EVENT_INSERTED = 'inserted'\nconst EVENT_CLICK = 'click'\nconst EVENT_FOCUSIN = 'focusin'\nconst EVENT_FOCUSOUT = 'focusout'\nconst EVENT_MOUSEENTER = 'mouseenter'\nconst EVENT_MOUSELEAVE = 'mouseleave'\n\nconst AttachmentMap = {\n AUTO: 'auto',\n TOP: 'top',\n RIGHT: isRTL() ? 'left' : 'right',\n BOTTOM: 'bottom',\n LEFT: isRTL() ? 'right' : 'left'\n}\n\nconst Default = {\n allowList: DefaultAllowlist,\n animation: true,\n boundary: 'clippingParents',\n container: false,\n customClass: '',\n delay: 0,\n fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n html: false,\n offset: [0, 6],\n placement: 'top',\n popperConfig: null,\n sanitize: true,\n sanitizeFn: null,\n selector: false,\n template: '
' +\n '
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',\n title: '',\n trigger: 'hover focus'\n}\n\nconst DefaultType = {\n allowList: 'object',\n animation: 'boolean',\n boundary: '(string|element)',\n container: '(string|element|boolean)',\n customClass: '(string|function)',\n delay: '(number|object)',\n fallbackPlacements: 'array',\n html: 'boolean',\n offset: '(array|string|function)',\n placement: '(string|function)',\n popperConfig: '(null|object|function)',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n selector: '(string|boolean)',\n template: 'string',\n title: '(string|element|function)',\n trigger: 'string'\n}\n\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n constructor(element, config) {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)')\n }\n\n super(element, config)\n\n // Private\n this._isEnabled = true\n this._timeout = 0\n this._isHovered = null\n this._activeTrigger = {}\n this._popper = null\n this._templateFactory = null\n this._newContent = null\n\n // Protected\n this.tip = null\n\n this._setListeners()\n\n if (!this._config.selector) {\n this._fixTitle()\n }\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n enable() {\n this._isEnabled = true\n }\n\n disable() {\n this._isEnabled = false\n }\n\n toggleEnabled() {\n this._isEnabled = !this._isEnabled\n }\n\n toggle() {\n if (!this._isEnabled) {\n return\n }\n\n this._activeTrigger.click = !this._activeTrigger.click\n if (this._isShown()) {\n this._leave()\n return\n }\n\n this._enter()\n }\n\n dispose() {\n clearTimeout(this._timeout)\n\n EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n\n if (this._element.getAttribute('data-bs-original-title')) {\n this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'))\n }\n\n this._disposePopper()\n super.dispose()\n }\n\n show() {\n if (this._element.style.display === 'none') {\n throw new Error('Please use show on visible elements')\n }\n\n if (!(this._isWithContent() && this._isEnabled)) {\n return\n }\n\n const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW))\n const shadowRoot = findShadowRoot(this._element)\n const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element)\n\n if (showEvent.defaultPrevented || !isInTheDom) {\n return\n }\n\n // TODO: v6 remove this or make it optional\n this._disposePopper()\n\n const tip = this._getTipElement()\n\n this._element.setAttribute('aria-describedby', tip.getAttribute('id'))\n\n const { container } = this._config\n\n if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n container.append(tip)\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED))\n }\n\n this._popper = this._createPopper(tip)\n\n tip.classList.add(CLASS_NAME_SHOW)\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop)\n }\n }\n\n const complete = () => {\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN))\n\n if (this._isHovered === false) {\n this._leave()\n }\n\n this._isHovered = false\n }\n\n this._queueCallback(complete, this.tip, this._isAnimated())\n }\n\n hide() {\n if (!this._isShown()) {\n return\n }\n\n const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE))\n if (hideEvent.defaultPrevented) {\n return\n }\n\n const tip = this._getTipElement()\n tip.classList.remove(CLASS_NAME_SHOW)\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop)\n }\n }\n\n this._activeTrigger[TRIGGER_CLICK] = false\n this._activeTrigger[TRIGGER_FOCUS] = false\n this._activeTrigger[TRIGGER_HOVER] = false\n this._isHovered = null // it is a trick to support manual triggering\n\n const complete = () => {\n if (this._isWithActiveTrigger()) {\n return\n }\n\n if (!this._isHovered) {\n this._disposePopper()\n }\n\n this._element.removeAttribute('aria-describedby')\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN))\n }\n\n this._queueCallback(complete, this.tip, this._isAnimated())\n }\n\n update() {\n if (this._popper) {\n this._popper.update()\n }\n }\n\n // Protected\n _isWithContent() {\n return Boolean(this._getTitle())\n }\n\n _getTipElement() {\n if (!this.tip) {\n this.tip = this._createTipElement(this._newContent || this._getContentForTemplate())\n }\n\n return this.tip\n }\n\n _createTipElement(content) {\n const tip = this._getTemplateFactory(content).toHtml()\n\n // TODO: remove this check in v6\n if (!tip) {\n return null\n }\n\n tip.classList.remove(CLASS_NAME_FADE, CLASS_NAME_SHOW)\n // TODO: v6 the following can be achieved with CSS only\n tip.classList.add(`bs-${this.constructor.NAME}-auto`)\n\n const tipId = getUID(this.constructor.NAME).toString()\n\n tip.setAttribute('id', tipId)\n\n if (this._isAnimated()) {\n tip.classList.add(CLASS_NAME_FADE)\n }\n\n return tip\n }\n\n setContent(content) {\n this._newContent = content\n if (this._isShown()) {\n this._disposePopper()\n this.show()\n }\n }\n\n _getTemplateFactory(content) {\n if (this._templateFactory) {\n this._templateFactory.changeContent(content)\n } else {\n this._templateFactory = new TemplateFactory({\n ...this._config,\n // the `content` var has to be after `this._config`\n // to override config.content in case of popover\n content,\n extraClass: this._resolvePossibleFunction(this._config.customClass)\n })\n }\n\n return this._templateFactory\n }\n\n _getContentForTemplate() {\n return {\n [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n }\n }\n\n _getTitle() {\n return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title')\n }\n\n // Private\n _initializeOnDelegatedTarget(event) {\n return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig())\n }\n\n _isAnimated() {\n return this._config.animation || (this.tip && this.tip.classList.contains(CLASS_NAME_FADE))\n }\n\n _isShown() {\n return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW)\n }\n\n _createPopper(tip) {\n const placement = execute(this._config.placement, [this, tip, this._element])\n const attachment = AttachmentMap[placement.toUpperCase()]\n return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment))\n }\n\n _getOffset() {\n const { offset } = this._config\n\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10))\n }\n\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element)\n }\n\n return offset\n }\n\n _resolvePossibleFunction(arg) {\n return execute(arg, [this._element])\n }\n\n _getPopperConfig(attachment) {\n const defaultBsPopperConfig = {\n placement: attachment,\n modifiers: [\n {\n name: 'flip',\n options: {\n fallbackPlacements: this._config.fallbackPlacements\n }\n },\n {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n },\n {\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n },\n {\n name: 'arrow',\n options: {\n element: `.${this.constructor.NAME}-arrow`\n }\n },\n {\n name: 'preSetPlacement',\n enabled: true,\n phase: 'beforeMain',\n fn: data => {\n // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n this._getTipElement().setAttribute('data-popper-placement', data.state.placement)\n }\n }\n ]\n }\n\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n }\n }\n\n _setListeners() {\n const triggers = this._config.trigger.split(' ')\n\n for (const trigger of triggers) {\n if (trigger === 'click') {\n EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK), this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event)\n context.toggle()\n })\n } else if (trigger !== TRIGGER_MANUAL) {\n const eventIn = trigger === TRIGGER_HOVER ?\n this.constructor.eventName(EVENT_MOUSEENTER) :\n this.constructor.eventName(EVENT_FOCUSIN)\n const eventOut = trigger === TRIGGER_HOVER ?\n this.constructor.eventName(EVENT_MOUSELEAVE) :\n this.constructor.eventName(EVENT_FOCUSOUT)\n\n EventHandler.on(this._element, eventIn, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event)\n context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true\n context._enter()\n })\n EventHandler.on(this._element, eventOut, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event)\n context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] =\n context._element.contains(event.relatedTarget)\n\n context._leave()\n })\n }\n }\n\n this._hideModalHandler = () => {\n if (this._element) {\n this.hide()\n }\n }\n\n EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n }\n\n _fixTitle() {\n const title = this._element.getAttribute('title')\n\n if (!title) {\n return\n }\n\n if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n this._element.setAttribute('aria-label', title)\n }\n\n this._element.setAttribute('data-bs-original-title', title) // DO NOT USE IT. Is only for backwards compatibility\n this._element.removeAttribute('title')\n }\n\n _enter() {\n if (this._isShown() || this._isHovered) {\n this._isHovered = true\n return\n }\n\n this._isHovered = true\n\n this._setTimeout(() => {\n if (this._isHovered) {\n this.show()\n }\n }, this._config.delay.show)\n }\n\n _leave() {\n if (this._isWithActiveTrigger()) {\n return\n }\n\n this._isHovered = false\n\n this._setTimeout(() => {\n if (!this._isHovered) {\n this.hide()\n }\n }, this._config.delay.hide)\n }\n\n _setTimeout(handler, timeout) {\n clearTimeout(this._timeout)\n this._timeout = setTimeout(handler, timeout)\n }\n\n _isWithActiveTrigger() {\n return Object.values(this._activeTrigger).includes(true)\n }\n\n _getConfig(config) {\n const dataAttributes = Manipulator.getDataAttributes(this._element)\n\n for (const dataAttribute of Object.keys(dataAttributes)) {\n if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n delete dataAttributes[dataAttribute]\n }\n }\n\n config = {\n ...dataAttributes,\n ...(typeof config === 'object' && config ? config : {})\n }\n config = this._mergeConfigObj(config)\n config = this._configAfterMerge(config)\n this._typeCheckConfig(config)\n return config\n }\n\n _configAfterMerge(config) {\n config.container = config.container === false ? document.body : getElement(config.container)\n\n if (typeof config.delay === 'number') {\n config.delay = {\n show: config.delay,\n hide: config.delay\n }\n }\n\n if (typeof config.title === 'number') {\n config.title = config.title.toString()\n }\n\n if (typeof config.content === 'number') {\n config.content = config.content.toString()\n }\n\n return config\n }\n\n _getDelegateConfig() {\n const config = {}\n\n for (const [key, value] of Object.entries(this._config)) {\n if (this.constructor.Default[key] !== value) {\n config[key] = value\n }\n }\n\n config.selector = false\n config.trigger = 'manual'\n\n // In the future can be replaced with:\n // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n // `Object.fromEntries(keysWithDifferentValues)`\n return config\n }\n\n _disposePopper() {\n if (this._popper) {\n this._popper.destroy()\n this._popper = null\n }\n\n if (this.tip) {\n this.tip.remove()\n this.tip = null\n }\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Tooltip.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n })\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tooltip)\n\nexport default Tooltip\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Tooltip from './tooltip.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'popover'\n\nconst SELECTOR_TITLE = '.popover-header'\nconst SELECTOR_CONTENT = '.popover-body'\n\nconst Default = {\n ...Tooltip.Default,\n content: '',\n offset: [0, 8],\n placement: 'right',\n template: '
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' +\n '
' +\n '
',\n trigger: 'click'\n}\n\nconst DefaultType = {\n ...Tooltip.DefaultType,\n content: '(null|string|element|function)'\n}\n\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Overrides\n _isWithContent() {\n return this._getTitle() || this._getContent()\n }\n\n // Private\n _getContentForTemplate() {\n return {\n [SELECTOR_TITLE]: this._getTitle(),\n [SELECTOR_CONTENT]: this._getContent()\n }\n }\n\n _getContent() {\n return this._resolvePossibleFunction(this._config.content)\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Popover.getOrCreateInstance(this, config)\n\n if (typeof config !== 'string') {\n return\n }\n\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`)\n }\n\n data[config]()\n })\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Popover)\n\nexport default Popover\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport { defineJQueryPlugin, getElement, isDisabled, isVisible } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'scrollspy'\nconst DATA_KEY = 'bs.scrollspy'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_ACTIVATE = `activate${EVENT_KEY}`\nconst EVENT_CLICK = `click${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item'\nconst CLASS_NAME_ACTIVE = 'active'\n\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]'\nconst SELECTOR_TARGET_LINKS = '[href]'\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group'\nconst SELECTOR_NAV_LINKS = '.nav-link'\nconst SELECTOR_NAV_ITEMS = '.nav-item'\nconst SELECTOR_LIST_ITEMS = '.list-group-item'\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`\nconst SELECTOR_DROPDOWN = '.dropdown'\nconst SELECTOR_DROPDOWN_TOGGLE = '.dropdown-toggle'\n\nconst Default = {\n offset: null, // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: '0px 0px -25%',\n smoothScroll: false,\n target: null,\n threshold: [0.1, 0.5, 1]\n}\n\nconst DefaultType = {\n offset: '(number|null)', // TODO v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: 'string',\n smoothScroll: 'boolean',\n target: 'element',\n threshold: 'array'\n}\n\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n constructor(element, config) {\n super(element, config)\n\n // this._element is the observablesContainer and config.target the menu links wrapper\n this._targetLinks = new Map()\n this._observableSections = new Map()\n this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element\n this._activeTarget = null\n this._observer = null\n this._previousScrollData = {\n visibleEntryTop: 0,\n parentScrollTop: 0\n }\n this.refresh() // initialize\n }\n\n // Getters\n static get Default() {\n return Default\n }\n\n static get DefaultType() {\n return DefaultType\n }\n\n static get NAME() {\n return NAME\n }\n\n // Public\n refresh() {\n this._initializeTargetsAndObservables()\n this._maybeEnableSmoothScroll()\n\n if (this._observer) {\n this._observer.disconnect()\n } else {\n this._observer = this._getNewObserver()\n }\n\n for (const section of this._observableSections.values()) {\n this._observer.observe(section)\n }\n }\n\n dispose() {\n this._observer.disconnect()\n super.dispose()\n }\n\n // Private\n _configAfterMerge(config) {\n // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n config.target = getElement(config.target) || document.body\n\n // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin\n\n if (typeof config.threshold === 'string') {\n config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value))\n }\n\n return config\n }\n\n _maybeEnableSmoothScroll() {\n if (!this._config.smoothScroll) {\n return\n }\n\n // unregister any previous listeners\n EventHandler.off(this._config.target, EVENT_CLICK)\n\n EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n const observableSection = this._observableSections.get(event.target.hash)\n if (observableSection) {\n event.preventDefault()\n const root = this._rootElement || window\n const height = observableSection.offsetTop - this._element.offsetTop\n if (root.scrollTo) {\n root.scrollTo({ top: height, behavior: 'smooth' })\n return\n }\n\n // Chrome 60 doesn't support `scrollTo`\n root.scrollTop = height\n }\n })\n }\n\n _getNewObserver() {\n const options = {\n root: this._rootElement,\n threshold: this._config.threshold,\n rootMargin: this._config.rootMargin\n }\n\n return new IntersectionObserver(entries => this._observerCallback(entries), options)\n }\n\n // The logic of selection\n _observerCallback(entries) {\n const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`)\n const activate = entry => {\n this._previousScrollData.visibleEntryTop = entry.target.offsetTop\n this._process(targetElement(entry))\n }\n\n const parentScrollTop = (this._rootElement || document.documentElement).scrollTop\n const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop\n this._previousScrollData.parentScrollTop = parentScrollTop\n\n for (const entry of entries) {\n if (!entry.isIntersecting) {\n this._activeTarget = null\n this._clearActiveClass(targetElement(entry))\n\n continue\n }\n\n const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop\n // if we are scrolling down, pick the bigger offsetTop\n if (userScrollsDown && entryIsLowerThanPrevious) {\n activate(entry)\n // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n if (!parentScrollTop) {\n return\n }\n\n continue\n }\n\n // if we are scrolling up, pick the smallest offsetTop\n if (!userScrollsDown && !entryIsLowerThanPrevious) {\n activate(entry)\n }\n }\n }\n\n _initializeTargetsAndObservables() {\n this._targetLinks = new Map()\n this._observableSections = new Map()\n\n const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target)\n\n for (const anchor of targetLinks) {\n // ensure that the anchor has an id and is not disabled\n if (!anchor.hash || isDisabled(anchor)) {\n continue\n }\n\n const observableSection = SelectorEngine.findOne(decodeURI(anchor.hash), this._element)\n\n // ensure that the observableSection exists & is visible\n if (isVisible(observableSection)) {\n this._targetLinks.set(decodeURI(anchor.hash), anchor)\n this._observableSections.set(anchor.hash, observableSection)\n }\n }\n }\n\n _process(target) {\n if (this._activeTarget === target) {\n return\n }\n\n this._clearActiveClass(this._config.target)\n this._activeTarget = target\n target.classList.add(CLASS_NAME_ACTIVE)\n this._activateParents(target)\n\n EventHandler.trigger(this._element, EVENT_ACTIVATE, { relatedTarget: target })\n }\n\n _activateParents(target) {\n // Activate dropdown parents\n if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE, target.closest(SELECTOR_DROPDOWN))\n .classList.add(CLASS_NAME_ACTIVE)\n return\n }\n\n for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n // Set triggered links parents as active\n // With both
    and
')},createChildNavList:function(e){var t=this.createNavList();return e.append(t),t},generateNavEl:function(e,t){var n=a('');n.attr("href","#"+e),n.text(t);var r=a("
  • ");return r.append(n),r},generateNavItem:function(e){var t=this.generateAnchor(e),n=a(e),r=n.data("toc-text")||n.text();return this.generateNavEl(t,r)},getTopLevel:function(e){for(var t=1;t<=6;t++){if(1 + + + + + + + + + + + + + diff --git a/v1.3.1/deps/font-awesome-6.4.2/css/all.css b/v1.3.1/deps/font-awesome-6.4.2/css/all.css new file mode 100644 index 000000000..bdb6e3ae8 --- /dev/null +++ b/v1.3.1/deps/font-awesome-6.4.2/css/all.css @@ -0,0 +1,7968 @@ +/*! + * Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com + * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) + * Copyright 2023 Fonticons, Inc. + */ +.fa { + font-family: var(--fa-style-family, "Font Awesome 6 Free"); + font-weight: var(--fa-style, 900); } + +.fa, +.fa-classic, +.fa-sharp, +.fas, +.fa-solid, +.far, +.fa-regular, +.fab, +.fa-brands { + -moz-osx-font-smoothing: grayscale; + -webkit-font-smoothing: antialiased; + display: var(--fa-display, inline-block); + font-style: normal; + font-variant: normal; + line-height: 1; + text-rendering: auto; } + +.fas, +.fa-classic, +.fa-solid, +.far, +.fa-regular { + font-family: 'Font Awesome 6 Free'; } + +.fab, +.fa-brands { + font-family: 'Font Awesome 6 Brands'; } + +.fa-1x { + font-size: 1em; } + +.fa-2x { + font-size: 2em; } + +.fa-3x { + font-size: 3em; } + +.fa-4x { + font-size: 4em; } + +.fa-5x { + font-size: 5em; } + +.fa-6x { + font-size: 6em; } + +.fa-7x { + font-size: 7em; } + +.fa-8x { + font-size: 8em; } + +.fa-9x { + font-size: 9em; } + +.fa-10x { + font-size: 10em; } + +.fa-2xs { + font-size: 0.625em; + line-height: 0.1em; + vertical-align: 0.225em; } + +.fa-xs { + font-size: 0.75em; + line-height: 0.08333em; + vertical-align: 0.125em; } + +.fa-sm { + font-size: 0.875em; + line-height: 0.07143em; + vertical-align: 0.05357em; } + +.fa-lg { + font-size: 1.25em; + line-height: 0.05em; + vertical-align: -0.075em; } + +.fa-xl { + font-size: 1.5em; + line-height: 0.04167em; + vertical-align: -0.125em; } + +.fa-2xl { + font-size: 2em; + line-height: 0.03125em; + vertical-align: -0.1875em; } + +.fa-fw { + text-align: center; + width: 1.25em; } + +.fa-ul { + list-style-type: none; + margin-left: var(--fa-li-margin, 2.5em); + padding-left: 0; } + .fa-ul > li { + position: relative; } + +.fa-li { + left: calc(var(--fa-li-width, 2em) * -1); + position: absolute; + text-align: center; + width: var(--fa-li-width, 2em); + line-height: inherit; } + +.fa-border { + border-color: var(--fa-border-color, #eee); + border-radius: var(--fa-border-radius, 0.1em); + border-style: var(--fa-border-style, solid); + border-width: var(--fa-border-width, 0.08em); + padding: var(--fa-border-padding, 0.2em 0.25em 0.15em); } + +.fa-pull-left { + float: left; + margin-right: var(--fa-pull-margin, 0.3em); } + +.fa-pull-right { + float: right; + margin-left: var(--fa-pull-margin, 0.3em); } + +.fa-beat { + -webkit-animation-name: fa-beat; + animation-name: fa-beat; + -webkit-animation-delay: var(--fa-animation-delay, 0s); + animation-delay: var(--fa-animation-delay, 0s); + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 1s); + animation-duration: var(--fa-animation-duration, 1s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, ease-in-out); + animation-timing-function: var(--fa-animation-timing, ease-in-out); } + +.fa-bounce { + -webkit-animation-name: fa-bounce; + animation-name: fa-bounce; + -webkit-animation-delay: var(--fa-animation-delay, 0s); + animation-delay: var(--fa-animation-delay, 0s); + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 1s); + animation-duration: var(--fa-animation-duration, 1s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.28, 0.84, 0.42, 1)); + animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.28, 0.84, 0.42, 1)); } + +.fa-fade { + -webkit-animation-name: fa-fade; + animation-name: fa-fade; + -webkit-animation-delay: var(--fa-animation-delay, 0s); + animation-delay: var(--fa-animation-delay, 0s); + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 1s); + animation-duration: var(--fa-animation-duration, 1s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); + animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); } + +.fa-beat-fade { + -webkit-animation-name: fa-beat-fade; + animation-name: fa-beat-fade; + -webkit-animation-delay: var(--fa-animation-delay, 0s); + animation-delay: var(--fa-animation-delay, 0s); + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 1s); + animation-duration: var(--fa-animation-duration, 1s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); + animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); } + +.fa-flip { + -webkit-animation-name: fa-flip; + animation-name: fa-flip; + -webkit-animation-delay: var(--fa-animation-delay, 0s); + animation-delay: var(--fa-animation-delay, 0s); + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 1s); + animation-duration: var(--fa-animation-duration, 1s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, ease-in-out); + animation-timing-function: var(--fa-animation-timing, ease-in-out); } + +.fa-shake { + -webkit-animation-name: fa-shake; + animation-name: fa-shake; + -webkit-animation-delay: var(--fa-animation-delay, 0s); + animation-delay: var(--fa-animation-delay, 0s); + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 1s); + animation-duration: var(--fa-animation-duration, 1s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, linear); + animation-timing-function: var(--fa-animation-timing, linear); } + +.fa-spin { + -webkit-animation-name: fa-spin; + animation-name: fa-spin; + -webkit-animation-delay: var(--fa-animation-delay, 0s); + animation-delay: var(--fa-animation-delay, 0s); + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 2s); + animation-duration: var(--fa-animation-duration, 2s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, linear); + animation-timing-function: var(--fa-animation-timing, linear); } + +.fa-spin-reverse { + --fa-animation-direction: reverse; } + +.fa-pulse, +.fa-spin-pulse { + -webkit-animation-name: fa-spin; + animation-name: fa-spin; + -webkit-animation-direction: var(--fa-animation-direction, normal); + animation-direction: var(--fa-animation-direction, normal); + -webkit-animation-duration: var(--fa-animation-duration, 1s); + animation-duration: var(--fa-animation-duration, 1s); + -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite); + animation-iteration-count: var(--fa-animation-iteration-count, infinite); + -webkit-animation-timing-function: var(--fa-animation-timing, steps(8)); + animation-timing-function: var(--fa-animation-timing, steps(8)); } + +@media (prefers-reduced-motion: reduce) { + .fa-beat, + .fa-bounce, + .fa-fade, + .fa-beat-fade, + .fa-flip, + .fa-pulse, + .fa-shake, + .fa-spin, + .fa-spin-pulse { + -webkit-animation-delay: -1ms; + animation-delay: -1ms; + -webkit-animation-duration: 1ms; + animation-duration: 1ms; + -webkit-animation-iteration-count: 1; + animation-iteration-count: 1; + -webkit-transition-delay: 0s; + transition-delay: 0s; + -webkit-transition-duration: 0s; + transition-duration: 0s; } } + +@-webkit-keyframes fa-beat { + 0%, 90% { + -webkit-transform: scale(1); + transform: scale(1); } + 45% { + -webkit-transform: scale(var(--fa-beat-scale, 1.25)); + transform: scale(var(--fa-beat-scale, 1.25)); } } + +@keyframes fa-beat { + 0%, 90% { + -webkit-transform: scale(1); + transform: scale(1); } + 45% { + -webkit-transform: scale(var(--fa-beat-scale, 1.25)); + transform: scale(var(--fa-beat-scale, 1.25)); } } + +@-webkit-keyframes fa-bounce { + 0% { + -webkit-transform: scale(1, 1) translateY(0); + transform: scale(1, 1) translateY(0); } + 10% { + -webkit-transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); + transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); } + 30% { + -webkit-transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); + transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); } + 50% { + -webkit-transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); + transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); } + 57% { + -webkit-transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); + transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); } + 64% { + -webkit-transform: scale(1, 1) translateY(0); + transform: scale(1, 1) translateY(0); } + 100% { + -webkit-transform: scale(1, 1) translateY(0); + transform: scale(1, 1) translateY(0); } } + +@keyframes fa-bounce { + 0% { + -webkit-transform: scale(1, 1) translateY(0); + transform: scale(1, 1) translateY(0); } + 10% { + -webkit-transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); + transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); } + 30% { + -webkit-transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); + transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); } + 50% { + -webkit-transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); + transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); } + 57% { + -webkit-transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); + transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); } + 64% { + -webkit-transform: scale(1, 1) translateY(0); + transform: scale(1, 1) translateY(0); } + 100% { + -webkit-transform: scale(1, 1) translateY(0); + transform: scale(1, 1) translateY(0); } } + +@-webkit-keyframes fa-fade { + 50% { + opacity: var(--fa-fade-opacity, 0.4); } } + +@keyframes fa-fade { + 50% { + opacity: var(--fa-fade-opacity, 0.4); } } + +@-webkit-keyframes fa-beat-fade { + 0%, 100% { + opacity: var(--fa-beat-fade-opacity, 0.4); + -webkit-transform: scale(1); + transform: scale(1); } + 50% { + opacity: 1; + -webkit-transform: scale(var(--fa-beat-fade-scale, 1.125)); + transform: scale(var(--fa-beat-fade-scale, 1.125)); } } + +@keyframes fa-beat-fade { + 0%, 100% { + opacity: var(--fa-beat-fade-opacity, 0.4); + -webkit-transform: scale(1); + transform: scale(1); } + 50% { + opacity: 1; + -webkit-transform: scale(var(--fa-beat-fade-scale, 1.125)); + transform: scale(var(--fa-beat-fade-scale, 1.125)); } } + +@-webkit-keyframes fa-flip { + 50% { + -webkit-transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); + transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); } } + +@keyframes fa-flip { + 50% { + -webkit-transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); + transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); } } + +@-webkit-keyframes fa-shake { + 0% { + -webkit-transform: rotate(-15deg); + transform: rotate(-15deg); } + 4% { + -webkit-transform: rotate(15deg); + transform: rotate(15deg); } + 8%, 24% { + -webkit-transform: rotate(-18deg); + transform: rotate(-18deg); } + 12%, 28% { + -webkit-transform: rotate(18deg); + transform: rotate(18deg); } + 16% { + -webkit-transform: rotate(-22deg); + transform: rotate(-22deg); } + 20% { + -webkit-transform: rotate(22deg); + transform: rotate(22deg); } + 32% { + -webkit-transform: rotate(-12deg); + transform: rotate(-12deg); } + 36% { + -webkit-transform: rotate(12deg); + transform: rotate(12deg); } + 40%, 100% { + -webkit-transform: rotate(0deg); + transform: rotate(0deg); } } + +@keyframes fa-shake { + 0% { + -webkit-transform: rotate(-15deg); + transform: rotate(-15deg); } + 4% { + -webkit-transform: rotate(15deg); + transform: rotate(15deg); } + 8%, 24% { + -webkit-transform: rotate(-18deg); + transform: rotate(-18deg); } + 12%, 28% { + -webkit-transform: rotate(18deg); + transform: rotate(18deg); } + 16% { + -webkit-transform: rotate(-22deg); + transform: rotate(-22deg); } + 20% { + -webkit-transform: rotate(22deg); + transform: rotate(22deg); } + 32% { + -webkit-transform: rotate(-12deg); + transform: rotate(-12deg); } + 36% { + -webkit-transform: rotate(12deg); + transform: rotate(12deg); } + 40%, 100% { + -webkit-transform: rotate(0deg); + transform: rotate(0deg); } } + +@-webkit-keyframes fa-spin { + 0% { + -webkit-transform: rotate(0deg); + transform: rotate(0deg); } + 100% { + -webkit-transform: rotate(360deg); + transform: rotate(360deg); } } + +@keyframes fa-spin { + 0% { + -webkit-transform: rotate(0deg); + transform: rotate(0deg); } + 100% { + -webkit-transform: rotate(360deg); + transform: rotate(360deg); } } + +.fa-rotate-90 { + -webkit-transform: rotate(90deg); + transform: rotate(90deg); } + +.fa-rotate-180 { + -webkit-transform: rotate(180deg); + transform: rotate(180deg); } + +.fa-rotate-270 { + -webkit-transform: rotate(270deg); + transform: rotate(270deg); } + +.fa-flip-horizontal { + -webkit-transform: scale(-1, 1); + transform: scale(-1, 1); } + +.fa-flip-vertical { + -webkit-transform: scale(1, -1); + transform: scale(1, -1); } + +.fa-flip-both, +.fa-flip-horizontal.fa-flip-vertical { + -webkit-transform: scale(-1, -1); + transform: scale(-1, -1); } + +.fa-rotate-by { + -webkit-transform: rotate(var(--fa-rotate-angle, none)); + transform: rotate(var(--fa-rotate-angle, none)); } + +.fa-stack { + display: inline-block; + height: 2em; + line-height: 2em; + position: relative; + vertical-align: middle; + width: 2.5em; } + +.fa-stack-1x, +.fa-stack-2x { + left: 0; + position: absolute; + text-align: center; + width: 100%; + z-index: var(--fa-stack-z-index, auto); } + +.fa-stack-1x { + line-height: inherit; } + +.fa-stack-2x { + font-size: 2em; } + +.fa-inverse { + color: var(--fa-inverse, #fff); } + +/* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen +readers do not read off random characters that represent icons */ + +.fa-0::before { + content: "\30"; } + +.fa-1::before { + content: "\31"; } + +.fa-2::before { + content: "\32"; } + +.fa-3::before { + content: "\33"; } + +.fa-4::before { + content: "\34"; } + +.fa-5::before { + content: "\35"; } + +.fa-6::before { + content: "\36"; } + +.fa-7::before { + content: "\37"; } + +.fa-8::before { + content: "\38"; } + +.fa-9::before { + content: "\39"; } + +.fa-fill-drip::before { + content: "\f576"; } + +.fa-arrows-to-circle::before { + content: "\e4bd"; } + +.fa-circle-chevron-right::before { + content: "\f138"; } + +.fa-chevron-circle-right::before { + content: "\f138"; } + +.fa-at::before { + content: "\40"; } + +.fa-trash-can::before { + content: "\f2ed"; } + +.fa-trash-alt::before { + content: "\f2ed"; } + +.fa-text-height::before { + content: "\f034"; } + +.fa-user-xmark::before { + content: "\f235"; } + +.fa-user-times::before { + content: "\f235"; } + +.fa-stethoscope::before { + content: "\f0f1"; } + +.fa-message::before { + content: "\f27a"; } + +.fa-comment-alt::before { + content: "\f27a"; } + +.fa-info::before { + content: "\f129"; } + +.fa-down-left-and-up-right-to-center::before { + content: "\f422"; } + +.fa-compress-alt::before { + content: "\f422"; } + +.fa-explosion::before { + content: "\e4e9"; } + +.fa-file-lines::before { + content: "\f15c"; } + +.fa-file-alt::before { + content: "\f15c"; } + +.fa-file-text::before { + content: "\f15c"; } + +.fa-wave-square::before { + content: "\f83e"; } + +.fa-ring::before { + content: "\f70b"; } + +.fa-building-un::before { + content: "\e4d9"; } + +.fa-dice-three::before { + content: "\f527"; } + +.fa-calendar-days::before { + content: "\f073"; } + +.fa-calendar-alt::before { + content: "\f073"; } + +.fa-anchor-circle-check::before { + content: "\e4aa"; } + +.fa-building-circle-arrow-right::before { + content: "\e4d1"; } + +.fa-volleyball::before { + content: "\f45f"; } + +.fa-volleyball-ball::before { + content: "\f45f"; } + +.fa-arrows-up-to-line::before { + content: "\e4c2"; } + +.fa-sort-down::before { + content: "\f0dd"; } + +.fa-sort-desc::before { + content: "\f0dd"; } + +.fa-circle-minus::before { + content: "\f056"; } + +.fa-minus-circle::before { + content: "\f056"; } + +.fa-door-open::before { + content: "\f52b"; } + +.fa-right-from-bracket::before { + content: "\f2f5"; } + +.fa-sign-out-alt::before { + content: "\f2f5"; } + +.fa-atom::before { + content: "\f5d2"; } + +.fa-soap::before { + content: "\e06e"; } + +.fa-icons::before { + content: "\f86d"; } + +.fa-heart-music-camera-bolt::before { + content: "\f86d"; } + +.fa-microphone-lines-slash::before { + content: "\f539"; } + +.fa-microphone-alt-slash::before { + content: "\f539"; } + +.fa-bridge-circle-check::before { + content: "\e4c9"; } + +.fa-pump-medical::before { + content: "\e06a"; } + +.fa-fingerprint::before { + content: "\f577"; } + +.fa-hand-point-right::before { + content: "\f0a4"; } + +.fa-magnifying-glass-location::before { + content: "\f689"; } + +.fa-search-location::before { + content: "\f689"; } + +.fa-forward-step::before { + content: "\f051"; } + +.fa-step-forward::before { + content: "\f051"; } + +.fa-face-smile-beam::before { + content: "\f5b8"; } + +.fa-smile-beam::before { + content: "\f5b8"; } + +.fa-flag-checkered::before { + content: "\f11e"; } + +.fa-football::before { + content: "\f44e"; } + +.fa-football-ball::before { + content: "\f44e"; } + +.fa-school-circle-exclamation::before { + content: "\e56c"; } + +.fa-crop::before { + content: "\f125"; } + +.fa-angles-down::before { + content: "\f103"; } + +.fa-angle-double-down::before { + content: "\f103"; } + +.fa-users-rectangle::before { + content: "\e594"; } + +.fa-people-roof::before { + content: "\e537"; } + +.fa-people-line::before { + content: "\e534"; } + +.fa-beer-mug-empty::before { + content: "\f0fc"; } + +.fa-beer::before { + content: "\f0fc"; } + +.fa-diagram-predecessor::before { + content: "\e477"; } + +.fa-arrow-up-long::before { + content: "\f176"; } + +.fa-long-arrow-up::before { + content: "\f176"; } + +.fa-fire-flame-simple::before { + content: "\f46a"; } + +.fa-burn::before { + content: "\f46a"; } + +.fa-person::before { + content: "\f183"; } + +.fa-male::before { + content: "\f183"; } + +.fa-laptop::before { + content: "\f109"; } + +.fa-file-csv::before { + content: "\f6dd"; } + +.fa-menorah::before { + content: "\f676"; } + +.fa-truck-plane::before { + content: "\e58f"; } + +.fa-record-vinyl::before { + content: "\f8d9"; } + +.fa-face-grin-stars::before { + content: "\f587"; } + +.fa-grin-stars::before { + content: "\f587"; } + +.fa-bong::before { + content: "\f55c"; } + +.fa-spaghetti-monster-flying::before { + content: "\f67b"; } + +.fa-pastafarianism::before { + content: "\f67b"; } + +.fa-arrow-down-up-across-line::before { + content: "\e4af"; } + +.fa-spoon::before { + content: "\f2e5"; } + +.fa-utensil-spoon::before { + content: "\f2e5"; } + +.fa-jar-wheat::before { + content: "\e517"; } + +.fa-envelopes-bulk::before { + content: "\f674"; } + +.fa-mail-bulk::before { + content: "\f674"; } + +.fa-file-circle-exclamation::before { + content: "\e4eb"; } + +.fa-circle-h::before { + content: "\f47e"; } + +.fa-hospital-symbol::before { + content: "\f47e"; } + +.fa-pager::before { + content: "\f815"; } + +.fa-address-book::before { + content: "\f2b9"; } + +.fa-contact-book::before { + content: "\f2b9"; } + +.fa-strikethrough::before { + content: "\f0cc"; } + +.fa-k::before { + content: "\4b"; } + +.fa-landmark-flag::before { + content: "\e51c"; } + +.fa-pencil::before { + content: "\f303"; } + +.fa-pencil-alt::before { + content: "\f303"; } + +.fa-backward::before { + content: "\f04a"; } + +.fa-caret-right::before { + content: "\f0da"; } + +.fa-comments::before { + content: "\f086"; } + +.fa-paste::before { + content: "\f0ea"; } + +.fa-file-clipboard::before { + content: "\f0ea"; } + +.fa-code-pull-request::before { + content: "\e13c"; } + +.fa-clipboard-list::before { + content: "\f46d"; } + +.fa-truck-ramp-box::before { + content: "\f4de"; } + +.fa-truck-loading::before { + content: "\f4de"; } + +.fa-user-check::before { + content: "\f4fc"; } + +.fa-vial-virus::before { + content: "\e597"; } + +.fa-sheet-plastic::before { + content: "\e571"; } + +.fa-blog::before { + content: "\f781"; } + +.fa-user-ninja::before { + content: "\f504"; } + +.fa-person-arrow-up-from-line::before { + content: "\e539"; } + +.fa-scroll-torah::before { + content: "\f6a0"; } + +.fa-torah::before { + content: "\f6a0"; } + +.fa-broom-ball::before { + content: "\f458"; } + +.fa-quidditch::before { + content: "\f458"; } + +.fa-quidditch-broom-ball::before { + content: "\f458"; } + +.fa-toggle-off::before { + content: "\f204"; } + +.fa-box-archive::before { + content: "\f187"; } + +.fa-archive::before { + content: "\f187"; } + +.fa-person-drowning::before { + content: "\e545"; } + +.fa-arrow-down-9-1::before { + content: "\f886"; } + +.fa-sort-numeric-desc::before { + content: "\f886"; } + +.fa-sort-numeric-down-alt::before { + content: "\f886"; } + +.fa-face-grin-tongue-squint::before { + content: "\f58a"; } + +.fa-grin-tongue-squint::before { + content: "\f58a"; } + +.fa-spray-can::before { + content: "\f5bd"; } + +.fa-truck-monster::before { + content: "\f63b"; } + +.fa-w::before { + content: "\57"; } + +.fa-earth-africa::before { + content: "\f57c"; } + +.fa-globe-africa::before { + content: "\f57c"; } + +.fa-rainbow::before { + content: "\f75b"; } + +.fa-circle-notch::before { + content: "\f1ce"; } + +.fa-tablet-screen-button::before { + content: "\f3fa"; } + +.fa-tablet-alt::before { + content: "\f3fa"; } + +.fa-paw::before { + content: "\f1b0"; } + +.fa-cloud::before { + content: "\f0c2"; } + +.fa-trowel-bricks::before { + content: "\e58a"; } + +.fa-face-flushed::before { + content: "\f579"; } + +.fa-flushed::before { + content: "\f579"; } + +.fa-hospital-user::before { + content: "\f80d"; } + +.fa-tent-arrow-left-right::before { + content: "\e57f"; } + +.fa-gavel::before { + content: "\f0e3"; } + +.fa-legal::before { + content: "\f0e3"; } + +.fa-binoculars::before { + content: "\f1e5"; } + +.fa-microphone-slash::before { + content: "\f131"; } + +.fa-box-tissue::before { + content: "\e05b"; } + +.fa-motorcycle::before { + content: "\f21c"; } + +.fa-bell-concierge::before { + content: "\f562"; } + +.fa-concierge-bell::before { + content: "\f562"; } + +.fa-pen-ruler::before { + content: "\f5ae"; } + +.fa-pencil-ruler::before { + content: "\f5ae"; } + +.fa-people-arrows::before { + content: "\e068"; } + +.fa-people-arrows-left-right::before { + content: "\e068"; } + +.fa-mars-and-venus-burst::before { + content: "\e523"; } + +.fa-square-caret-right::before { + content: "\f152"; } + +.fa-caret-square-right::before { + content: "\f152"; } + +.fa-scissors::before { + content: "\f0c4"; } + +.fa-cut::before { + content: "\f0c4"; } + +.fa-sun-plant-wilt::before { + content: "\e57a"; } + +.fa-toilets-portable::before { + content: "\e584"; } + +.fa-hockey-puck::before { + content: "\f453"; } + +.fa-table::before { + content: "\f0ce"; } + +.fa-magnifying-glass-arrow-right::before { + content: "\e521"; } + +.fa-tachograph-digital::before { + content: "\f566"; } + +.fa-digital-tachograph::before { + content: "\f566"; } + +.fa-users-slash::before { + content: "\e073"; } + +.fa-clover::before { + content: "\e139"; } + +.fa-reply::before { + content: "\f3e5"; } + +.fa-mail-reply::before { + content: "\f3e5"; } + +.fa-star-and-crescent::before { + content: "\f699"; } + +.fa-house-fire::before { + content: "\e50c"; } + +.fa-square-minus::before { + content: "\f146"; } + +.fa-minus-square::before { + content: "\f146"; } + +.fa-helicopter::before { + content: "\f533"; } + +.fa-compass::before { + content: "\f14e"; } + +.fa-square-caret-down::before { + content: "\f150"; } + +.fa-caret-square-down::before { + content: "\f150"; } + +.fa-file-circle-question::before { + content: "\e4ef"; } + +.fa-laptop-code::before { + content: "\f5fc"; } + +.fa-swatchbook::before { + content: "\f5c3"; } + +.fa-prescription-bottle::before { + content: "\f485"; } + +.fa-bars::before { + content: "\f0c9"; } + +.fa-navicon::before { + content: "\f0c9"; } + +.fa-people-group::before { + content: "\e533"; } + +.fa-hourglass-end::before { + content: "\f253"; } + +.fa-hourglass-3::before { + content: "\f253"; } + +.fa-heart-crack::before { + content: "\f7a9"; } + +.fa-heart-broken::before { + content: "\f7a9"; } + +.fa-square-up-right::before { + content: "\f360"; } + +.fa-external-link-square-alt::before { + content: "\f360"; } + +.fa-face-kiss-beam::before { + content: "\f597"; } + +.fa-kiss-beam::before { + content: "\f597"; } + +.fa-film::before { + content: "\f008"; } + +.fa-ruler-horizontal::before { + content: "\f547"; } + +.fa-people-robbery::before { + content: "\e536"; } + +.fa-lightbulb::before { + content: "\f0eb"; } + +.fa-caret-left::before { + content: "\f0d9"; } + +.fa-circle-exclamation::before { + content: "\f06a"; } + +.fa-exclamation-circle::before { + content: "\f06a"; } + +.fa-school-circle-xmark::before { + content: "\e56d"; } + +.fa-arrow-right-from-bracket::before { + content: "\f08b"; } + +.fa-sign-out::before { + content: "\f08b"; } + +.fa-circle-chevron-down::before { + content: "\f13a"; } + +.fa-chevron-circle-down::before { + content: "\f13a"; } + +.fa-unlock-keyhole::before { + content: "\f13e"; } + +.fa-unlock-alt::before { + content: "\f13e"; } + +.fa-cloud-showers-heavy::before { + content: "\f740"; } + +.fa-headphones-simple::before { + content: "\f58f"; } + +.fa-headphones-alt::before { + content: "\f58f"; } + +.fa-sitemap::before { + content: "\f0e8"; } + +.fa-circle-dollar-to-slot::before { + content: "\f4b9"; } + +.fa-donate::before { + content: "\f4b9"; } + +.fa-memory::before { + content: "\f538"; } + +.fa-road-spikes::before { + content: "\e568"; } + +.fa-fire-burner::before { + content: "\e4f1"; } + +.fa-flag::before { + content: "\f024"; } + +.fa-hanukiah::before { + content: "\f6e6"; } + +.fa-feather::before { + content: "\f52d"; } + +.fa-volume-low::before { + content: "\f027"; } + +.fa-volume-down::before { + content: "\f027"; } + +.fa-comment-slash::before { + content: "\f4b3"; } + +.fa-cloud-sun-rain::before { + content: "\f743"; } + +.fa-compress::before { + content: "\f066"; } + +.fa-wheat-awn::before { + content: "\e2cd"; } + +.fa-wheat-alt::before { + content: "\e2cd"; } + +.fa-ankh::before { + content: "\f644"; } + +.fa-hands-holding-child::before { + content: "\e4fa"; } + +.fa-asterisk::before { + content: "\2a"; } + +.fa-square-check::before { + content: "\f14a"; } + +.fa-check-square::before { + content: "\f14a"; } + +.fa-peseta-sign::before { + content: "\e221"; } + +.fa-heading::before { + content: "\f1dc"; } + +.fa-header::before { + content: "\f1dc"; } + +.fa-ghost::before { + content: "\f6e2"; } + +.fa-list::before { + content: "\f03a"; } + +.fa-list-squares::before { + content: "\f03a"; } + +.fa-square-phone-flip::before { + content: "\f87b"; } + +.fa-phone-square-alt::before { + content: "\f87b"; } + +.fa-cart-plus::before { + content: "\f217"; } + +.fa-gamepad::before { + content: "\f11b"; } + +.fa-circle-dot::before { + content: "\f192"; } + +.fa-dot-circle::before { + content: "\f192"; } + +.fa-face-dizzy::before { + content: "\f567"; } + +.fa-dizzy::before { + content: "\f567"; } + +.fa-egg::before { + content: "\f7fb"; } + +.fa-house-medical-circle-xmark::before { + content: "\e513"; } + +.fa-campground::before { + content: "\f6bb"; } + +.fa-folder-plus::before { + content: "\f65e"; } + +.fa-futbol::before { + content: "\f1e3"; } + +.fa-futbol-ball::before { + content: "\f1e3"; } + +.fa-soccer-ball::before { + content: "\f1e3"; } + +.fa-paintbrush::before { + content: "\f1fc"; } + +.fa-paint-brush::before { + content: "\f1fc"; } + +.fa-lock::before { + content: "\f023"; } + +.fa-gas-pump::before { + content: "\f52f"; } + +.fa-hot-tub-person::before { + content: "\f593"; } + +.fa-hot-tub::before { + content: "\f593"; } + +.fa-map-location::before { + content: "\f59f"; } + +.fa-map-marked::before { + content: "\f59f"; } + +.fa-house-flood-water::before { + content: "\e50e"; } + +.fa-tree::before { + content: "\f1bb"; } + +.fa-bridge-lock::before { + content: "\e4cc"; } + +.fa-sack-dollar::before { + content: "\f81d"; } + +.fa-pen-to-square::before { + content: "\f044"; } + +.fa-edit::before { + content: "\f044"; } + +.fa-car-side::before { + content: "\f5e4"; } + +.fa-share-nodes::before { + content: "\f1e0"; } + +.fa-share-alt::before { + content: "\f1e0"; } + +.fa-heart-circle-minus::before { + content: "\e4ff"; } + +.fa-hourglass-half::before { + content: "\f252"; } + +.fa-hourglass-2::before { + content: "\f252"; } + +.fa-microscope::before { + content: "\f610"; } + +.fa-sink::before { + content: "\e06d"; } + +.fa-bag-shopping::before { + content: "\f290"; } + +.fa-shopping-bag::before { + content: "\f290"; } + +.fa-arrow-down-z-a::before { + content: "\f881"; } + +.fa-sort-alpha-desc::before { + content: "\f881"; } + +.fa-sort-alpha-down-alt::before { + content: "\f881"; } + +.fa-mitten::before { + content: "\f7b5"; } + 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content: "\f0a8"; } + +.fa-group-arrows-rotate::before { + content: "\e4f6"; } + +.fa-bowl-food::before { + content: "\e4c6"; } + +.fa-candy-cane::before { + content: "\f786"; } + +.fa-arrow-down-wide-short::before { + content: "\f160"; } + +.fa-sort-amount-asc::before { + content: "\f160"; } + +.fa-sort-amount-down::before { + content: "\f160"; } + +.fa-cloud-bolt::before { + content: "\f76c"; } + +.fa-thunderstorm::before { + content: "\f76c"; } + +.fa-text-slash::before { + content: "\f87d"; } + +.fa-remove-format::before { + content: "\f87d"; } + +.fa-face-smile-wink::before { + content: "\f4da"; } + +.fa-smile-wink::before { + content: "\f4da"; } + +.fa-file-word::before { + content: "\f1c2"; } + +.fa-file-powerpoint::before { + content: "\f1c4"; } + +.fa-arrows-left-right::before { + content: "\f07e"; } + +.fa-arrows-h::before { + content: "\f07e"; } + +.fa-house-lock::before { + content: "\e510"; } + +.fa-cloud-arrow-down::before { + content: "\f0ed"; } + 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content: "\f3ed"; } + +.fa-shield-alt::before { + content: "\f3ed"; } + +.fa-book-atlas::before { + content: "\f558"; } + +.fa-atlas::before { + content: "\f558"; } + +.fa-virus::before { + content: "\e074"; } + +.fa-envelope-circle-check::before { + content: "\e4e8"; } + +.fa-layer-group::before { + content: "\f5fd"; } + +.fa-arrows-to-dot::before { + content: "\e4be"; } + +.fa-archway::before { + content: "\f557"; } + +.fa-heart-circle-check::before { + content: "\e4fd"; } + +.fa-house-chimney-crack::before { + content: "\f6f1"; } + +.fa-house-damage::before { + content: "\f6f1"; } + +.fa-file-zipper::before { + content: "\f1c6"; } + +.fa-file-archive::before { + content: "\f1c6"; } + +.fa-square::before { + content: "\f0c8"; } + +.fa-martini-glass-empty::before { + content: "\f000"; } + +.fa-glass-martini::before { + content: "\f000"; } + +.fa-couch::before { + content: "\f4b8"; } + +.fa-cedi-sign::before { + content: "\e0df"; } + +.fa-italic::before { + content: "\f033"; } + 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} + +.fa-locust::before { + content: "\e520"; } + +.fa-sort::before { + content: "\f0dc"; } + +.fa-unsorted::before { + content: "\f0dc"; } + +.fa-list-ol::before { + content: "\f0cb"; } + +.fa-list-1-2::before { + content: "\f0cb"; } + +.fa-list-numeric::before { + content: "\f0cb"; } + +.fa-person-dress-burst::before { + content: "\e544"; } + +.fa-money-check-dollar::before { + content: "\f53d"; } + +.fa-money-check-alt::before { + content: "\f53d"; } + +.fa-vector-square::before { + content: "\f5cb"; } + +.fa-bread-slice::before { + content: "\f7ec"; } + +.fa-language::before { + content: "\f1ab"; } + +.fa-face-kiss-wink-heart::before { + content: "\f598"; } + +.fa-kiss-wink-heart::before { + content: "\f598"; } + +.fa-filter::before { + content: "\f0b0"; } + +.fa-question::before { + content: "\3f"; } + +.fa-file-signature::before { + content: "\f573"; } + +.fa-up-down-left-right::before { + content: "\f0b2"; } + +.fa-arrows-alt::before { + content: "\f0b2"; } + 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content: "\e0a9"; } + +.fa-f::before { + content: "\46"; } + +.fa-leaf::before { + content: "\f06c"; } + +.fa-road::before { + content: "\f018"; } + +.fa-taxi::before { + content: "\f1ba"; } + +.fa-cab::before { + content: "\f1ba"; } + +.fa-person-circle-plus::before { + content: "\e541"; } + +.fa-chart-pie::before { + content: "\f200"; } + +.fa-pie-chart::before { + content: "\f200"; } + +.fa-bolt-lightning::before { + content: "\e0b7"; } + +.fa-sack-xmark::before { + content: "\e56a"; } + +.fa-file-excel::before { + content: "\f1c3"; } + +.fa-file-contract::before { + content: "\f56c"; } + +.fa-fish-fins::before { + content: "\e4f2"; } + +.fa-building-flag::before { + content: "\e4d5"; } + +.fa-face-grin-beam::before { + content: "\f582"; } + +.fa-grin-beam::before { + content: "\f582"; } + +.fa-object-ungroup::before { + content: "\f248"; } + +.fa-poop::before { + content: "\f619"; } + +.fa-location-pin::before { + content: "\f041"; } + +.fa-map-marker::before { + content: "\f041"; } + +.fa-kaaba::before { + content: "\f66b"; } + +.fa-toilet-paper::before { + content: "\f71e"; } + +.fa-helmet-safety::before { + content: "\f807"; } + +.fa-hard-hat::before { + content: "\f807"; } + +.fa-hat-hard::before { + content: "\f807"; } + +.fa-eject::before { + content: "\f052"; } + +.fa-circle-right::before { + content: "\f35a"; } + +.fa-arrow-alt-circle-right::before { + content: "\f35a"; } + +.fa-plane-circle-check::before { + content: "\e555"; } + +.fa-face-rolling-eyes::before { + content: "\f5a5"; } + +.fa-meh-rolling-eyes::before { + content: "\f5a5"; } + +.fa-object-group::before { + content: "\f247"; } + +.fa-chart-line::before { + content: "\f201"; } + +.fa-line-chart::before { + content: "\f201"; } + +.fa-mask-ventilator::before { + content: "\e524"; } + +.fa-arrow-right::before { + content: "\f061"; } + +.fa-signs-post::before { + content: "\f277"; } + +.fa-map-signs::before { + content: "\f277"; } + +.fa-cash-register::before { + content: "\f788"; } + 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content: "\f885"; } + +.fa-house-medical::before { + content: "\e3b2"; } + +.fa-golf-ball-tee::before { + content: "\f450"; } + +.fa-golf-ball::before { + content: "\f450"; } + +.fa-circle-chevron-left::before { + content: "\f137"; } + +.fa-chevron-circle-left::before { + content: "\f137"; } + +.fa-house-chimney-window::before { + content: "\e00d"; } + +.fa-pen-nib::before { + content: "\f5ad"; } + +.fa-tent-arrow-turn-left::before { + content: "\e580"; } + +.fa-tents::before { + content: "\e582"; } + +.fa-wand-magic::before { + content: "\f0d0"; } + +.fa-magic::before { + content: "\f0d0"; } + +.fa-dog::before { + content: "\f6d3"; } + +.fa-carrot::before { + content: "\f787"; } + +.fa-moon::before { + content: "\f186"; } + +.fa-wine-glass-empty::before { + content: "\f5ce"; } + +.fa-wine-glass-alt::before { + content: "\f5ce"; } + +.fa-cheese::before { + content: "\f7ef"; } + +.fa-yin-yang::before { + content: "\f6ad"; } + +.fa-music::before { + content: "\f001"; } + 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{ + content: "\f234"; } + +.fa-check::before { + content: "\f00c"; } + +.fa-battery-three-quarters::before { + content: "\f241"; } + +.fa-battery-4::before { + content: "\f241"; } + +.fa-house-circle-check::before { + content: "\e509"; } + +.fa-angle-left::before { + content: "\f104"; } + +.fa-diagram-successor::before { + content: "\e47a"; } + +.fa-truck-arrow-right::before { + content: "\e58b"; } + +.fa-arrows-split-up-and-left::before { + content: "\e4bc"; } + +.fa-hand-fist::before { + content: "\f6de"; } + +.fa-fist-raised::before { + content: "\f6de"; } + +.fa-cloud-moon::before { + content: "\f6c3"; } + +.fa-briefcase::before { + content: "\f0b1"; } + +.fa-person-falling::before { + content: "\e546"; } + +.fa-image-portrait::before { + content: "\f3e0"; } + +.fa-portrait::before { + content: "\f3e0"; } + +.fa-user-tag::before { + content: "\f507"; } + +.fa-rug::before { + content: "\e569"; } + +.fa-earth-europe::before { + content: "\f7a2"; } + +.fa-globe-europe::before { + content: "\f7a2"; } + +.fa-cart-flatbed-suitcase::before { + content: "\f59d"; } + +.fa-luggage-cart::before { + content: "\f59d"; } + +.fa-rectangle-xmark::before { + content: "\f410"; } + +.fa-rectangle-times::before { + content: "\f410"; } + +.fa-times-rectangle::before { + content: "\f410"; } + +.fa-window-close::before { + content: "\f410"; } + +.fa-baht-sign::before { + content: "\e0ac"; } + +.fa-book-open::before { + content: "\f518"; } + +.fa-book-journal-whills::before { + content: "\f66a"; } + +.fa-journal-whills::before { + content: "\f66a"; } + +.fa-handcuffs::before { + content: "\e4f8"; } + +.fa-triangle-exclamation::before { + content: "\f071"; } + +.fa-exclamation-triangle::before { + content: "\f071"; } + +.fa-warning::before { + content: "\f071"; } + +.fa-database::before { + content: "\f1c0"; } + +.fa-share::before { + content: "\f064"; } + +.fa-arrow-turn-right::before { + content: "\f064"; } + +.fa-mail-forward::before { + content: "\f064"; } + 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+.fa-xmark-circle::before { + content: "\f057"; } + +.fa-gifts::before { + content: "\f79c"; } + +.fa-hotel::before { + content: "\f594"; } + +.fa-earth-asia::before { + content: "\f57e"; } + +.fa-globe-asia::before { + content: "\f57e"; } + +.fa-id-card-clip::before { + content: "\f47f"; } + +.fa-id-card-alt::before { + content: "\f47f"; } + +.fa-magnifying-glass-plus::before { + content: "\f00e"; } + +.fa-search-plus::before { + content: "\f00e"; } + +.fa-thumbs-up::before { + content: "\f164"; } + +.fa-user-clock::before { + content: "\f4fd"; } + +.fa-hand-dots::before { + content: "\f461"; } + +.fa-allergies::before { + content: "\f461"; } + +.fa-file-invoice::before { + content: "\f570"; } + +.fa-window-minimize::before { + content: "\f2d1"; } + +.fa-mug-saucer::before { + content: "\f0f4"; } + +.fa-coffee::before { + content: "\f0f4"; } + +.fa-brush::before { + content: "\f55d"; } + +.fa-mask::before { + content: "\f6fa"; } + +.fa-magnifying-glass-minus::before { + content: "\f010"; } + +.fa-search-minus::before { + content: "\f010"; } + +.fa-ruler-vertical::before { + content: "\f548"; } + +.fa-user-large::before { + content: "\f406"; } + +.fa-user-alt::before { + content: "\f406"; } + +.fa-train-tram::before { + content: "\e5b4"; } + +.fa-user-nurse::before { + content: "\f82f"; } + +.fa-syringe::before { + content: "\f48e"; } + +.fa-cloud-sun::before { + content: "\f6c4"; } + +.fa-stopwatch-20::before { + content: "\e06f"; } + +.fa-square-full::before { + content: "\f45c"; } + +.fa-magnet::before { + content: "\f076"; } + +.fa-jar::before { + content: "\e516"; } + +.fa-note-sticky::before { + content: "\f249"; } + +.fa-sticky-note::before { + content: "\f249"; } + +.fa-bug-slash::before { + content: "\e490"; } + +.fa-arrow-up-from-water-pump::before { + content: "\e4b6"; } + +.fa-bone::before { + content: "\f5d7"; } + +.fa-user-injured::before { + content: "\f728"; } + +.fa-face-sad-tear::before { + content: "\f5b4"; } + +.fa-sad-tear::before { + content: "\f5b4"; } + +.fa-plane::before { + content: "\f072"; } + +.fa-tent-arrows-down::before { + content: "\e581"; } + +.fa-exclamation::before { + content: "\21"; } + +.fa-arrows-spin::before { + content: "\e4bb"; } + +.fa-print::before { + content: "\f02f"; } + +.fa-turkish-lira-sign::before { + content: "\e2bb"; } + +.fa-try::before { + content: "\e2bb"; } + +.fa-turkish-lira::before { + content: "\e2bb"; } + +.fa-dollar-sign::before { + content: "\24"; } + +.fa-dollar::before { + content: "\24"; } + +.fa-usd::before { + content: "\24"; } + +.fa-x::before { + content: "\58"; } + +.fa-magnifying-glass-dollar::before { + content: "\f688"; } + +.fa-search-dollar::before { + content: "\f688"; } + +.fa-users-gear::before { + content: "\f509"; } + +.fa-users-cog::before { + content: "\f509"; } + +.fa-person-military-pointing::before { + content: "\e54a"; } + +.fa-building-columns::before { + content: "\f19c"; } + +.fa-bank::before { + content: "\f19c"; } + +.fa-institution::before { + content: "\f19c"; } + +.fa-museum::before { + content: "\f19c"; } + +.fa-university::before { + content: "\f19c"; } + +.fa-umbrella::before { + content: "\f0e9"; } + +.fa-trowel::before { + content: "\e589"; } + +.fa-d::before { + content: "\44"; } + +.fa-stapler::before { + content: "\e5af"; } + +.fa-masks-theater::before { + content: "\f630"; } + +.fa-theater-masks::before { + content: "\f630"; } + +.fa-kip-sign::before { + content: "\e1c4"; } + +.fa-hand-point-left::before { + content: "\f0a5"; } + +.fa-handshake-simple::before { + content: "\f4c6"; } + +.fa-handshake-alt::before { + content: "\f4c6"; } + +.fa-jet-fighter::before { + content: "\f0fb"; } + +.fa-fighter-jet::before { + content: "\f0fb"; } + +.fa-square-share-nodes::before { + content: "\f1e1"; } + +.fa-share-alt-square::before { + content: "\f1e1"; } + +.fa-barcode::before { + content: "\f02a"; } + +.fa-plus-minus::before { + content: "\e43c"; } + +.fa-video::before { + content: "\f03d"; } + +.fa-video-camera::before { + content: "\f03d"; } + +.fa-graduation-cap::before { + content: "\f19d"; } + +.fa-mortar-board::before { + content: "\f19d"; } + +.fa-hand-holding-medical::before { + content: "\e05c"; } + +.fa-person-circle-check::before { + content: "\e53e"; } + +.fa-turn-up::before { + content: "\f3bf"; } + +.fa-level-up-alt::before { + content: "\f3bf"; } + +.sr-only, +.fa-sr-only { + position: absolute; + width: 1px; + height: 1px; + padding: 0; + margin: -1px; + overflow: hidden; + clip: rect(0, 0, 0, 0); + white-space: nowrap; + border-width: 0; } + +.sr-only-focusable:not(:focus), +.fa-sr-only-focusable:not(:focus) { + position: absolute; + width: 1px; + height: 1px; + padding: 0; + margin: -1px; + overflow: hidden; + clip: rect(0, 0, 0, 0); + white-space: nowrap; + border-width: 0; } +:root, :host { + --fa-style-family-brands: 'Font Awesome 6 Brands'; + --fa-font-brands: normal 400 1em/1 'Font Awesome 6 Brands'; } + +@font-face { + font-family: 'Font Awesome 6 Brands'; + font-style: normal; + font-weight: 400; + font-display: block; + src: url("../webfonts/fa-brands-400.woff2") format("woff2"), url("../webfonts/fa-brands-400.ttf") format("truetype"); } + +.fab, +.fa-brands { + font-weight: 400; } + +.fa-monero:before { + content: "\f3d0"; } + +.fa-hooli:before { + content: "\f427"; } + +.fa-yelp:before { + content: "\f1e9"; } + +.fa-cc-visa:before { + content: "\f1f0"; } + +.fa-lastfm:before { + content: "\f202"; } + +.fa-shopware:before { + content: "\f5b5"; } + +.fa-creative-commons-nc:before { + content: "\f4e8"; } + +.fa-aws:before { + content: "\f375"; } + +.fa-redhat:before { + content: "\f7bc"; } + +.fa-yoast:before { + content: "\f2b1"; } + +.fa-cloudflare:before { + content: "\e07d"; } + +.fa-ups:before { + content: "\f7e0"; } + +.fa-wpexplorer:before { + content: "\f2de"; } + +.fa-dyalog:before { + content: "\f399"; } + +.fa-bity:before { + content: "\f37a"; } + +.fa-stackpath:before { + content: "\f842"; } + +.fa-buysellads:before { + content: "\f20d"; } + +.fa-first-order:before { + content: "\f2b0"; } + +.fa-modx:before { + content: "\f285"; } + +.fa-guilded:before { + content: "\e07e"; } + +.fa-vnv:before { + content: "\f40b"; } + +.fa-square-js:before { + content: "\f3b9"; } + +.fa-js-square:before { + content: "\f3b9"; } + +.fa-microsoft:before { + content: "\f3ca"; } + +.fa-qq:before { + content: "\f1d6"; } + +.fa-orcid:before { + content: "\f8d2"; } + +.fa-java:before { + content: "\f4e4"; } + +.fa-invision:before { + content: "\f7b0"; } + +.fa-creative-commons-pd-alt:before { + content: "\f4ed"; } + +.fa-centercode:before { + content: "\f380"; } + +.fa-glide-g:before { + content: "\f2a6"; } + +.fa-drupal:before { + content: "\f1a9"; } + +.fa-hire-a-helper:before { + content: "\f3b0"; } + +.fa-creative-commons-by:before { + content: "\f4e7"; } + +.fa-unity:before { + content: "\e049"; } + +.fa-whmcs:before { + content: "\f40d"; } + +.fa-rocketchat:before { + content: "\f3e8"; } + +.fa-vk:before { + content: "\f189"; } + +.fa-untappd:before { + content: "\f405"; } + +.fa-mailchimp:before { + content: "\f59e"; } + +.fa-css3-alt:before { + content: "\f38b"; } + +.fa-square-reddit:before { + content: "\f1a2"; } + +.fa-reddit-square:before { + content: "\f1a2"; } + +.fa-vimeo-v:before { + content: "\f27d"; } + +.fa-contao:before { + content: "\f26d"; } + +.fa-square-font-awesome:before { + content: "\e5ad"; } + +.fa-deskpro:before { + content: "\f38f"; } + +.fa-sistrix:before { + content: "\f3ee"; } + +.fa-square-instagram:before { + content: "\e055"; } + +.fa-instagram-square:before { + content: "\e055"; } + +.fa-battle-net:before { + content: "\f835"; } + +.fa-the-red-yeti:before { + content: "\f69d"; } + +.fa-square-hacker-news:before { + content: "\f3af"; } + +.fa-hacker-news-square:before { + content: "\f3af"; } + +.fa-edge:before { + content: "\f282"; } + +.fa-threads:before { + content: "\e618"; } + +.fa-napster:before { + content: "\f3d2"; } + +.fa-square-snapchat:before { + content: "\f2ad"; } + 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+.fa.fa-thumb-tack:before { + content: "\f08d"; } + +.fa.fa-external-link:before { + content: "\f35d"; } + +.fa.fa-sign-in:before { + content: "\f2f6"; } + +.fa.fa-github-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-github-square:before { + content: "\f092"; } + +.fa.fa-lemon-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-lemon-o:before { + content: "\f094"; } + +.fa.fa-square-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-square-o:before { + content: "\f0c8"; } + +.fa.fa-bookmark-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-bookmark-o:before { + content: "\f02e"; } + +.fa.fa-twitter { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-facebook { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-facebook:before { + content: "\f39e"; } + +.fa.fa-facebook-f { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-facebook-f:before { + content: "\f39e"; } + +.fa.fa-github { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-credit-card { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-feed:before { + content: "\f09e"; } + +.fa.fa-hdd-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hdd-o:before { + content: "\f0a0"; } + +.fa.fa-hand-o-right { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-o-right:before { + content: "\f0a4"; } + +.fa.fa-hand-o-left { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-o-left:before { + content: "\f0a5"; } + +.fa.fa-hand-o-up { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-o-up:before { + content: "\f0a6"; } + +.fa.fa-hand-o-down { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-o-down:before { + content: "\f0a7"; } + +.fa.fa-globe:before { + content: "\f57d"; } + +.fa.fa-tasks:before { + content: "\f828"; } + +.fa.fa-arrows-alt:before { + content: "\f31e"; } + +.fa.fa-group:before { + content: "\f0c0"; } + +.fa.fa-chain:before { + content: "\f0c1"; } + +.fa.fa-cut:before { + content: "\f0c4"; } + +.fa.fa-files-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-files-o:before { + content: "\f0c5"; } + +.fa.fa-floppy-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-floppy-o:before { + content: "\f0c7"; } + +.fa.fa-save { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-save:before { + content: "\f0c7"; } + +.fa.fa-navicon:before { + content: "\f0c9"; } + +.fa.fa-reorder:before { + content: "\f0c9"; } + +.fa.fa-magic:before { + content: "\e2ca"; } + +.fa.fa-pinterest { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-pinterest-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-pinterest-square:before { + content: "\f0d3"; } + +.fa.fa-google-plus-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-google-plus-square:before { + content: "\f0d4"; } + +.fa.fa-google-plus { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-google-plus:before { + content: "\f0d5"; } + +.fa.fa-money:before { + content: "\f3d1"; } + +.fa.fa-unsorted:before { + content: "\f0dc"; } + +.fa.fa-sort-desc:before { + content: "\f0dd"; } + +.fa.fa-sort-asc:before { + content: "\f0de"; } + +.fa.fa-linkedin { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-linkedin:before { + content: "\f0e1"; } + +.fa.fa-rotate-left:before { + content: "\f0e2"; } + +.fa.fa-legal:before { + content: "\f0e3"; } + +.fa.fa-tachometer:before { + content: "\f625"; } + +.fa.fa-dashboard:before { + content: "\f625"; } + +.fa.fa-comment-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-comment-o:before { + content: "\f075"; } + +.fa.fa-comments-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-comments-o:before { + content: "\f086"; } + +.fa.fa-flash:before { + content: "\f0e7"; } + +.fa.fa-clipboard:before { + content: "\f0ea"; } + +.fa.fa-lightbulb-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-lightbulb-o:before { + content: "\f0eb"; } + +.fa.fa-exchange:before { + content: "\f362"; } + +.fa.fa-cloud-download:before { + content: "\f0ed"; } + +.fa.fa-cloud-upload:before { + content: "\f0ee"; } + +.fa.fa-bell-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-bell-o:before { + content: "\f0f3"; } + +.fa.fa-cutlery:before { + content: "\f2e7"; } + +.fa.fa-file-text-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-text-o:before { + content: "\f15c"; } + +.fa.fa-building-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-building-o:before { + content: "\f1ad"; } + +.fa.fa-hospital-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hospital-o:before { + content: "\f0f8"; } + +.fa.fa-tablet:before { + content: "\f3fa"; } + +.fa.fa-mobile:before { + content: "\f3cd"; } + +.fa.fa-mobile-phone:before { + content: "\f3cd"; } + +.fa.fa-circle-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-circle-o:before { + content: "\f111"; } + +.fa.fa-mail-reply:before { + content: "\f3e5"; } + +.fa.fa-github-alt { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-folder-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-folder-o:before { + content: "\f07b"; } + +.fa.fa-folder-open-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-folder-open-o:before { + content: "\f07c"; } + +.fa.fa-smile-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-smile-o:before { + content: "\f118"; } + +.fa.fa-frown-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-frown-o:before { + content: "\f119"; } + +.fa.fa-meh-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-meh-o:before { + content: "\f11a"; } + +.fa.fa-keyboard-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-keyboard-o:before { + content: "\f11c"; } + +.fa.fa-flag-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-flag-o:before { + content: "\f024"; } + +.fa.fa-mail-reply-all:before { + content: "\f122"; } + +.fa.fa-star-half-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-star-half-o:before { + content: "\f5c0"; } + +.fa.fa-star-half-empty { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-star-half-empty:before { + content: "\f5c0"; } + +.fa.fa-star-half-full { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-star-half-full:before { + content: "\f5c0"; } + +.fa.fa-code-fork:before { + content: "\f126"; } + +.fa.fa-chain-broken:before { + content: "\f127"; } + +.fa.fa-unlink:before { + content: "\f127"; } + +.fa.fa-calendar-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-calendar-o:before { + content: "\f133"; } + +.fa.fa-maxcdn { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-html5 { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-css3 { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-unlock-alt:before { + content: "\f09c"; } + +.fa.fa-minus-square-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-minus-square-o:before { + content: "\f146"; } + +.fa.fa-level-up:before { + content: "\f3bf"; } + +.fa.fa-level-down:before { + content: "\f3be"; } + +.fa.fa-pencil-square:before { + content: "\f14b"; } + +.fa.fa-external-link-square:before { + content: "\f360"; } + +.fa.fa-compass { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-caret-square-o-down { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-caret-square-o-down:before { + content: "\f150"; } + +.fa.fa-toggle-down { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-toggle-down:before { + content: "\f150"; } + +.fa.fa-caret-square-o-up { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-caret-square-o-up:before { + content: "\f151"; } + +.fa.fa-toggle-up { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-toggle-up:before { + content: "\f151"; } + +.fa.fa-caret-square-o-right { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-caret-square-o-right:before { + content: "\f152"; } + +.fa.fa-toggle-right { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-toggle-right:before { + content: "\f152"; } + +.fa.fa-eur:before { + content: "\f153"; } + +.fa.fa-euro:before { + content: "\f153"; } + +.fa.fa-gbp:before { + content: "\f154"; } + +.fa.fa-usd:before { + content: "\24"; } + +.fa.fa-dollar:before { + content: "\24"; } + +.fa.fa-inr:before { + content: "\e1bc"; } + +.fa.fa-rupee:before { + content: "\e1bc"; } + +.fa.fa-jpy:before { + content: "\f157"; } + +.fa.fa-cny:before { + content: "\f157"; } + +.fa.fa-rmb:before { + content: "\f157"; } + +.fa.fa-yen:before { + content: "\f157"; } + +.fa.fa-rub:before { + content: "\f158"; } + +.fa.fa-ruble:before { + content: "\f158"; } + +.fa.fa-rouble:before { + content: "\f158"; } + +.fa.fa-krw:before { + content: "\f159"; } + +.fa.fa-won:before { + content: "\f159"; } + +.fa.fa-btc { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-bitcoin { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-bitcoin:before { + content: "\f15a"; } + +.fa.fa-file-text:before { + content: "\f15c"; } + +.fa.fa-sort-alpha-asc:before { + content: "\f15d"; } + +.fa.fa-sort-alpha-desc:before { + content: "\f881"; } + +.fa.fa-sort-amount-asc:before { + content: "\f884"; } + +.fa.fa-sort-amount-desc:before { + content: "\f160"; } + +.fa.fa-sort-numeric-asc:before { + content: "\f162"; } + +.fa.fa-sort-numeric-desc:before { + content: "\f886"; } + +.fa.fa-youtube-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-youtube-square:before { + content: "\f431"; } + +.fa.fa-youtube { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-xing { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-xing-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-xing-square:before { + content: "\f169"; } + +.fa.fa-youtube-play { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-youtube-play:before { + content: "\f167"; } + +.fa.fa-dropbox { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-stack-overflow { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-instagram { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-flickr { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-adn { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-bitbucket { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-bitbucket-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-bitbucket-square:before { + content: "\f171"; } + +.fa.fa-tumblr { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-tumblr-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-tumblr-square:before { + content: "\f174"; } + +.fa.fa-long-arrow-down:before { + content: "\f309"; } + +.fa.fa-long-arrow-up:before { + content: "\f30c"; } + +.fa.fa-long-arrow-left:before { + content: "\f30a"; } + +.fa.fa-long-arrow-right:before { + content: "\f30b"; } + +.fa.fa-apple { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-windows { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-android { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-linux { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-dribbble { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-skype { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-foursquare { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-trello { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-gratipay { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-gittip { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-gittip:before { + content: "\f184"; } + +.fa.fa-sun-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-sun-o:before { + content: "\f185"; } + +.fa.fa-moon-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-moon-o:before { + content: "\f186"; } + +.fa.fa-vk { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-weibo { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-renren { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-pagelines { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-stack-exchange { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-arrow-circle-o-right { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-arrow-circle-o-right:before { + content: "\f35a"; } + +.fa.fa-arrow-circle-o-left { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-arrow-circle-o-left:before { + content: "\f359"; } + +.fa.fa-caret-square-o-left { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-caret-square-o-left:before { + content: "\f191"; } + +.fa.fa-toggle-left { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-toggle-left:before { + content: "\f191"; } + +.fa.fa-dot-circle-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-dot-circle-o:before { + content: "\f192"; } + +.fa.fa-vimeo-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-vimeo-square:before { + content: "\f194"; } + +.fa.fa-try:before { + content: "\e2bb"; } + +.fa.fa-turkish-lira:before { + content: "\e2bb"; } + +.fa.fa-plus-square-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-plus-square-o:before { + content: "\f0fe"; } + +.fa.fa-slack { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wordpress { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-openid { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-institution:before { + content: "\f19c"; } + +.fa.fa-bank:before { + content: "\f19c"; } + +.fa.fa-mortar-board:before { + content: "\f19d"; } + +.fa.fa-yahoo { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-google { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-reddit { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-reddit-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-reddit-square:before { + content: "\f1a2"; } + +.fa.fa-stumbleupon-circle { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-stumbleupon { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-delicious { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-digg { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-pied-piper-pp { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-pied-piper-alt { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-drupal { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-joomla { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-behance { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-behance-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-behance-square:before { + content: "\f1b5"; } + +.fa.fa-steam { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-steam-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-steam-square:before { + content: "\f1b7"; } + +.fa.fa-automobile:before { + content: "\f1b9"; } + +.fa.fa-cab:before { + content: "\f1ba"; } + +.fa.fa-spotify { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-deviantart { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-soundcloud { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-file-pdf-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-pdf-o:before { + content: "\f1c1"; } + +.fa.fa-file-word-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-word-o:before { + content: "\f1c2"; } + +.fa.fa-file-excel-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-excel-o:before { + content: "\f1c3"; } + +.fa.fa-file-powerpoint-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-powerpoint-o:before { + content: "\f1c4"; } + +.fa.fa-file-image-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-image-o:before { + content: "\f1c5"; } + +.fa.fa-file-photo-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-photo-o:before { + content: "\f1c5"; } + +.fa.fa-file-picture-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-picture-o:before { + content: "\f1c5"; } + +.fa.fa-file-archive-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-archive-o:before { + content: "\f1c6"; } + +.fa.fa-file-zip-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-zip-o:before { + content: "\f1c6"; } + +.fa.fa-file-audio-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-audio-o:before { + content: "\f1c7"; } + +.fa.fa-file-sound-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-sound-o:before { + content: "\f1c7"; } + +.fa.fa-file-video-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-video-o:before { + content: "\f1c8"; } + +.fa.fa-file-movie-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-movie-o:before { + content: "\f1c8"; } + +.fa.fa-file-code-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-file-code-o:before { + content: "\f1c9"; } + +.fa.fa-vine { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-codepen { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-jsfiddle { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-life-bouy:before { + content: "\f1cd"; } + +.fa.fa-life-buoy:before { + content: "\f1cd"; } + +.fa.fa-life-saver:before { + content: "\f1cd"; } + +.fa.fa-support:before { + content: "\f1cd"; } + +.fa.fa-circle-o-notch:before { + content: "\f1ce"; } + +.fa.fa-rebel { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-ra { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-ra:before { + content: "\f1d0"; } + +.fa.fa-resistance { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-resistance:before { + content: "\f1d0"; } + +.fa.fa-empire { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-ge { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-ge:before { + content: "\f1d1"; } + +.fa.fa-git-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-git-square:before { + content: "\f1d2"; } + +.fa.fa-git { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-hacker-news { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-y-combinator-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-y-combinator-square:before { + content: "\f1d4"; } + +.fa.fa-yc-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-yc-square:before { + content: "\f1d4"; } + +.fa.fa-tencent-weibo { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-qq { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-weixin { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wechat { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wechat:before { + content: "\f1d7"; } + +.fa.fa-send:before { + content: "\f1d8"; } + +.fa.fa-paper-plane-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-paper-plane-o:before { + content: "\f1d8"; } + +.fa.fa-send-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-send-o:before { + content: "\f1d8"; } + +.fa.fa-circle-thin { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-circle-thin:before { + content: "\f111"; } + +.fa.fa-header:before { + content: "\f1dc"; } + +.fa.fa-futbol-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-futbol-o:before { + content: "\f1e3"; } + +.fa.fa-soccer-ball-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-soccer-ball-o:before { + content: "\f1e3"; } + +.fa.fa-slideshare { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-twitch { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-yelp { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-newspaper-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-newspaper-o:before { + content: "\f1ea"; } + +.fa.fa-paypal { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-google-wallet { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc-visa { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc-mastercard { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc-discover { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc-amex { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc-paypal { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc-stripe { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-bell-slash-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-bell-slash-o:before { + content: "\f1f6"; } + +.fa.fa-trash:before { + content: "\f2ed"; } + +.fa.fa-copyright { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-eyedropper:before { + content: "\f1fb"; } + +.fa.fa-area-chart:before { + content: "\f1fe"; } + +.fa.fa-pie-chart:before { + content: "\f200"; } + +.fa.fa-line-chart:before { + content: "\f201"; } + +.fa.fa-lastfm { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-lastfm-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-lastfm-square:before { + content: "\f203"; } + +.fa.fa-ioxhost { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-angellist { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-cc:before { + content: "\f20a"; } + +.fa.fa-ils:before { + content: "\f20b"; } + +.fa.fa-shekel:before { + content: "\f20b"; } + +.fa.fa-sheqel:before { + content: "\f20b"; } + +.fa.fa-buysellads { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-connectdevelop { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-dashcube { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-forumbee { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-leanpub { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-sellsy { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-shirtsinbulk { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-simplybuilt { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-skyatlas { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-diamond { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-diamond:before { + content: "\f3a5"; } + +.fa.fa-transgender:before { + content: "\f224"; } + +.fa.fa-intersex:before { + content: "\f224"; } + +.fa.fa-transgender-alt:before { + content: "\f225"; } + +.fa.fa-facebook-official { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-facebook-official:before { + content: "\f09a"; } + +.fa.fa-pinterest-p { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-whatsapp { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-hotel:before { + content: "\f236"; } + +.fa.fa-viacoin { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-medium { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-y-combinator { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-yc { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-yc:before { + content: "\f23b"; } + +.fa.fa-optin-monster { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-opencart { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-expeditedssl { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-battery-4:before { + content: "\f240"; } + +.fa.fa-battery:before { + content: "\f240"; } + +.fa.fa-battery-3:before { + content: "\f241"; } + +.fa.fa-battery-2:before { + content: "\f242"; } + +.fa.fa-battery-1:before { + content: "\f243"; } + +.fa.fa-battery-0:before { + content: "\f244"; } + +.fa.fa-object-group { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-object-ungroup { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-sticky-note-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-sticky-note-o:before { + content: "\f249"; } + +.fa.fa-cc-jcb { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-cc-diners-club { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-clone { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hourglass-o:before { + content: "\f254"; } + +.fa.fa-hourglass-1:before { + content: "\f251"; } + +.fa.fa-hourglass-2:before { + content: "\f252"; } + +.fa.fa-hourglass-3:before { + content: "\f253"; } + +.fa.fa-hand-rock-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-rock-o:before { + content: "\f255"; } + +.fa.fa-hand-grab-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-grab-o:before { + content: "\f255"; } + +.fa.fa-hand-paper-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-paper-o:before { + content: "\f256"; } + +.fa.fa-hand-stop-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-stop-o:before { + content: "\f256"; } + +.fa.fa-hand-scissors-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-scissors-o:before { + content: "\f257"; } + +.fa.fa-hand-lizard-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-lizard-o:before { + content: "\f258"; } + +.fa.fa-hand-spock-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-spock-o:before { + content: "\f259"; } + +.fa.fa-hand-pointer-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-pointer-o:before { + content: "\f25a"; } + +.fa.fa-hand-peace-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-hand-peace-o:before { + content: "\f25b"; } + +.fa.fa-registered { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-creative-commons { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-gg { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-gg-circle { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-odnoklassniki { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-odnoklassniki-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-odnoklassniki-square:before { + content: "\f264"; } + +.fa.fa-get-pocket { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wikipedia-w { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-safari { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-chrome { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-firefox { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-opera { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-internet-explorer { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-television:before { + content: "\f26c"; } + +.fa.fa-contao { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-500px { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-amazon { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-calendar-plus-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-calendar-plus-o:before { + content: "\f271"; } + +.fa.fa-calendar-minus-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-calendar-minus-o:before { + content: "\f272"; } + +.fa.fa-calendar-times-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-calendar-times-o:before { + content: "\f273"; } + +.fa.fa-calendar-check-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-calendar-check-o:before { + content: "\f274"; } + +.fa.fa-map-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-map-o:before { + content: "\f279"; } + +.fa.fa-commenting:before { + content: "\f4ad"; } + +.fa.fa-commenting-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-commenting-o:before { + content: "\f4ad"; } + +.fa.fa-houzz { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-vimeo { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-vimeo:before { + content: "\f27d"; } + +.fa.fa-black-tie { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-fonticons { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-reddit-alien { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-edge { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-credit-card-alt:before { + content: "\f09d"; } + +.fa.fa-codiepie { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-modx { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-fort-awesome { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-usb { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-product-hunt { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-mixcloud { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-scribd { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-pause-circle-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-pause-circle-o:before { + content: "\f28b"; } + +.fa.fa-stop-circle-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-stop-circle-o:before { + content: "\f28d"; } + +.fa.fa-bluetooth { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-bluetooth-b { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-gitlab { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wpbeginner { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wpforms { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-envira { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wheelchair-alt { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-wheelchair-alt:before { + content: "\f368"; } + +.fa.fa-question-circle-o { + font-family: 'Font Awesome 6 Free'; + font-weight: 400; } + +.fa.fa-question-circle-o:before { + content: "\f059"; } + +.fa.fa-volume-control-phone:before { + content: "\f2a0"; } + +.fa.fa-asl-interpreting:before { + content: "\f2a3"; } + +.fa.fa-deafness:before { + content: "\f2a4"; } + +.fa.fa-hard-of-hearing:before { + content: "\f2a4"; } + +.fa.fa-glide { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-glide-g { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-signing:before { + content: "\f2a7"; } + +.fa.fa-viadeo { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-viadeo-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-viadeo-square:before { + content: "\f2aa"; } + +.fa.fa-snapchat { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-snapchat-ghost { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-snapchat-ghost:before { + content: "\f2ab"; } + +.fa.fa-snapchat-square { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-snapchat-square:before { + content: "\f2ad"; } + +.fa.fa-pied-piper { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-first-order { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; } + +.fa.fa-yoast { + font-family: 'Font Awesome 6 Brands'; + font-weight: 400; 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Hide your header until you need it + * Copyright (c) 2017 Nick Williams - http://wicky.nillia.ms/headroom.js + * License: MIT + */ + +!function(a){a&&(a.fn.headroom=function(b){return this.each(function(){var c=a(this),d=c.data("headroom"),e="object"==typeof b&&b;e=a.extend(!0,{},Headroom.options,e),d||(d=new Headroom(this,e),d.init(),c.data("headroom",d)),"string"==typeof b&&(d[b](),"destroy"===b&&c.removeData("headroom"))})},a("[data-headroom]").each(function(){var b=a(this);b.headroom(b.data())}))}(window.Zepto||window.jQuery); \ No newline at end of file diff --git a/v1.3.1/deps/jquery-3.6.0/jquery-3.6.0.js b/v1.3.1/deps/jquery-3.6.0/jquery-3.6.0.js new file mode 100644 index 000000000..fc6c299b7 --- /dev/null +++ b/v1.3.1/deps/jquery-3.6.0/jquery-3.6.0.js @@ -0,0 +1,10881 @@ +/*! + * jQuery JavaScript Library v3.6.0 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright OpenJS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2021-03-02T17:08Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + // Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5 + // Plus for old WebKit, typeof returns "function" for HTML collections + // (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756) + return typeof obj === "function" && typeof obj.nodeType !== "number" && + typeof obj.item !== "function"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.6.0", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), + function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); + } ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.6 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2021-02-16 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem && elem.namespaceURI, + docElem = elem && ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +} +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the primary Deferred + primary = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + primary.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( primary.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return primary.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject ); + } + + return primary.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
    " ], + col: [ 2, "", "
    " ], + tr: [ 2, "", "
    " ], + td: [ 3, "", "
    " ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + + // Support: Chrome 86+ + // In Chrome, if an element having a focusout handler is blurred by + // clicking outside of it, it invokes the handler synchronously. If + // that handler calls `.remove()` on the element, the data is cleared, + // leaving `result` undefined. We need to guard against this. + return result && result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + which: true +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + // Suppress native focus or blur as it's already being fired + // in leverageNative. + _default: function() { + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + // + // Support: Firefox 70+ + // Only Firefox includes border widths + // in computed dimensions. (gh-4529) + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate"; + tr.style.cssText = "border:1px solid"; + + // Support: Chrome 86+ + // Height set through cssText does not get applied. + // Computed height then comes back as 0. + tr.style.height = "1px"; + trChild.style.height = "9px"; + + // Support: Android 8 Chrome 86+ + // In our bodyBackground.html iframe, + // display for all div elements is set to "inline", + // which causes a problem only in Android 8 Chrome 86. + // Ensuring the div is display: block + // gets around this issue. + trChild.style.display = "block"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) + + parseInt( trStyle.borderTopWidth, 10 ) + + parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml, parserErrorElem; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) {} + + parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ]; + if ( !xml || parserErrorElem ) { + jQuery.error( "Invalid XML: " + ( + parserErrorElem ? + jQuery.map( parserErrorElem.childNodes, function( el ) { + return el.textContent; + } ).join( "\n" ) : + data + ) ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ).filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ).map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + +originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script but not if jsonp + if ( !isSuccess && + jQuery.inArray( "script", s.dataTypes ) > -1 && + jQuery.inArray( "json", s.dataTypes ) < 0 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " + + + + + + + + + + Skip to contents + + +
    +
    +
    +
    +
    +

    Reference Based Multiple Imputation (rbmi) + +

    +
    +
    +

    Overview +

    +

    The rbmi package is used for the imputation of missing data in clinical trials with continuous multivariate normal longitudinal outcomes. It supports imputation under a missing at random (MAR) assumption, reference-based imputation methods, and delta adjustments (as required for sensitivity analysis such as tipping point analyses). The package implements both Bayesian and approximate Bayesian multiple imputation combined with Rubin’s rules for inference, and frequentist conditional mean imputation combined with (jackknife or bootstrap) resampling.

    +
    +
    +

    Installation +

    +

    The package can be installed directly from CRAN via:

    +
    install.packages("rbmi")
    +

    Note that the usage of Bayesian multiple imputation requires the installation of the suggested package rstan.

    +
    install.packages("rstan")
    +
    +
    +

    Usage +

    +

    The package is designed around its 4 core functions:

    +
      +
    • +draws() - Fits multiple imputation models
      • +
    • +impute() - Imputes multiple datasets
      • +
    • +analyse() - Analyses multiple datasets
      • +
    • +pool() - Pools multiple results into a single statistic
      • +
    +

    The basic usage of these core functions is described in the quickstart vignette:

    +
    vignette(topic = "quickstart", package = "rbmi")
    +
    +
    +

    Validation +

    +

    For clarification on the current validation status of rbmi please see the FAQ vignette.

    +
    +
    +

    Support +

    +

    For any help with regards to using the package or if you find a bug please create a GitHub issue

    +
    +
    + +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    +
    + + + + + + + diff --git a/v1.3.1/katex-auto.js b/v1.3.1/katex-auto.js new file mode 100644 index 000000000..20651d9fd --- /dev/null +++ b/v1.3.1/katex-auto.js @@ -0,0 +1,14 @@ +// https://github.com/jgm/pandoc/blob/29fa97ab96b8e2d62d48326e1b949a71dc41f47a/src/Text/Pandoc/Writers/HTML.hs#L332-L345 +document.addEventListener("DOMContentLoaded", function () { + var mathElements = document.getElementsByClassName("math"); + var macros = []; + for (var i = 0; i < mathElements.length; i++) { + var texText = mathElements[i].firstChild; + if (mathElements[i].tagName == "SPAN") { + katex.render(texText.data, mathElements[i], { + displayMode: mathElements[i].classList.contains("display"), + throwOnError: false, + macros: macros, + fleqn: false + }); + }}}); diff --git a/v1.3.1/lightswitch.js b/v1.3.1/lightswitch.js new file mode 100644 index 000000000..9467125ae --- /dev/null +++ b/v1.3.1/lightswitch.js @@ -0,0 +1,85 @@ + +/*! + * Color mode toggler for Bootstrap's docs (https://getbootstrap.com/) + * Copyright 2011-2023 The Bootstrap Authors + * Licensed under the Creative Commons Attribution 3.0 Unported License. + * Updates for {pkgdown} by the {bslib} authors, also licensed under CC-BY-3.0. + */ + +const getStoredTheme = () => localStorage.getItem('theme') +const setStoredTheme = theme => localStorage.setItem('theme', theme) + +const getPreferredTheme = () => { + const storedTheme = getStoredTheme() + if (storedTheme) { + return storedTheme + } + + return window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light' +} + +const setTheme = theme => { + if (theme === 'auto') { + document.documentElement.setAttribute('data-bs-theme', (window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light')) + } else { + document.documentElement.setAttribute('data-bs-theme', theme) + } +} + +function bsSetupThemeToggle () { + 'use strict' + + const showActiveTheme = (theme, focus = false) => { + var activeLabel, activeIcon; + + document.querySelectorAll('[data-bs-theme-value]').forEach(element => { + const buttonTheme = element.getAttribute('data-bs-theme-value') + const isActive = buttonTheme == theme + + element.classList.toggle('active', isActive) + element.setAttribute('aria-pressed', isActive) + + if (isActive) { + activeLabel = element.textContent; + activeIcon = element.querySelector('span').classList.value; + } + }) + + const themeSwitcher = document.querySelector('#dropdown-lightswitch') + if (!themeSwitcher) { + return + } + + themeSwitcher.setAttribute('aria-label', activeLabel) + themeSwitcher.querySelector('span').classList.value = activeIcon; + + if (focus) { + themeSwitcher.focus() + } + } + + window.matchMedia('(prefers-color-scheme: dark)').addEventListener('change', () => { + const storedTheme = getStoredTheme() + if (storedTheme !== 'light' && storedTheme !== 'dark') { + setTheme(getPreferredTheme()) + } + }) + + window.addEventListener('DOMContentLoaded', () => { + showActiveTheme(getPreferredTheme()) + + document + .querySelectorAll('[data-bs-theme-value]') + .forEach(toggle => { + toggle.addEventListener('click', () => { + const theme = toggle.getAttribute('data-bs-theme-value') + setTheme(theme) + setStoredTheme(theme) + showActiveTheme(theme, true) + }) + }) + }) +} + +setTheme(getPreferredTheme()); +bsSetupThemeToggle(); diff --git a/v1.3.1/link.svg b/v1.3.1/link.svg new file mode 100644 index 000000000..88ad82769 --- /dev/null +++ b/v1.3.1/link.svg @@ -0,0 +1,12 @@ + + + + + + diff --git a/v1.3.1/logo.png b/v1.3.1/logo.png new file mode 100644 index 000000000..08fbb4fcd Binary files /dev/null and b/v1.3.1/logo.png differ diff --git a/v1.3.1/news/index.html b/v1.3.1/news/index.html new file mode 100644 index 000000000..52a82ac26 --- /dev/null +++ b/v1.3.1/news/index.html @@ -0,0 +1,134 @@ + +Changelog • rbmi + Skip to contents + + +
    +
    +
    +

    Changelog

    + Source: NEWS.md +
    + +
    +

    rbmi 1.3.1

    +
    • Fixed bug where stale caches of the rstan model were not being correctly cleared (#459)
      • +
    +
    +

    rbmi 1.3.0

    CRAN release: 2024-10-16

    +
    +

    Breaking Changes

    +
    • Convert rstan to be a suggested package to simplify the installation process. This means that the Bayesian imputation functionality will not be available by default. To use this feature, you will need to install rstan separately (#441)
      • +
    • Deprecated the seed argument to method_bayes() in favour of using the base set.seed() function (#431)
      • +
    +
    +

    New Features

    +
    • Added vignette on how to implement retrieved dropout models with time-varying intercurrent event (ICE) indicators (#414)
      • +
    • Added vignette on how to obtain frequentist and information-anchored inference with conditional mean imputation using rbmi (#406)
      • +
    • Added FAQ vignette including a statement on validation (#407 #440)
      • +
    • Updates to lsmeans() for better consistency with the emmeans package (#412) +
      • Renamed lsmeans(..., weights = "proportional") to lsmeans(..., weights = "counterfactual")to more accurately reflect the weights used in the calculation.
        • +
      • Added lsmeans(..., weights = "proportional_em") which provides consistent results with emmeans(..., weights = "proportional") +
        • +
      • +lsmeans(..., weights = "proportional") has been left in the package for backwards compatibility and is an alias for lsmeans(..., weights = "counterfactual") but now gives a message prompting users to use either “proptional_em” or “counterfactual” instead.
        • +
      • +
    • Added support for parallel processing in the analyse() function (#370)
      • +
    • Added documentation clarifying potential false-positive warnings from rstan (#288)
      • +
    • Added support for all covariance structures supported by the mmrm package (#437)
      • +
    • Updated rbmi citation detail (#423 #425)
      • +
    +
    +

    Miscellaneous Bug Fixes

    +
    • Stopped warning messages being accidentally supressed when changing the ICE type in impute() (#408)
      • +
    • Fixed equations not rendering properly in the pkgdown website (#433)
      • +
    +
    +
    +

    rbmi 1.2.6

    CRAN release: 2023-11-24

    +
    • Updated unit tests to fix false-positive error on CRAN’s testing servers
      • +
    +
    +

    rbmi 1.2.5

    CRAN release: 2023-09-20

    +
    • Updated internal Stan code to ensure future compatibility (@andrjohns, #390)
      • +
    • Updated package description to include relevant references (#393)
      • +
    • Fixed documentation typos (#393)
      • +
    +
    +

    rbmi 1.2.3

    CRAN release: 2022-11-14

    +
    • Minor internal tweaks to ensure compatibility with the packages rbmi depends on
      • +
    +
    +

    rbmi 1.2.1

    CRAN release: 2022-10-25

    +
    • Removed native pipes |> in testing code so package is backwards compatible with older servers
      • +
    • Replaced our glmmTMB dependency with the mmrm package. This has resulted in the package being more stable (less model fitting convergence issues) as well as speeding up run times 3-fold.
      • +
    +
    +

    rbmi 1.1.4

    CRAN release: 2022-05-18

    +
    • Updated urls for references in vignettes
      • +
    • Fixed a bug where visit factor levels were re-constructed incorrectly in delta_template() +
      • +
    • Fixed a bug where the wrong visit was displayed in the error message for when a specific visit doesn’t have any data in draws() +
      • +
    • Fixed a bug where the wrong input parameter was displayed in an error message in simulate_data() +
      • +
    +
    +

    rbmi 1.1.1 & 1.1.3

    CRAN release: 2022-03-08

    +
    • No change in functionality from 1.1.0
      • +
    • Various minor tweaks to address CRAN checks messages
      • +
    +
    +

    rbmi 1.1.0

    CRAN release: 2022-03-02

    +
    • Initial public release
      • +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/pkgdown.js b/v1.3.1/pkgdown.js new file mode 100644 index 000000000..1a99c65f5 --- /dev/null +++ b/v1.3.1/pkgdown.js @@ -0,0 +1,162 @@ +/* http://gregfranko.com/blog/jquery-best-practices/ */ +(function($) { + $(function() { + + $('nav.navbar').headroom(); + + Toc.init({ + $nav: $("#toc"), + $scope: $("main h2, main h3, main h4, main h5, main h6") + }); + + if ($('#toc').length) { + $('body').scrollspy({ + target: '#toc', + offset: $("nav.navbar").outerHeight() + 1 + }); + } + + // Activate popovers + $('[data-bs-toggle="popover"]').popover({ + container: 'body', + html: true, + trigger: 'focus', + placement: "top", + sanitize: false, + }); + + $('[data-bs-toggle="tooltip"]').tooltip(); + + /* Clipboard --------------------------*/ + + function changeTooltipMessage(element, msg) { + var tooltipOriginalTitle=element.getAttribute('data-bs-original-title'); + element.setAttribute('data-bs-original-title', msg); + $(element).tooltip('show'); + element.setAttribute('data-bs-original-title', tooltipOriginalTitle); + } + + if(ClipboardJS.isSupported()) { + $(document).ready(function() { + var copyButton = ""; + + $("div.sourceCode").addClass("hasCopyButton"); + + // Insert copy buttons: + $(copyButton).prependTo(".hasCopyButton"); + + // Initialize tooltips: + $('.btn-copy-ex').tooltip({container: 'body'}); + + // Initialize clipboard: + var clipboard = new ClipboardJS('[data-clipboard-copy]', { + text: function(trigger) { + return trigger.parentNode.textContent.replace(/\n#>[^\n]*/g, ""); + } + }); + + clipboard.on('success', function(e) { + changeTooltipMessage(e.trigger, 'Copied!'); + e.clearSelection(); + }); + + clipboard.on('error', function(e) { + changeTooltipMessage(e.trigger,'Press Ctrl+C or Command+C to copy'); + }); + + }); + } + + /* Search marking --------------------------*/ + var url = new URL(window.location.href); + var toMark = url.searchParams.get("q"); + var mark = new Mark("main#main"); + if (toMark) { + mark.mark(toMark, { + accuracy: { + value: "complementary", + limiters: [",", ".", ":", "/"], + } + }); + } + + /* Search --------------------------*/ + /* Adapted from https://github.com/rstudio/bookdown/blob/2d692ba4b61f1e466c92e78fd712b0ab08c11d31/inst/resources/bs4_book/bs4_book.js#L25 */ + // Initialise search index on focus + var fuse; + $("#search-input").focus(async function(e) { + if (fuse) { + return; + } + + $(e.target).addClass("loading"); + var response = await fetch($("#search-input").data("search-index")); + var data = await response.json(); + + var options = { + keys: ["what", "text", "code"], + ignoreLocation: true, + threshold: 0.1, + includeMatches: true, + includeScore: true, + }; + fuse = new Fuse(data, options); + + $(e.target).removeClass("loading"); + }); + + // Use algolia autocomplete + var options = { + autoselect: true, + debug: true, + hint: false, + minLength: 2, + }; + var q; +async function searchFuse(query, callback) { + await fuse; + + var items; + if (!fuse) { + items = []; + } else { + q = query; + var results = fuse.search(query, { limit: 20 }); + items = results + .filter((x) => x.score <= 0.75) + .map((x) => x.item); + if (items.length === 0) { + items = [{dir:"Sorry 😿",previous_headings:"",title:"No results found.",what:"No results found.",path:window.location.href}]; + } + } + callback(items); +} + $("#search-input").autocomplete(options, [ + { + name: "content", + source: searchFuse, + templates: { + suggestion: (s) => { + if (s.title == s.what) { + return `${s.dir} >
    ${s.title}
    `; + } else if (s.previous_headings == "") { + return `${s.dir} >
    ${s.title}
    > ${s.what}`; + } else { + return `${s.dir} >
    ${s.title}
    > ${s.previous_headings} > ${s.what}`; + } + }, + }, + }, + ]).on('autocomplete:selected', function(event, s) { + window.location.href = s.path + "?q=" + q + "#" + s.id; + }); + }); +})(window.jQuery || window.$) + +document.addEventListener('keydown', function(event) { + // Check if the pressed key is '/' + if (event.key === '/') { + event.preventDefault(); // Prevent any default action associated with the '/' key + document.getElementById('search-input').focus(); // Set focus to the search input + } +}); diff --git a/v1.3.1/pkgdown.yml b/v1.3.1/pkgdown.yml new file mode 100644 index 000000000..849f7ec2b --- /dev/null +++ b/v1.3.1/pkgdown.yml @@ -0,0 +1,11 @@ +pandoc: '3.4' +pkgdown: 2.1.1 +pkgdown_sha: ~ +articles: + advanced: advanced.html + CondMean_Inference: CondMean_Inference.html + FAQ: FAQ.html + quickstart: quickstart.html + retrieved_dropout: retrieved_dropout.html + stat_specs: stat_specs.html +last_built: 2024-12-10T16:19Z diff --git a/v1.3.1/reference/QR_decomp.html b/v1.3.1/reference/QR_decomp.html new file mode 100644 index 000000000..37d637baf --- /dev/null +++ b/v1.3.1/reference/QR_decomp.html @@ -0,0 +1,84 @@ + +QR decomposition — QR_decomp • rbmi + Skip to contents + + +
    +
    +
    +

    QR decomposition

    + Source: R/mcmc.R +
    QR_decomp.Rd
    +
    + +
    +

    QR decomposition as defined in the +Stan user's guide (section 1.2).

    +
    + +
    +

    Usage

    + 
    QR_decomp(mat)
    +
    + +
    +

    Arguments

    + + +
    mat
    +

    A matrix to perform the QR decomposition on.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/Stack.html b/v1.3.1/reference/Stack.html new file mode 100644 index 000000000..a93bc76fa --- /dev/null +++ b/v1.3.1/reference/Stack.html @@ -0,0 +1,138 @@ + +R6 Class for a FIFO stack — Stack • rbmi + Skip to contents + + +
    +
    +
    +

    R6 Class for a FIFO stack

    + Source: R/stack.R +
    Stack.Rd
    +
    + +
    +

    This is a simple stack object offering add / pop functionality

    +
    + + +
    +

    Public fields

    +

    stack
    +

    A list containing the current stack

    + + +

    +
    +
    +

    Methods

    + +
    +

    Public methods

    + +

    +

    Method add()

    +

    Adds content to the end of the stack (must be a list)

    +

    Usage

    +

    Stack$add(x)

    +
    + +
    +

    Arguments

    +

    x
    +

    content to add to the stack

    + + +

    +
    + +

    +

    Method pop()

    +

    Retrieve content from the stack

    +

    Usage

    +

    Stack$pop(i)

    +
    + +
    +

    Arguments

    +

    i
    +

    the number of items to retrieve from the stack. If there are less than i +items left on the stack it will just return everything that is left.

    + + +

    +
    + +

    +

    Method clone()

    +

    The objects of this class are cloneable with this method.

    +

    Usage

    +

    Stack$clone(deep = FALSE)

    +
    + +
    +

    Arguments

    +

    deep
    +

    Whether to make a deep clone.

    + + +

    +
    + +
    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/add_class.html b/v1.3.1/reference/add_class.html new file mode 100644 index 000000000..0f06fe724 --- /dev/null +++ b/v1.3.1/reference/add_class.html @@ -0,0 +1,88 @@ + +Add a class — add_class • rbmi + Skip to contents + + +
    +
    +
    +

    Add a class

    + Source: R/utilities.R +
    add_class.Rd
    +
    + +
    +

    Utility function to add a class to an object. Adds the new class +after any existing classes.

    +
    + +
    +

    Usage

    + 
    add_class(x, cls)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    object to add a class to.

    + + +
    cls
    +

    the class to be added.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/adjust_trajectories.html b/v1.3.1/reference/adjust_trajectories.html new file mode 100644 index 000000000..b6c0fceb7 --- /dev/null +++ b/v1.3.1/reference/adjust_trajectories.html @@ -0,0 +1,126 @@ + +Adjust trajectories due to the intercurrent event (ICE) — adjust_trajectories • rbmi + Skip to contents + + +
    +
    +
    +

    Adjust trajectories due to the intercurrent event (ICE)

    + Source: R/simulate_data.R +
    adjust_trajectories.Rd
    +
    + +
    +

    Adjust trajectories due to the intercurrent event (ICE)

    +
    + +
    +

    Usage

    + 
    adjust_trajectories(
+  distr_pars_group,
+  outcome,
+  ids,
+  ind_ice,
+  strategy_fun,
+  distr_pars_ref = NULL
+)
    +
    + +
    +

    Arguments

    + + +
    distr_pars_group
    +

    Named list containing the simulation parameters of the multivariate +normal distribution assumed for the given treatment group. It contains the following elements:

    • mu: Numeric vector indicating the mean outcome trajectory. It should include the outcome +at baseline.

      • +

    • sigma Covariance matrix of the outcome trajectory.

      • +
    + + +
    outcome
    +

    Numeric variable that specifies the longitudinal outcome.

    + + +
    ids
    +

    Factor variable that specifies the id of each subject.

    + + +
    ind_ice
    +

    A binary variable that takes value 1 if the corresponding outcome is affected +by the ICE and 0 otherwise.

    + + +
    strategy_fun
    +

    Function implementing trajectories after the intercurrent event (ICE). Must +be one of getStrategies(). See getStrategies() for details.

    + + +
    distr_pars_ref
    +

    Optional. Named list containing the simulation parameters of the +reference arm. It contains the following elements:

    • mu: Numeric vector indicating the mean outcome trajectory assuming no ICEs. It should +include the outcome at baseline.

      • +

    • sigma Covariance matrix of the outcome trajectory assuming no ICEs.

      • +
    + +
    +
    +

    Value

    +

    A numeric vector containing the adjusted trajectories.

    +
    +
    +

    See also

    +

    adjust_trajectories_single().

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/adjust_trajectories_single.html b/v1.3.1/reference/adjust_trajectories_single.html new file mode 100644 index 000000000..023f57a65 --- /dev/null +++ b/v1.3.1/reference/adjust_trajectories_single.html @@ -0,0 +1,117 @@ + +Adjust trajectory of a subject's outcome due to the intercurrent event (ICE) — adjust_trajectories_single • rbmi + Skip to contents + + +
    +
    +
    +

    Adjust trajectory of a subject's outcome due to the intercurrent event (ICE)

    + Source: R/simulate_data.R +
    adjust_trajectories_single.Rd
    +
    + +
    +

    Adjust trajectory of a subject's outcome due to the intercurrent event (ICE)

    +
    + +
    +

    Usage

    + 
    adjust_trajectories_single(
+  distr_pars_group,
+  outcome,
+  strategy_fun,
+  distr_pars_ref = NULL
+)
    +
    + +
    +

    Arguments

    + + +
    distr_pars_group
    +

    Named list containing the simulation parameters of the multivariate +normal distribution assumed for the given treatment group. It contains the following elements:

    • mu: Numeric vector indicating the mean outcome trajectory. It should include the +outcome at baseline.

      • +

    • sigma Covariance matrix of the outcome trajectory.

      • +
    + + +
    outcome
    +

    Numeric variable that specifies the longitudinal outcome.

    + + +
    strategy_fun
    +

    Function implementing trajectories after the intercurrent event (ICE). +Must be one of getStrategies(). See getStrategies() for details.

    + + +
    distr_pars_ref
    +

    Optional. Named list containing the simulation parameters of the +reference arm. It contains the following elements:

    • mu: Numeric vector indicating the mean outcome trajectory assuming no ICEs. It should +include the outcome at baseline.

      • +

    • sigma Covariance matrix of the outcome trajectory assuming no ICEs.

      • +
    + +
    +
    +

    Value

    +

    A numeric vector containing the adjusted trajectory for a single subject.

    +
    +
    +

    Details

    +

    outcome should be specified such that all-and-only the post-ICE observations +(i.e. the +observations to be adjusted) are set to NA.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/analyse.html b/v1.3.1/reference/analyse.html new file mode 100644 index 000000000..017af7868 --- /dev/null +++ b/v1.3.1/reference/analyse.html @@ -0,0 +1,270 @@ + +Analyse Multiple Imputed Datasets — analyse • rbmi + Skip to contents + + +
    +
    +
    +

    Analyse Multiple Imputed Datasets

    + Source: R/analyse.R +
    analyse.Rd
    +
    + +
    +

    This function takes multiple imputed datasets (as generated by +the impute() function) and runs an analysis function on +each of them.

    +
    + +
    +

    Usage

    + 
    analyse(
+  imputations,
+  fun = ancova,
+  delta = NULL,
+  ...,
+  ncores = 1,
+  .validate = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    imputations
    +

    An imputations object as created by impute().

    + + +
    fun
    +

    An analysis function to be applied to each imputed dataset. See details.

    + + +
    delta
    +

    A data.frame containing the delta transformation to be applied to the imputed +datasets prior to running fun. See details.

    + + +
    ...
    +

    Additional arguments passed onto fun.

    + + +
    ncores
    +

    The number of parallel processes to use when running this function. Can also be a +cluster object created by make_rbmi_cluster(). See the parallisation section below.

    + + +
    .validate
    +

    Should inputations be checked to ensure it conforms to the required format +(default = TRUE) ? Can gain a small performance increase if this is set to FALSE when +analysing a large number of samples.

    + +
    +
    +

    Details

    +

    This function works by performing the following steps:

    1. Extract a dataset from the imputations object.

      2. +

    2. Apply any delta adjustments as specified by the delta argument.

      3. +

    3. Run the analysis function fun on the dataset.

      4. +

    4. Repeat steps 1-3 across all of the datasets inside the imputations +object.

      5. +

    5. Collect and return all of the analysis results.

      6. +

    The analysis function fun must take a data.frame as its first +argument. All other options to analyse() are passed onto fun +via .... +fun must return a named list with each element itself being a +list containing a single +numeric element called est (or additionally se and df if +you had originally specified method_bayes() or method_approxbayes()) +i.e.:

    +

    myfun <- function(dat, ...) {
+    mod_1 <- lm(data = dat, outcome ~ group)
+    mod_2 <- lm(data = dat, outcome ~ group + covar)
+    x <- list(
+        trt_1 = list(
+            est = coef(mod_1)[[group]],
+            se = sqrt(vcov(mod_1)[group, group]),
+            df = df.residual(mod_1)
+        ),
+        trt_2 = list(
+            est = coef(mod_2)[[group]],
+            se = sqrt(vcov(mod_2)[group, group]),
+            df = df.residual(mod_2)
+        )
+     )
+     return(x)
+ }

    +

    Please note that the vars$subjid column (as defined in the original call to +draws()) will be scrambled in the data.frames that are provided to fun. +This is to say they will not contain the original subject values and as such +any hard coding of subject ids is strictly to be avoided.

    +

    By default fun is the ancova() function. +Please note that this function +requires that a vars object, as created by set_vars(), is provided via +the vars argument e.g. analyse(imputeObj, vars = set_vars(...)). Please +see the documentation for ancova() for full details. +Please also note that the theoretical justification for the conditional mean imputation +method (method = method_condmean() in draws()) relies on the fact that ANCOVA is +a linear transformation of the outcomes. +Thus care is required when applying alternative analysis functions in this setting.

    +

    The delta argument can be used to specify offsets to be applied +to the outcome variable in the imputed datasets prior to the analysis. +This is typically used for sensitivity or tipping point analyses. The +delta dataset must contain columns vars$subjid, vars$visit (as specified +in the original call to draws()) and delta. Essentially this data.frame +is merged onto the imputed dataset by vars$subjid and vars$visit and then +the outcome variable is modified by:

    +

    imputed_data[[vars$outcome]] <- imputed_data[[vars$outcome]] + imputed_data[["delta"]]

    +

    Please note that in order to provide maximum flexibility, the delta argument +can be used to modify any/all outcome values including those that were not +imputed. Care must be taken when defining offsets. It is recommend that you +use the helper function delta_template() to define the delta datasets as +this provides utility variables such as is_missing which can be used to identify +exactly which visits have been imputed.

    +
    +
    +

    Parallelisation

    + + +

    To speed up the evaluation of analyse() you can use the ncores argument to enable parallelisation. +Simply providing an integer will get rbmi to automatically spawn that many background processes +to parallelise across. If you are using a custom analysis function then you need to ensure +that any libraries or global objects required by your function are available in the +sub-processes. To do this you need to use the make_rbmi_cluster() function for example:

    +

    my_custom_fun <- function(...) <some analysis code>
+cl <- make_rbmi_cluster(
+    4,
+    objects = list("my_custom_fun" = my_custom_fun),
+    packages = c("dplyr", "nlme")
+)
+analyse(
+    imputations = imputeObj,
+    fun = my_custom_fun,
+    ncores = cl
+)
+parallel::stopCluster(cl)

    +

    Note that there is significant overhead both with setting up the sub-processes and with +transferring data back-and-forth between the main process and the sub-processes. As such +parallelisation of the analyse() function tends to only be worth it when you have +> 2000 samples generated by draws(). Conversely using parallelisation if your samples +are smaller than this may lead to longer run times than just running it sequentially.

    +

    It is important to note that the implementation of parallel processing within analyse() has +been optimised around the assumption that the parallel processes will be spawned on the same +machine and not a remote cluster. One such optimisation is that the required data is saved to +a temporary file on the local disk from which it is then read into each sub-process. This is +done to avoid the overhead of transferring the data over the network. Our assumption is that +if you are at the stage where you need to be parallelising your analysis over a remote cluster +then you would likely be better off parallelising across multiple rbmi runs rather than within +a single rbmi run.

    +

    Finally, if you are doing a tipping point analysis you can get a reasonable performance +improvement by re-using the cluster between each call to analyse() e.g.

    +

    cl <- make_rbmi_cluster(4)
+ana_1 <- analyse(
+    imputations = imputeObj,
+    delta = delta_plan_1,
+    ncores = cl
+)
+ana_2 <- analyse(
+    imputations = imputeObj,
+    delta = delta_plan_2,
+    ncores = cl
+)
+ana_3 <- analyse(
+    imputations = imputeObj,
+    delta = delta_plan_3,
+    ncores = cl
+)
+parallel::clusterStop(cl)

    +
    +
    +

    See also

    +

    extract_imputed_dfs() for manually extracting imputed +datasets.

    +

    delta_template() for creating delta data.frames.

    +

    ancova() for the default analysis function.

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+vars <- set_vars(
+    subjid = "subjid",
+    visit = "visit",
+    outcome = "outcome",
+    group = "group",
+    covariates = c("sex", "age", "sex*age")
+)
+
+analyse(
+    imputations = imputeObj,
+    vars = vars
+)
+
+deltadf <- data.frame(
+    subjid = c("Pt1", "Pt1", "Pt2"),
+    visit = c("Visit_1", "Visit_2", "Visit_2"),
+    delta = c( 5, 9, -10)
+)
+
+analyse(
+    imputations = imputeObj,
+    delta = deltadf,
+    vars = vars
+)
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/ancova.html b/v1.3.1/reference/ancova.html new file mode 100644 index 000000000..9e47363ff --- /dev/null +++ b/v1.3.1/reference/ancova.html @@ -0,0 +1,192 @@ + +Analysis of Covariance — ancova • rbmi + Skip to contents + + +
    +
    +
    +

    Analysis of Covariance

    + Source: R/ancova.R +
    ancova.Rd
    +
    + +
    +

    Performs an analysis of covariance between two groups returning the estimated +"treatment effect" (i.e. the contrast between the two treatment groups) and +the least square means estimates in each group.

    +
    + +
    +

    Usage

    + 
    ancova(
+  data,
+  vars,
+  visits = NULL,
+  weights = c("counterfactual", "equal", "proportional_em", "proportional")
+)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    A data.frame containing the data to be used in the model.

    + + +
    vars
    +

    A vars object as generated by set_vars(). Only the group, +visit, outcome and covariates elements are required. See details.

    + + +
    visits
    +

    An optional character vector specifying which visits to +fit the ancova model at. If NULL, a separate ancova model will be fit to the +outcomes for each visit (as determined by unique(data[[vars$visit]])). +See details.

    + + +
    weights
    +

    Character, either "counterfactual" (default), "equal", +"proportional_em" or "proportional". +Specifies the weighting strategy to be used when calculating the lsmeans. +See the weighting section for more details.

    + +
    +
    +

    Details

    +

    The function works as follows:

    1. Select the first value from visits.

      2. +

    2. Subset the data to only the observations that occurred on this visit.

      3. +

    3. Fit a linear model as vars$outcome ~ vars$group + vars$covariates.

      4. +

    4. Extract the "treatment effect" & least square means for each treatment group.

      5. +

    5. Repeat points 2-3 for all other values in visits.

      6. +

    If no value for visits is provided then it will be set to +unique(data[[vars$visit]]).

    +

    In order to meet the formatting standards set by analyse() the results will be collapsed +into a single list suffixed by the visit name, e.g.:

    +

    list(
+   trt_visit_1 = list(est = ...),
+   lsm_ref_visit_1 = list(est = ...),
+   lsm_alt_visit_1 = list(est = ...),
+   trt_visit_2 = list(est = ...),
+   lsm_ref_visit_2 = list(est = ...),
+   lsm_alt_visit_2 = list(est = ...),
+   ...
+)

    +

    Please note that "ref" refers to the first factor level of vars$group which does not necessarily +coincide with the control arm. Analogously, "alt" refers to the second factor level of vars$group. +"trt" refers to the model contrast translating the mean difference between the second level and first level.

    +

    If you want to include interaction terms in your model this can be done +by providing them to the covariates argument of set_vars() +e.g. set_vars(covariates = c("sex*age")).

    +
    +
    +

    Weighting

    + + +
    +

    Counterfactual

    + + +

    For weights = "counterfactual" (the default) the lsmeans are obtained by +taking the average of the predicted values for each patient after assigning all patients +to each arm in turn. +This approach is equivalent to standardization or g-computation. +In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", counterfactual = "<treatment>")

    +

    Note that to ensure backwards compatibility with previous versions of rbmi +weights = "proportional" is an alias for weights = "counterfactual". +To get results consistent with emmeans's weights = "proportional" +please use weights = "proportional_em".

    +
    + +
    +

    Equal

    + + +

    For weights = "equal" the lsmeans are obtained by taking the model fitted +value of a hypothetical patient whose covariates are defined as follows:

    • Continuous covariates are set to mean(X)

      • +

    • Dummy categorical variables are set to 1/N where N is the number of levels

      • +

    • Continuous * continuous interactions are set to mean(X) * mean(Y)

      • +

    • Continuous * categorical interactions are set to mean(X) * 1/N

      • +

    • Dummy categorical * categorical interactions are set to 1/N * 1/M

      • +

    In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", weights = "equal")

    +
    + +
    +

    Proportional

    + + +

    For weights = "proportional_em" the lsmeans are obtained as per weights = "equal" +except instead of weighting each observation equally they are weighted by the proportion +in which the given combination of categorical values occurred in the data. +In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", weights = "proportional")

    +

    Note that this is not to be confused with weights = "proportional" which is an alias +for weights = "counterfactual".

    +
    + +
    +
    +

    See also

    +

    analyse()

    +

    stats::lm()

    +

    set_vars()

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/ancova_single.html b/v1.3.1/reference/ancova_single.html new file mode 100644 index 000000000..b6118b7ab --- /dev/null +++ b/v1.3.1/reference/ancova_single.html @@ -0,0 +1,174 @@ + +Implements an Analysis of Covariance (ANCOVA) — ancova_single • rbmi + Skip to contents + + +
    +
    +
    +

    Implements an Analysis of Covariance (ANCOVA)

    + Source: R/ancova.R +
    ancova_single.Rd
    +
    + +
    +

    Performance analysis of covariance. See ancova() for full details.

    +
    + +
    +

    Usage

    + 
    ancova_single(
+  data,
+  outcome,
+  group,
+  covariates,
+  weights = c("counterfactual", "equal", "proportional_em", "proportional")
+)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    A data.frame containing the data to be used in the model.

    + + +
    outcome
    +

    Character, the name of the outcome variable in data.

    + + +
    group
    +

    Character, the name of the group variable in data.

    + + +
    covariates
    +

    Character vector containing the name of any additional covariates +to be included in the model as well as any interaction terms.

    + + +
    weights
    +

    Character, either "counterfactual" (default), "equal", +"proportional_em" or "proportional". +Specifies the weighting strategy to be used when calculating the lsmeans. +See the weighting section for more details.

    + +
    +
    +

    Details

    + +

    • group must be a factor variable with only 2 levels.

      • +

    • outcome must be a continuous numeric variable.

      • +
    +
    +

    Weighting

    + + +
    +

    Counterfactual

    + + +

    For weights = "counterfactual" (the default) the lsmeans are obtained by +taking the average of the predicted values for each patient after assigning all patients +to each arm in turn. +This approach is equivalent to standardization or g-computation. +In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", counterfactual = "<treatment>")

    +

    Note that to ensure backwards compatibility with previous versions of rbmi +weights = "proportional" is an alias for weights = "counterfactual". +To get results consistent with emmeans's weights = "proportional" +please use weights = "proportional_em".

    +
    + +
    +

    Equal

    + + +

    For weights = "equal" the lsmeans are obtained by taking the model fitted +value of a hypothetical patient whose covariates are defined as follows:

    • Continuous covariates are set to mean(X)

      • +

    • Dummy categorical variables are set to 1/N where N is the number of levels

      • +

    • Continuous * continuous interactions are set to mean(X) * mean(Y)

      • +

    • Continuous * categorical interactions are set to mean(X) * 1/N

      • +

    • Dummy categorical * categorical interactions are set to 1/N * 1/M

      • +

    In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", weights = "equal")

    +
    + +
    +

    Proportional

    + + +

    For weights = "proportional_em" the lsmeans are obtained as per weights = "equal" +except instead of weighting each observation equally they are weighted by the proportion +in which the given combination of categorical values occurred in the data. +In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", weights = "proportional")

    +

    Note that this is not to be confused with weights = "proportional" which is an alias +for weights = "counterfactual".

    +
    + +
    +
    +

    See also

    +

    ancova()

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+iris2 <- iris[ iris$Species %in% c("versicolor", "virginica"), ]
+iris2$Species <- factor(iris2$Species)
+ancova_single(iris2, "Sepal.Length", "Species", c("Petal.Length * Petal.Width"))
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/antidepressant_data.html b/v1.3.1/reference/antidepressant_data.html new file mode 100644 index 000000000..165892b7f --- /dev/null +++ b/v1.3.1/reference/antidepressant_data.html @@ -0,0 +1,130 @@ + +Antidepressant trial data — antidepressant_data • rbmi + Skip to contents + + +
    +
    +
    +

    Antidepressant trial data

    + Source: R/data.R +
    antidepressant_data.Rd
    +
    + +
    +

    A dataset containing data from a publicly available example data set from an antidepressant +clinical trial. +The dataset is available on the website of the +Drug Information Association Scientific Working Group on Estimands and Missing Data. +As per that website, the original data are from an antidepressant clinical trial with four +treatments; two doses of an experimental medication, +a positive control, and placebo and was published in Goldstein et al (2004). To mask the real +data, week 8 observations were removed and two arms were created: +the original placebo arm and a "drug arm" created by randomly selecting patients from the +three non-placebo arms.

    +
    + +
    +

    Usage

    + 
    antidepressant_data
    +
    + +
    +

    Format

    +

    A data.frame with 608 rows and 11 variables:

    • PATIENT: patients IDs.

      • +

    • HAMATOTL: total score Hamilton Anxiety Rating Scale.

      • +

    • PGIIMP: patient's Global Impression of Improvement Rating Scale.

      • +

    • RELDAYS: number of days between visit and baseline.

      • +

    • VISIT: post-baseline visit. Has levels 4,5,6,7.

      • +

    • THERAPY: the treatment group variable. It is equal to PLACEBO for observations from +the placebo arm, or DRUG for observations from the active arm.

      • +

    • GENDER: patient's gender.

      • +

    • POOLINV: pooled investigator.

      • +

    • BASVAL: baseline outcome value.

      • +

    • HAMDTL17: Hamilton 17-item rating scale value.

      • +

    • CHANGE: change from baseline in the Hamilton 17-item rating scale.

      • +
    +
    +

    Details

    +

    The relevant endpoint is the Hamilton 17-item rating scale for depression (HAMD17) for +which baseline and weeks 1, 2, 4, and 6 assessments are included. +Study drug discontinuation occurred in 24% subjects from the active drug and 26% from +placebo. +All data after study drug discontinuation are missing and there is a single additional +intermittent missing observation.

    +
    +
    +

    References

    +

    Goldstein, Lu, Detke, Wiltse, Mallinckrodt, Demitrack. Duloxetine in the treatment of +depression: a double-blind placebo-controlled comparison with paroxetine. +J Clin Psychopharmacol 2004;24: 389-399.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/apply_delta.html b/v1.3.1/reference/apply_delta.html new file mode 100644 index 000000000..5df448bc6 --- /dev/null +++ b/v1.3.1/reference/apply_delta.html @@ -0,0 +1,97 @@ + +Applies delta adjustment — apply_delta • rbmi + Skip to contents + + +
    +
    +
    +

    Applies delta adjustment

    + Source: R/delta.R +
    apply_delta.Rd
    +
    + +
    +

    Takes a delta dataset and adjusts the outcome variable by adding the +corresponding delta.

    +
    + +
    +

    Usage

    + 
    apply_delta(data, delta = NULL, group = NULL, outcome = NULL)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    data.frame which will have its outcome column adjusted.

    + + +
    delta
    +

    data.frame (must contain a column called delta).

    + + +
    group
    +

    character vector of variables in both data and delta that will be used +to merge the 2 data.frames together by.

    + + +
    outcome
    +

    character, name of the outcome variable in data.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_analysis.html b/v1.3.1/reference/as_analysis.html new file mode 100644 index 000000000..6ae41ac9b --- /dev/null +++ b/v1.3.1/reference/as_analysis.html @@ -0,0 +1,103 @@ + +Construct an analysis object — as_analysis • rbmi + Skip to contents + + +
    +
    +
    +

    Construct an analysis object

    + Source: R/analyse.R +
    as_analysis.Rd
    +
    + +
    +

    Creates an analysis object ensuring that all components are +correctly defined.

    +
    + +
    +

    Usage

    + 
    as_analysis(results, method, delta = NULL, fun = NULL, fun_name = NULL)
    +
    + +
    +

    Arguments

    + + +
    results
    +

    A list of lists contain the analysis results for each imputation +See analyse() for details on what this object should look like.

    + + +
    method
    +

    The method object as specified in draws().

    + + +
    delta
    +

    The delta dataset used. See analyse() for details on how this +should be specified.

    + + +
    fun
    +

    The analysis function that was used.

    + + +
    fun_name
    +

    The character name of the analysis function (used for printing) +purposes.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_ascii_table.html b/v1.3.1/reference/as_ascii_table.html new file mode 100644 index 000000000..c35781545 --- /dev/null +++ b/v1.3.1/reference/as_ascii_table.html @@ -0,0 +1,98 @@ + +as_ascii_table — as_ascii_table • rbmi + Skip to contents + + +
    +
    +
    +

    as_ascii_table

    + Source: R/as_ascii_table.R +
    as_ascii_table.Rd
    +
    + +
    +

    This function takes a data.frame and attempts to convert it into +a simple ascii format suitable for printing to the screen +It is assumed all variable values have a as.character() method +in order to cast them to character.

    +
    + +
    +

    Usage

    + 
    as_ascii_table(dat, line_prefix = "  ", pcol = NULL)
    +
    + +
    +

    Arguments

    + + +
    dat
    +

    Input dataset to convert into a ascii table

    + + +
    line_prefix
    +

    Symbols to prefix infront of every line of the table

    + + +
    pcol
    +

    name of column to be handled as a p-value. Sets the value to <0.001 if the value is 0 after rounding

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_class.html b/v1.3.1/reference/as_class.html new file mode 100644 index 000000000..ce50055ee --- /dev/null +++ b/v1.3.1/reference/as_class.html @@ -0,0 +1,85 @@ + +Set Class — as_class • rbmi + Skip to contents + + +
    +
    +
    +

    Set Class

    + Source: R/utilities.R +
    as_class.Rd
    +
    + +
    +

    Utility function to set an objects class.

    +
    + +
    +

    Usage

    + 
    as_class(x, cls)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    object to set the class of.

    + + +
    cls
    +

    the class to be set.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_cropped_char.html b/v1.3.1/reference/as_cropped_char.html new file mode 100644 index 000000000..64c43c8aa --- /dev/null +++ b/v1.3.1/reference/as_cropped_char.html @@ -0,0 +1,92 @@ + +as_cropped_char — as_cropped_char • rbmi + Skip to contents + + +
    +
    +
    +

    as_cropped_char

    + Source: R/as_ascii_table.R +
    as_cropped_char.Rd
    +
    + +
    +

    Makes any character string above x chars +Reduce down to a x char string with ...

    +
    + +
    +

    Usage

    + 
    as_cropped_char(inval, crop_at = 30, ndp = 3)
    +
    + +
    +

    Arguments

    + + +
    inval
    +

    a single element value

    + + +
    crop_at
    +

    character limit

    + + +
    ndp
    +

    Number of decimal places to display

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_dataframe.html b/v1.3.1/reference/as_dataframe.html new file mode 100644 index 000000000..070f16617 --- /dev/null +++ b/v1.3.1/reference/as_dataframe.html @@ -0,0 +1,83 @@ + +Convert object to dataframe — as_dataframe • rbmi + Skip to contents + + +
    +
    +
    +

    Convert object to dataframe

    + Source: R/utilities.R +
    as_dataframe.Rd
    +
    + +
    +

    Convert object to dataframe

    +
    + +
    +

    Usage

    + 
    as_dataframe(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a data.frame like object

    +

    Utility function to convert a "data.frame-like" object to an actual data.frame +to avoid issues with inconsistency on methods (such as [() and dplyr's grouped dataframes)

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_draws.html b/v1.3.1/reference/as_draws.html new file mode 100644 index 000000000..f51c91978 --- /dev/null +++ b/v1.3.1/reference/as_draws.html @@ -0,0 +1,120 @@ + +Creates a draws object — as_draws • rbmi + Skip to contents + + +
    +
    +
    +

    Creates a draws object

    + Source: R/draws.R +
    as_draws.Rd
    +
    + +
    +

    Creates a draws object which is the final output of a call to draws().

    +
    + +
    +

    Usage

    + 
    as_draws(method, samples, data, formula, n_failures = NULL, fit = NULL)
    +
    + +
    +

    Arguments

    + + +
    method
    +

    A method object as generated by either method_bayes(), +method_approxbayes(), method_condmean() or method_bmlmi().

    + + +
    samples
    +

    A list of sample_single objects. See sample_single().

    + + +
    data
    +

    R6 longdata object containing all relevant input data information.

    + + +
    formula
    +

    Fixed effects formula object used for the model specification.

    + + +
    n_failures
    +

    Absolute number of failures of the model fit.

    + + +
    fit
    +

    If method_bayes() is chosen, returns the MCMC Stan fit object. Otherwise NULL.

    + +
    +
    +

    Value

    +

    A draws object which is a named list containing the following:

    • data: R6 longdata object containing all relevant input data information.

      • +

    • method: A method object as generated by either method_bayes(), +method_approxbayes() or method_condmean().

      • +

    • samples: list containing the estimated parameters of interest. +Each element of samples is a named list containing the following:

      • ids: vector of characters containing the ids of the subjects included in the original dataset.

        • +

      • beta: numeric vector of estimated regression coefficients.

        • +

      • sigma: list of estimated covariance matrices (one for each level of vars$group).

        • +

      • theta: numeric vector of transformed covariances.

        • +

      • failed: Logical. TRUE if the model fit failed.

        • +

      • ids_samp: vector of characters containing the ids of the subjects included in the given sample.

        • +
      • +

    • fit: if method_bayes() is chosen, returns the MCMC Stan fit object. Otherwise NULL.

      • +

    • n_failures: absolute number of failures of the model fit. +Relevant only for method_condmean(type = "bootstrap"), method_approxbayes() and method_bmlmi().

      • +

    • formula: fixed effects formula object used for the model specification.

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_imputation.html b/v1.3.1/reference/as_imputation.html new file mode 100644 index 000000000..8b970949e --- /dev/null +++ b/v1.3.1/reference/as_imputation.html @@ -0,0 +1,101 @@ + +Create an imputation object — as_imputation • rbmi + Skip to contents + + +
    +
    +
    +

    Create an imputation object

    + Source: R/impute.R +
    as_imputation.Rd
    +
    + +
    +

    This function creates the object that is returned from impute(). Essentially +it is a glorified wrapper around list() ensuring that the required elements have been +set and that the class is added as expected.

    +
    + +
    +

    Usage

    + 
    as_imputation(imputations, data, method, references)
    +
    + +
    +

    Arguments

    + + +
    imputations
    +

    A list of imputations_list's as created by imputation_df()

    + + +
    data
    +

    A longdata object as created by longDataConstructor()

    + + +
    method
    +

    A method object as created by method_condmean(), method_bayes() or +method_approxbayes()

    + + +
    references
    +

    A named vector. Identifies the references to be used when generating the +imputed values. Should be of the form c("Group" = "Reference", "Group" = "Reference").

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_indices.html b/v1.3.1/reference/as_indices.html new file mode 100644 index 000000000..034b82166 --- /dev/null +++ b/v1.3.1/reference/as_indices.html @@ -0,0 +1,90 @@ + +Convert indicator to index — as_indices • rbmi + Skip to contents + + +
    +
    +
    +

    Convert indicator to index

    + Source: R/mcmc.R +
    as_indices.Rd
    +
    + +
    +

    Converts a string of 0's and 1's into index positions of the 1's +padding the results by 0's so they are all the same length

    +
    + +
    +

    Usage

    + 
    as_indices(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a character vector whose values are all either "0" or "1". All elements of +the vector must be the same length

    + +
    +
    +

    Details

    +

    i.e.

    +

    patmap(c("1101", "0001"))  ->   list(c(1,2,4,999), c(4,999, 999, 999))

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_mmrm_df.html b/v1.3.1/reference/as_mmrm_df.html new file mode 100644 index 000000000..07df6286a --- /dev/null +++ b/v1.3.1/reference/as_mmrm_df.html @@ -0,0 +1,121 @@ + +Creates a "MMRM" ready dataset — as_mmrm_df • rbmi + Skip to contents + + +
    +
    +
    +

    Creates a "MMRM" ready dataset

    + Source: R/mmrm.R +
    as_mmrm_df.Rd
    +
    + +
    +

    Converts a design matrix + key variables into a common format +In particular this function does the following:

    • Renames all covariates as V1, V2, etc to avoid issues of special characters in variable names

      • +

    • Ensures all key variables are of the right type

      • +

    • Inserts the outcome, visit and subjid variables into the data.frame +naming them as outcome, visit and subjid

      • +

    • If provided will also insert the group variable into the data.frame named as group

      • +
    + +
    +

    Usage

    + 
    as_mmrm_df(designmat, outcome, visit, subjid, group = NULL)
    +
    + +
    +

    Arguments

    + + +
    designmat
    +

    a data.frame or matrix containing the covariates to use in the MMRM model. +Dummy variables must already be expanded out, i.e. via stats::model.matrix(). Cannot contain +any missing values

    + + +
    outcome
    +

    a numeric vector. The outcome value to be regressed on in the MMRM model.

    + + +
    visit
    +

    a character / factor vector. Indicates which visit the outcome value occurred on.

    + + +
    subjid
    +

    a character / factor vector. The subject identifier used to link separate visits +that belong to the same subject.

    + + +
    group
    +

    a character / factor vector. Indicates which treatment group the patient belongs to.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_mmrm_formula.html b/v1.3.1/reference/as_mmrm_formula.html new file mode 100644 index 000000000..4fce95e6a --- /dev/null +++ b/v1.3.1/reference/as_mmrm_formula.html @@ -0,0 +1,93 @@ + +Create MMRM formula — as_mmrm_formula • rbmi + Skip to contents + + +
    +
    +
    +

    Create MMRM formula

    + Source: R/mmrm.R +
    as_mmrm_formula.Rd
    +
    + +
    +

    Derives the MMRM model formula from the structure of mmrm_df. +returns a formula object of the form:

    +
    + +
    +

    Usage

    + 
    as_mmrm_formula(mmrm_df, cov_struct)
    +
    + +
    +

    Arguments

    + + +
    mmrm_df
    +

    an mmrm data.frame as created by as_mmrm_df()

    + + +
    cov_struct
    +

    Character - The covariance structure to be used, must be one of "us" (default), +"ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", or "toeph")

    + +
    +
    +

    Details

    + 

    outcome ~ 0 + V1 + V2 + V4 + ... + us(visit | group / subjid)

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_model_df.html b/v1.3.1/reference/as_model_df.html new file mode 100644 index 000000000..f47761909 --- /dev/null +++ b/v1.3.1/reference/as_model_df.html @@ -0,0 +1,96 @@ + +Expand data.frame into a design matrix — as_model_df • rbmi + Skip to contents + + +
    +
    +
    +

    Expand data.frame into a design matrix

    + Source: R/utilities.R +
    as_model_df.Rd
    +
    + +
    +

    Expands out a data.frame using a formula to create a design matrix. +Key details are that it will always place the outcome variable into +the first column of the return object.

    +
    + +
    +

    Usage

    + 
    as_model_df(dat, frm)
    +
    + +
    +

    Arguments

    + + +
    dat
    +

    a data.frame

    + + +
    frm
    +

    a formula

    + +
    +
    +

    Details

    +

    The outcome column may contain NA's but none of the other variables +listed in the formula should contain missing values

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_simple_formula.html b/v1.3.1/reference/as_simple_formula.html new file mode 100644 index 000000000..813ff40c7 --- /dev/null +++ b/v1.3.1/reference/as_simple_formula.html @@ -0,0 +1,89 @@ + +Creates a simple formula object from a string — as_simple_formula • rbmi + Skip to contents + + +
    +
    +
    +

    Creates a simple formula object from a string

    + Source: R/utilities.R +
    as_simple_formula.Rd
    +
    + +
    +

    Converts a string list of variables into a formula object

    +
    + +
    +

    Usage

    + 
    as_simple_formula(outcome, covars)
    +
    + +
    +

    Arguments

    + + +
    outcome
    +

    character (length 1 vector). Name of the outcome variable

    + + +
    covars
    +

    character (vector). Name of covariates

    + +
    +
    +

    Value

    +

    A formula

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_stan_array.html b/v1.3.1/reference/as_stan_array.html new file mode 100644 index 000000000..bc6b50b8e --- /dev/null +++ b/v1.3.1/reference/as_stan_array.html @@ -0,0 +1,87 @@ + +As array — as_stan_array • rbmi + Skip to contents + + +
    +
    +
    +

    As array

    + Source: R/mcmc.R +
    as_stan_array.Rd
    +
    + +
    +

    Converts a numeric value of length 1 into a 1 dimension array. +This is to avoid type errors that are thrown by stan when length 1 numeric vectors +are provided by R for stan::vector inputs

    +
    + +
    +

    Usage

    + 
    as_stan_array(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a numeric vector

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/as_strata.html b/v1.3.1/reference/as_strata.html new file mode 100644 index 000000000..33d7db639 --- /dev/null +++ b/v1.3.1/reference/as_strata.html @@ -0,0 +1,104 @@ + +Create vector of Stratas — as_strata • rbmi + Skip to contents + + +
    +
    +
    +

    Create vector of Stratas

    + Source: R/bootstrap.R +
    as_strata.Rd
    +
    + +
    +

    Collapse multiple categorical variables into distinct unique categories. +e.g.

    +

    as_strata(c(1,1,2,2,2,1), c(5,6,5,5,6,5))

    +

    would return

    +

    c(1,2,3,3,4,1)

    +
    + +
    +

    Usage

    + 
    as_strata(...)
    +
    + +
    +

    Arguments

    + + +
    ...
    +

    numeric/character/factor vectors of the same length

    + +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+as_strata(c(1,1,2,2,2,1), c(5,6,5,5,6,5))
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/assert_variables_exist.html b/v1.3.1/reference/assert_variables_exist.html new file mode 100644 index 000000000..8c5b520bd --- /dev/null +++ b/v1.3.1/reference/assert_variables_exist.html @@ -0,0 +1,85 @@ + +Assert that all variables exist within a dataset — assert_variables_exist • rbmi + Skip to contents + + +
    +
    +
    +

    Assert that all variables exist within a dataset

    + Source: R/expand.R +
    assert_variables_exist.Rd
    +
    + +
    +

    Performs an assertion check to ensure that a vector of variable exists within a data.frame as expected.

    +
    + +
    +

    Usage

    + 
    assert_variables_exist(data, vars)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    a data.frame

    + + +
    vars
    +

    a character vector of variable names

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/char2fct.html b/v1.3.1/reference/char2fct.html new file mode 100644 index 000000000..c6a7edef4 --- /dev/null +++ b/v1.3.1/reference/char2fct.html @@ -0,0 +1,91 @@ + +Convert character variables to factor — char2fct • rbmi + Skip to contents + + +
    +
    +
    +

    Convert character variables to factor

    + Source: R/utilities.R +
    char2fct.Rd
    +
    + +
    +

    Provided a vector of variable names this function converts any +character variables into factors. Has no affect on numeric or existing +factor variables

    +
    + +
    +

    Usage

    + 
    char2fct(data, vars = NULL)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    A data.frame

    + + +
    vars
    +

    a character vector of variables in data

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/check_ESS.html b/v1.3.1/reference/check_ESS.html new file mode 100644 index 000000000..19ef5f6bf --- /dev/null +++ b/v1.3.1/reference/check_ESS.html @@ -0,0 +1,105 @@ + +Diagnostics of the MCMC based on ESS — check_ESS • rbmi + Skip to contents + + +
    +
    +
    +

    Diagnostics of the MCMC based on ESS

    + Source: R/mcmc.R +
    check_ESS.Rd
    +
    + +
    +

    Check the quality of the MCMC draws from the posterior distribution +by checking whether the relative ESS is sufficiently large.

    +
    + +
    +

    Usage

    + 
    check_ESS(stan_fit, n_draws, threshold_lowESS = 0.4)
    +
    + +
    +

    Arguments

    + + +
    stan_fit
    +

    A stanfit object.

    + + +
    n_draws
    +

    Number of MCMC draws.

    + + +
    threshold_lowESS
    +

    A number in [0,1] indicating the minimum acceptable +value of the relative ESS. See details.

    + +
    +
    +

    Value

    +

    A warning message in case of detected problems.

    +
    +
    +

    Details

    +

    check_ESS() works as follows:

    1. Extract the ESS from stan_fit for each parameter of the model.

      2. +

    2. Compute the relative ESS (i.e. the ESS divided by the number of draws).

      3. +

    3. Check whether for any of the parameter the ESS is lower than threshold. +If for at least one parameter the relative ESS is below the threshold, +a warning is thrown.

      4. +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/check_hmc_diagn.html b/v1.3.1/reference/check_hmc_diagn.html new file mode 100644 index 000000000..eeacc5691 --- /dev/null +++ b/v1.3.1/reference/check_hmc_diagn.html @@ -0,0 +1,100 @@ + +Diagnostics of the MCMC based on HMC-related measures. — check_hmc_diagn • rbmi + Skip to contents + + +
    +
    +
    +

    Diagnostics of the MCMC based on HMC-related measures.

    + Source: R/mcmc.R +
    check_hmc_diagn.Rd
    +
    + +
    +

    Check that:

    1. There are no divergent iterations.

      2. +

    2. The Bayesian Fraction of Missing Information (BFMI) is sufficiently low.

      3. +

    3. The number of iterations that saturated the max treedepth is zero.

      4. +

    Please see rstan::check_hmc_diagnostics() for details.

    +
    + +
    +

    Usage

    + 
    check_hmc_diagn(stan_fit)
    +
    + +
    +

    Arguments

    + + +
    stan_fit
    +

    A stanfit object.

    + +
    +
    +

    Value

    +

    A warning message in case of detected problems.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/check_mcmc.html b/v1.3.1/reference/check_mcmc.html new file mode 100644 index 000000000..e1fd1885d --- /dev/null +++ b/v1.3.1/reference/check_mcmc.html @@ -0,0 +1,99 @@ + +Diagnostics of the MCMC — check_mcmc • rbmi + Skip to contents + + +
    +
    +
    +

    Diagnostics of the MCMC

    + Source: R/mcmc.R +
    check_mcmc.Rd
    +
    + +
    +

    Diagnostics of the MCMC

    +
    + +
    +

    Usage

    + 
    check_mcmc(stan_fit, n_draws, threshold_lowESS = 0.4)
    +
    + +
    +

    Arguments

    + + +
    stan_fit
    +

    A stanfit object.

    + + +
    n_draws
    +

    Number of MCMC draws.

    + + +
    threshold_lowESS
    +

    A number in [0,1] indicating the minimum acceptable +value of the relative ESS. See details.

    + +
    +
    +

    Value

    +

    A warning message in case of detected problems.

    +
    +
    +

    Details

    +

    Performs checks of the quality of the MCMC. See check_ESS() and check_hmc_diagn() +for details.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/compute_sigma.html b/v1.3.1/reference/compute_sigma.html new file mode 100644 index 000000000..daeff7bed --- /dev/null +++ b/v1.3.1/reference/compute_sigma.html @@ -0,0 +1,109 @@ + +Compute covariance matrix for some reference-based methods (JR, CIR) — compute_sigma • rbmi + Skip to contents + + +
    +
    +
    +

    Compute covariance matrix for some reference-based methods (JR, CIR)

    + Source: R/strategies.R +
    compute_sigma.Rd
    +
    + +
    +

    Adapt covariance matrix in reference-based methods. Used for Copy Increments in +Reference (CIR) and Jump To Reference (JTR) methods, to adapt the covariance matrix +to different pre-deviation and post deviation covariance structures. See Carpenter +et al. (2013)

    +
    + +
    +

    Usage

    + 
    compute_sigma(sigma_group, sigma_ref, index_mar)
    +
    + +
    +

    Arguments

    + + +
    sigma_group
    +

    the covariance matrix with dimensions equal to index_mar for +the subjects original group

    + + +
    sigma_ref
    +

    the covariance matrix with dimensions equal to index_mar for +the subjects reference group

    + + +
    index_mar
    +

    A logical vector indicating which visits meet the MAR assumption +for the subject. I.e. this identifies the observations that after a non-MAR +intercurrent event (ICE).

    + +
    +
    +

    References

    +

    Carpenter, James R., James H. Roger, and Michael G. Kenward. "Analysis of longitudinal +trials with protocol deviation: a framework for relevant, accessible assumptions, and +inference via multiple imputation." Journal of Biopharmaceutical statistics 23.6 (2013): +1352-1371.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/convert_to_imputation_list_df.html b/v1.3.1/reference/convert_to_imputation_list_df.html new file mode 100644 index 000000000..1d939f67a --- /dev/null +++ b/v1.3.1/reference/convert_to_imputation_list_df.html @@ -0,0 +1,142 @@ + +Convert list of imputation_list_single() objects to an imputation_list_df() object (i.e. a list of imputation_df() objects's) — convert_to_imputation_list_df • rbmi + Skip to contents + + +
    +
    +
    +

    Convert list of imputation_list_single() objects to an imputation_list_df() object (i.e. a list of imputation_df() objects's)

    + Source: R/impute.R +
    convert_to_imputation_list_df.Rd
    +
    + +
    +

    Convert list of imputation_list_single() objects to an imputation_list_df() object +(i.e. a list of imputation_df() objects's)

    +
    + +
    +

    Usage

    + 
    convert_to_imputation_list_df(imputes, sample_ids)
    +
    + +
    +

    Arguments

    + + +
    imputes
    +

    a list of imputation_list_single() objects

    + + +
    sample_ids
    +

    A list with 1 element per required imputation_df. Each element +must contain a vector of "ID"'s which correspond to the imputation_single() ID's +that are required for that dataset. The total number of ID's must by equal to the +total number of rows within all of imputes$imputations

    +

    To accommodate for method_bmlmi() the impute_data_individual() function returns +a list of imputation_list_single() objects with 1 object per each subject.

    +

    imputation_list_single() stores the subjects imputations as a matrix where the columns +of the matrix correspond to the D of method_bmlmi(). Note that all other methods +(i.e. methods_*()) are a special case of this with D = 1. The number of rows in the +matrix varies for each subject and is equal to the number of times the patient was selected +for imputation (for non-conditional mean methods this should be 1 per subject per imputed +dataset).

    +

    This function is best illustrated by an example:

    +

    imputes = list(
+    imputation_list_single(
+        id = "Tom",
+        imputations = matrix(
+             imputation_single_t_1_1,  imputation_single_t_1_2,
+             imputation_single_t_2_1,  imputation_single_t_2_2,
+             imputation_single_t_3_1,  imputation_single_t_3_2
+        )
+    ),
+    imputation_list_single(
+        id = "Tom",
+        imputations = matrix(
+             imputation_single_h_1_1,  imputation_single_h_1_2,
+        )
+    )
+)
+
+sample_ids <- list(
+    c("Tom", "Harry", "Tom"),
+    c("Tom")
+)

    +

    Then convert_to_imputation_df(imputes, sample_ids) would result in:

    +

    imputation_list_df(
+    imputation_df(
+        imputation_single_t_1_1,
+        imputation_single_h_1_1,
+        imputation_single_t_2_1
+    ),
+    imputation_df(
+        imputation_single_t_1_2,
+        imputation_single_h_1_2,
+        imputation_single_t_2_2
+    ),
+    imputation_df(
+        imputation_single_t_3_1
+    ),
+    imputation_df(
+        imputation_single_t_3_2
+    )
+)

    +

    Note that the different repetitions (i.e. the value set for D) are grouped together +sequentially.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/d_lagscale.html b/v1.3.1/reference/d_lagscale.html new file mode 100644 index 000000000..e16013642 --- /dev/null +++ b/v1.3.1/reference/d_lagscale.html @@ -0,0 +1,100 @@ + +Calculate delta from a lagged scale coefficient — d_lagscale • rbmi + Skip to contents + + +
    +
    +
    +

    Calculate delta from a lagged scale coefficient

    + Source: R/delta.R +
    d_lagscale.Rd
    +
    + +
    +

    Calculates a delta value based upon a baseline delta value and a +post ICE scaling coefficient.

    +
    + +
    +

    Usage

    + 
    d_lagscale(delta, dlag, is_post_ice)
    +
    + +
    +

    Arguments

    + + +
    delta
    +

    a numeric vector. Determines the baseline amount of delta +to be applied to each visit.

    + + +
    dlag
    +

    a numeric vector. Determines the scaling to be applied +to delta based upon with visit the ICE occurred on. Must be the same +length as delta.

    + + +
    is_post_ice
    +

    logical vector. Indicates whether a visit is "post-ICE" or +not.

    + +
    +
    +

    Details

    +

    See delta_template() for full details on how this calculation is performed.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/delta_template.html b/v1.3.1/reference/delta_template.html new file mode 100644 index 000000000..2b420ccdc --- /dev/null +++ b/v1.3.1/reference/delta_template.html @@ -0,0 +1,197 @@ + +Create a delta data.frame template — delta_template • rbmi + Skip to contents + + +
    +
    +
    +

    Create a delta data.frame template

    + Source: R/delta.R +
    delta_template.Rd
    +
    + +
    +

    Creates a data.frame in the format required by analyse() for the use +of applying a delta adjustment.

    +
    + +
    +

    Usage

    + 
    delta_template(imputations, delta = NULL, dlag = NULL, missing_only = TRUE)
    +
    + +
    +

    Arguments

    + + +
    imputations
    +

    an imputation object as created by impute().

    + + +
    delta
    +

    NULL or a numeric vector. Determines the baseline amount of delta +to be applied to each visit. See details. If a numeric vector it must have +the same length as the number of unique visits in the original dataset.

    + + +
    dlag
    +

    NULL or a numeric vector. Determines the scaling to be applied +to delta based upon which visit the ICE occurred on. See details. If a +numeric vector it must have the same length as the number of unique visits in +the original dataset.

    + + +
    missing_only
    +

    Logical, if TRUE then non-missing post-ICE data will have a delta value +of 0 assigned. Note that the calculation (as described in the details section) is performed +first and then overwritten with 0's at the end (i.e. the delta values for missing +post-ICE visits will stay the same regardless of this option).

    + +
    +
    +

    Details

    +

    To apply a delta adjustment the analyse() function expects +a delta data.frame with 3 variables: vars$subjid, vars$visit and delta +(where vars is the object supplied in the original call to draws() +as created by the set_vars() function).

    +

    This function will return a data.frame with the aforementioned variables with one +row per subject per visit. If the delta argument to this function is NULL +then the delta column in the returned data.frame will be 0 for all observations. +If the delta argument is not NULL then delta will be calculated separately +for each subject as the accumulative sum of delta multiplied by the scaling +coefficient dlag based upon how many visits after the subject's intercurrent +event (ICE) the visit in question is. +This is best illustrated with an example:

    +

    Let delta = c(5,6,7,8) and dlag=c(1,2,3,4) (i.e. assuming there are 4 visits) +and lets say that the subject had an ICE on visit 2. The calculation would then be +as follows:

    +

    v1  v2  v3  v4
+--------------
+ 5   6   7   8  # delta assigned to each visit
+ 0   1   2   3  # lagged scaling starting from the first visit after the subjects ICE
+--------------
+ 0   6  14  24  # delta * lagged scaling
+--------------
+ 0   6  20  44  # accumulative sum of delta to be applied to each visit

    +

    That is to say the subject would have a delta offset of 0 applied for visit-1, 6 +for visit-2, 20 for visit-3 and 44 for visit-4. As a comparison, lets say that the +subject instead had their ICE on visit 3, the calculation would then be as follows:

    +

    v1  v2  v3  v4
+--------------
+ 5   6   7   8  # delta assigned to each visit
+ 0   0   1   2  # lagged scaling starting from the first visit after the subjects ICE
+--------------
+ 0   0   7  16  # delta * lagged scaling
+--------------
+ 0   0   7  23  # accumulative sum of delta to be applied to each visit

    +

    In terms of practical usage, lets say that you wanted a delta of 5 to be used for all post ICE visits +regardless of their proximity to the ICE visit. This can be achieved by setting +delta = c(5,5,5,5) and dlag = c(1,0,0,0). For example lets say a subject had their +ICE on visit-1, then the calculation would be as follows:

    +

    v1  v2  v3  v4
+--------------
+ 5   5   5   5  # delta assigned to each visit
+ 1   0   0   0  # lagged scaling starting from the first visit after the subjects ICE
+--------------
+ 5   0   0  0  # delta * lagged scaling
+--------------
+ 5   5   5  5  # accumulative sum of delta to be applied to each visit

    +

    Another way of using these arguments +is to set delta to be the difference in time between visits and dlag to be the +amount of delta per unit of time. For example lets say that we have a visit on weeks +1, 5, 6 & 9 and that we want a delta of 3 to be applied for each week after an ICE. This +can be achieved by setting delta = c(0,4,1,3) (the difference in weeks between each visit) +and dlag = c(3, 3, 3, 3). For example lets say we have a subject who had their ICE on week-5 +(i.e. visit-2) then the calculation would be:

    +

    v1  v2  v3  v4
+--------------
+ 0   4   1   3  # delta assigned to each visit
+ 0   0   3   3  # lagged scaling starting from the first visit after the subjects ICE
+--------------
+ 0   0   3   9  # delta * lagged scaling
+--------------
+ 0   0   3  12  # accumulative sum of delta to be applied to each visit

    +

    i.e. on week-6 (1 week after the ICE) they have a delta of 3 and on week-9 (4 weeks after the ICE) +they have a delta of 12.

    +

    Please note that this function also returns several utility variables so that +the user can create their own custom logic for defining what delta +should be set to. These additional variables include:

    • is_mar - If the observation was missing would it be regarded as MAR? This variable +is set to FALSE for observations that occurred after a non-MAR ICE, otherwise it is set to TRUE.

      • +

    • is_missing - Is the outcome variable for this observation missing.

      • +

    • is_post_ice - Does the observation occur after the patient's ICE as defined by the +data_ice dataset supplied to draws().

      • +

    • strategy - What imputation strategy was assigned to for this subject.

      • +

    The design and implementation of this function is largely based upon the same functionality +as implemented in the so called "five marcos" by James Roger. See Roger (2021).

    +
    +
    +

    References

    +

    Roger, James. Reference-based mi via multivariate normal rm (the “five macros” and miwithd), 2021. URL +https://www.lshtm.ac.uk/research/centres-projects-groups/missing-data#dia-missing-data.

    +
    +
    +

    See also

    +

    analyse()

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+delta_template(imputeObj)
+delta_template(imputeObj, delta = c(5,6,7,8), dlag = c(1,2,3,4))
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/draws.html b/v1.3.1/reference/draws.html new file mode 100644 index 000000000..1c8c8b04f --- /dev/null +++ b/v1.3.1/reference/draws.html @@ -0,0 +1,311 @@ + +Fit the base imputation model and get parameter estimates — draws • rbmi + Skip to contents + + +
    +
    +
    +

    Fit the base imputation model and get parameter estimates

    + Source: R/draws.R +
    draws.Rd
    +
    + +
    +

    draws fits the base imputation model to the observed outcome data +according to the given multiple imputation methodology. +According to the user's method specification, it returns either draws from the posterior distribution of the +model parameters as required for Bayesian multiple imputation or frequentist parameter estimates from the +original data and bootstrapped or leave-one-out datasets as required for conditional mean imputation. +The purpose of the imputation model is to estimate model parameters +in the absence of intercurrent events (ICEs) handled using reference-based imputation methods. +For this reason, any observed outcome data after ICEs, for which reference-based imputation methods are +specified, are removed and considered as missing for the purpose of estimating the imputation model, and for +this purpose only. The imputation model is a mixed model for repeated measures (MMRM) that is valid +under a missing-at-random (MAR) assumption. +It can be fit using maximum likelihood (ML) or restricted ML (REML) estimation, +a Bayesian approach, or an approximate Bayesian approach according to the user's method specification. +The ML/REML approaches and the approximate Bayesian approach support several possible covariance structures, +while the Bayesian approach based on MCMC sampling supports only an unstructured covariance structure. +In any case the covariance matrix can be assumed to be the same or different across each group.

    +
    + +
    +

    Usage

    + 
    draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE)
+
+# S3 method for class 'approxbayes'
+draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE)
+
+# S3 method for class 'condmean'
+draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE)
+
+# S3 method for class 'bmlmi'
+draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE)
+
+# S3 method for class 'bayes'
+draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    A data.frame containing the data to be used in the model. See details.

    + + +
    data_ice
    +

    A data.frame that specifies the information related +to the ICEs and the imputation strategies. See details.

    + + +
    vars
    +

    A vars object as generated by set_vars(). See details.

    + + +
    method
    +

    A method object as generated by either method_bayes(), +method_approxbayes(), method_condmean() or method_bmlmi(). +It specifies the multiple imputation methodology to be used. See details.

    + + +
    ncores
    +

    A single numeric specifying the number of cores to use in creating the draws object. +Note that this parameter is ignored for method_bayes() (Default = 1). Can also be a cluster object +generated by make_rbmi_cluster()

    + + +
    quiet
    +

    Logical, if TRUE will suppress printing of progress information that is printed to +the console.

    + +
    +
    +

    Value

    +

    A draws object which is a named list containing the following:

    • data: R6 longdata object containing all relevant input data information.

      • +

    • method: A method object as generated by either method_bayes(), +method_approxbayes() or method_condmean().

      • +

    • samples: list containing the estimated parameters of interest. +Each element of samples is a named list containing the following:

      • ids: vector of characters containing the ids of the subjects included in the original dataset.

        • +

      • beta: numeric vector of estimated regression coefficients.

        • +

      • sigma: list of estimated covariance matrices (one for each level of vars$group).

        • +

      • theta: numeric vector of transformed covariances.

        • +

      • failed: Logical. TRUE if the model fit failed.

        • +

      • ids_samp: vector of characters containing the ids of the subjects included in the given sample.

        • +
      • +

    • fit: if method_bayes() is chosen, returns the MCMC Stan fit object. Otherwise NULL.

      • +

    • n_failures: absolute number of failures of the model fit. +Relevant only for method_condmean(type = "bootstrap"), method_approxbayes() and method_bmlmi().

      • +

    • formula: fixed effects formula object used for the model specification.

      • +
    +
    +

    Details

    +

    draws performs the first step of the multiple imputation (MI) procedure: fitting the +base imputation model. The goal is to estimate the parameters of interest needed +for the imputation phase (i.e. the regression coefficients and the covariance matrices +from a MMRM model).

    +

    The function distinguishes between the following methods:

    • Bayesian MI based on MCMC sampling: draws returns the draws +from the posterior distribution of the parameters using a Bayesian approach based on +MCMC sampling. This method can be specified by using method = method_bayes().

      • +

    • Approximate Bayesian MI based on bootstrapping: draws returns +the draws from the posterior distribution of the parameters using an approximate Bayesian approach, +where the sampling from the posterior distribution is simulated by fitting the MMRM model +on bootstrap samples of the original dataset. This method can be specified by using +method = method_approxbayes()].

      • +

    • Conditional mean imputation with bootstrap re-sampling: draws returns the +MMRM parameter estimates from the original dataset and from n_samples bootstrap samples. +This method can be specified by using method = method_condmean() with +argument type = "bootstrap".

      • +

    • Conditional mean imputation with jackknife re-sampling: draws returns the +MMRM parameter estimates from the original dataset and from each leave-one-subject-out sample. +This method can be specified by using method = method_condmean() with +argument type = "jackknife".

      • +

    • Bootstrapped Maximum Likelihood MI: draws returns the MMRM parameter estimates from +a given number of bootstrap samples needed to perform random imputations of the bootstrapped samples. +This method can be specified by using method = method_bmlmi().

      • +

    Bayesian MI based on MCMC sampling has been proposed in Carpenter, Roger, and Kenward (2013) who first introduced +reference-based imputation methods. Approximate Bayesian MI is discussed in Little and Rubin (2002). +Conditional mean imputation methods are discussed in Wolbers et al (2022). +Bootstrapped Maximum Likelihood MI is described in Von Hippel & Bartlett (2021).

    +

    The argument data contains the longitudinal data. It must have at least the following variables:

    • subjid: a factor vector containing the subject ids.

      • +

    • visit: a factor vector containing the visit the outcome was observed on.

      • +

    • group: a factor vector containing the group that the subject belongs to.

      • +

    • outcome: a numeric vector containing the outcome variable. It might contain missing values. +Additional baseline or time-varying covariates must be included in data.

      • +

    data must have one row per visit per subject. This means that incomplete +outcome data must be set as NA instead of having the related row missing. Missing values +in the covariates are not allowed. +If data is incomplete +then the expand_locf() helper function can be used to insert any missing rows using +Last Observation Carried Forward (LOCF) imputation to impute the covariates values. +Note that LOCF is generally not a principled imputation method and should only be used when appropriate +for the specific covariate.

    +

    Please note that there is no special provisioning for the baseline outcome values. If you do not want baseline +observations to be included in the model as part of the response variable then these should be removed in advance +from the outcome variable in data. At the same time if you want to include the baseline outcome as covariate in +the model, then this should be included as a separate column of data (as any other covariate).

    +

    Character covariates will be explicitly +cast to factors. If you use a custom analysis function that requires specific reference +levels for the character covariates (for example in the computation of the least square means +computation) then you are advised +to manually cast your character covariates to factor in advance of running draws().

    +

    The argument data_ice contains information about the occurrence of ICEs. It is a +data.frame with 3 columns:

    • Subject ID: a character vector containing the ids of the subjects that experienced +the ICE. This column must be named as specified in vars$subjid.

      • +

    • Visit: a character vector containing the first visit after the occurrence of the ICE +(i.e. the first visit affected by the ICE). +The visits must be equal to one of the levels of data[[vars$visit]]. +If multiple ICEs happen for the same subject, then only the first non-MAR visit should be used. +This column must be named as specified in vars$visit.

      • +

    • Strategy: a character vector specifying the imputation strategy to address the ICE for this subject. +This column must be named as specified in vars$strategy. +Possible imputation strategies are:

      • "MAR": Missing At Random.

        • +

      • "CIR": Copy Increments in Reference.

        • +

      • "CR": Copy Reference.

        • +

      • "JR": Jump to Reference.

        • +

      • "LMCF": Last Mean Carried Forward. +For explanations of these imputation strategies, see Carpenter, Roger, and Kenward (2013), Cro et al (2021), +and Wolbers et al (2022). +Please note that user-defined imputation strategies can also be set.

        • +
      • +

    The data_ice argument is necessary at this stage since (as explained in Wolbers et al (2022)), the model is fitted +after removing the observations which are incompatible with the imputation model, i.e. +any observed data on or after data_ice[[vars$visit]] that are addressed with an imputation +strategy different from MAR are excluded for the model fit. However such observations +will not be discarded from the data in the imputation phase +(performed with the function (impute()). To summarize, at this stage only pre-ICE data +and post-ICE data that is after ICEs for which MAR imputation is specified are used.

    +

    If the data_ice argument is omitted, or if a subject doesn't have a record within data_ice, then it is +assumed that all of the relevant subject's data is pre-ICE and as such all missing +visits will be imputed under the MAR assumption and all observed data will be used to fit the base imputation model. +Please note that the ICE visit cannot be updated via the update_strategy argument +in impute(); this means that subjects who didn't have a record in data_ice will always have their +missing data imputed under the MAR assumption even if their strategy is updated.

    +

    The vars argument is a named list that specifies the names of key variables within +data and data_ice. This list is created by set_vars() and contains the following named elements:

    • subjid: name of the column in data and data_ice which contains the subject ids variable.

      • +

    • visit: name of the column in data and data_ice which contains the visit variable.

      • +

    • group: name of the column in data which contains the group variable.

      • +

    • outcome: name of the column in data which contains the outcome variable.

      • +

    • covariates: vector of characters which contains the covariates to be included +in the model (including interactions which are specified as "covariateName1*covariateName2"). +If no covariates are provided the default model specification of outcome ~ 1 + visit + group will be used. +Please note that the group*visit interaction +is not included in the model by default.

      • +

    • strata: covariates used as stratification variables in the bootstrap sampling. +By default only the vars$group is set as stratification variable. +Needed only for method_condmean(type = "bootstrap") and method_approxbayes().

      • +

    • strategy: name of the column in data_ice which contains the subject-specific imputation strategy.

      • +

    In our experience, Bayesian MI (method = method_bayes()) with a relatively low number of +samples (e.g. n_samples below 100) frequently triggers STAN warnings about R-hat such as +"The largest R-hat is X.XX, indicating chains have not mixed". In many instances, this warning +might be spurious, i.e. standard diagnostics analysis of the MCMC samples do not indicate any +issues and results look reasonable. Increasing the number of samples to e.g. above 150 usually +gets rid of the warning.

    +
    +
    +

    References

    +

    James R Carpenter, James H Roger, and Michael G Kenward. Analysis of longitudinal trials with protocol deviation: a +framework for relevant, accessible assumptions, and inference via multiple imputation. Journal of Biopharmaceutical +Statistics, 23(6):1352–1371, 2013.

    +

    Suzie Cro, Tim P Morris, Michael G Kenward, and James R Carpenter. Sensitivity analysis for clinical trials with +missing continuous outcome data using controlled multiple imputation: a practical guide. Statistics in +Medicine, 39(21):2815–2842, 2020.

    +

    Roderick J. A. Little and Donald B. Rubin. Statistical Analysis with Missing Data, Second Edition. John Wiley & Sons, +Hoboken, New Jersey, 2002. [Section 10.2.3]

    +

    Marcel Wolbers, Alessandro Noci, Paul Delmar, Craig Gower-Page, Sean Yiu, Jonathan W. Bartlett. +Standard and reference-based +conditional mean imputation. https://arxiv.org/abs/2109.11162, 2022.

    +

    Von Hippel, Paul T and Bartlett, Jonathan W. +Maximum likelihood multiple imputation: Faster imputations and consistent standard errors without +posterior draws. 2021.

    +
    +
    +

    See also

    +

    method_bayes(), method_approxbayes(), method_condmean(), method_bmlmi() for setting method.

    +

    set_vars() for setting vars.

    +

    expand_locf() for expanding data in case of missing rows.

    +

    For more details see the quickstart vignette: +vignette("quickstart", package = "rbmi").

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/ensure_rstan.html b/v1.3.1/reference/ensure_rstan.html new file mode 100644 index 000000000..f804123ee --- /dev/null +++ b/v1.3.1/reference/ensure_rstan.html @@ -0,0 +1,72 @@ + +Ensure rstan exists — ensure_rstan • rbmi + Skip to contents + + +
    +
    +
    +

    Ensure rstan exists

    + Source: R/utilities.R +
    ensure_rstan.Rd
    +
    + +
    +

    Checks to see if rstan exists and if not throws a helpful error message

    +
    + +
    +

    Usage

    + 
    ensure_rstan()
    +
    + + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/eval_mmrm.html b/v1.3.1/reference/eval_mmrm.html new file mode 100644 index 000000000..f48ddc836 --- /dev/null +++ b/v1.3.1/reference/eval_mmrm.html @@ -0,0 +1,116 @@ + +Evaluate a call to mmrm — eval_mmrm • rbmi + Skip to contents + + +
    +
    +
    +

    Evaluate a call to mmrm

    + Source: R/mmrm.R +
    eval_mmrm.Rd
    +
    + +
    +

    This is a utility function that attempts to evaluate a call to mmrm +managing any warnings or errors that are thrown. In particular +this function attempts to catch any warnings or errors and instead +of surfacing them it will simply add an additional element failed +with a value of TRUE. This allows for multiple calls to be made +without the program exiting.

    +
    + +
    +

    Usage

    + 
    eval_mmrm(expr)
    +
    + +
    +

    Arguments

    + + +
    expr
    +

    An expression to be evaluated. Should be a call to mmrm::mmrm().

    + +
    +
    +

    Details

    +

    This function was originally developed for use with glmmTMB which needed +more hand-holding and dropping of false-positive warnings. It is not +as important now but is kept around encase we need to catch +false-positive warnings again in the future.

    +
    +
    +

    See also

    +

    record()

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+eval_mmrm({
+    mmrm::mmrm(formula, data)
+})
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/expand.html b/v1.3.1/reference/expand.html new file mode 100644 index 000000000..880c06003 --- /dev/null +++ b/v1.3.1/reference/expand.html @@ -0,0 +1,179 @@ + +Expand and fill in missing data.frame rows — expand • rbmi + Skip to contents + + +
    +
    +
    +

    Expand and fill in missing data.frame rows

    + Source: R/expand.R +
    expand.Rd
    +
    + +
    +

    These functions are essentially wrappers around base::expand.grid() to ensure that missing +combinations of data are inserted into a data.frame with imputation/fill methods for updating +covariate values of newly created rows.

    +
    + +
    +

    Usage

    + 
    expand(data, ...)
+
+fill_locf(data, vars, group = NULL, order = NULL)
+
+expand_locf(data, ..., vars, group, order)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    dataset to expand or fill in.

    + + +
    ...
    +

    variables and the levels that should be expanded out (note that duplicate entries of +levels will result in multiple rows for that level).

    + + +
    vars
    +

    character vector containing the names of variables that need to be filled in.

    + + +
    group
    +

    character vector containing the names of variables to group +by when performing LOCF imputation of var.

    + + +
    order
    +

    character vector containing the names of additional variables to sort the data.frame +by before performing LOCF.

    + +
    +
    +

    Details

    +

    The draws() function makes the assumption that all subjects and visits are present +in the data.frame and that all covariate values are non missing; expand(), +fill_locf() and expand_locf() are utility functions to support users in ensuring +that their data.frame's conform to these assumptions.

    +

    expand() takes vectors for expected levels in a data.frame and expands out all +combinations inserting any missing rows into the data.frame. Note that all "expanded" +variables are cast as factors.

    +

    fill_locf() applies LOCF imputation to named covariates to fill in any NAs created +by the insertion of new rows by expand() (though do note that no distinction is +made between existing NAs and newly created NAs). Note that the data.frame is sorted +by c(group, order) before performing the LOCF imputation; the data.frame +will be returned in the original sort order however.

    +

    expand_locf() a simple composition function of fill_locf() and expand() i.e. +fill_locf(expand(...)).

    +

    Missing First Values

    + + +

    The fill_locf() function performs last observation carried forward imputation. +A natural consequence of this is that it is unable to impute missing observations if the +observation is the first value for a given subject / grouping. +These values are deliberately not imputed as doing so risks silent errors in the case of time +varying covariates. +One solution is to first use expand_locf() on just +the visit variable and time varying covariates and then merge on the baseline covariates +afterwards i.e.

    +

    library(dplyr)
+
+dat_expanded <- expand(
+    data = dat,
+    subject = c("pt1", "pt2", "pt3", "pt4"),
+    visit = c("vis1", "vis2", "vis3")
+)
+
+dat_filled <- dat_expanded %>%
+    left_join(baseline_covariates, by = "subject")

    +
    + +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+dat_expanded <- expand(
+    data = dat,
+    subject = c("pt1", "pt2", "pt3", "pt4"),
+    visit = c("vis1", "vis2", "vis3")
+)
+
+dat_filled <- fill_loc(
+    data = dat_expanded,
+    vars = c("Sex", "Age"),
+    group = "subject",
+    order = "visit"
+)
+
+## Or
+
+dat_filled <- expand_locf(
+    data = dat,
+    subject = c("pt1", "pt2", "pt3", "pt4"),
+    visit = c("vis1", "vis2", "vis3"),
+    vars = c("Sex", "Age"),
+    group = "subject",
+    order = "visit"
+)
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/extract_covariates.html b/v1.3.1/reference/extract_covariates.html new file mode 100644 index 000000000..542173735 --- /dev/null +++ b/v1.3.1/reference/extract_covariates.html @@ -0,0 +1,88 @@ + +Extract Variables from string vector — extract_covariates • rbmi + Skip to contents + + +
    +
    +
    +

    Extract Variables from string vector

    + Source: R/utilities.R +
    extract_covariates.Rd
    +
    + +
    +

    Takes a string including potentially model terms like * and : and +extracts out the individual variables

    +
    + +
    +

    Usage

    + 
    extract_covariates(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    string of variable names potentially including interaction terms

    + +
    +
    +

    Details

    +

    i.e. c("v1", "v2", "v2*v3", "v1:v2") becomes c("v1", "v2", "v3")

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/extract_data_nmar_as_na.html b/v1.3.1/reference/extract_data_nmar_as_na.html new file mode 100644 index 000000000..3846f8e45 --- /dev/null +++ b/v1.3.1/reference/extract_data_nmar_as_na.html @@ -0,0 +1,89 @@ + +Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy) — extract_data_nmar_as_na • rbmi + Skip to contents + + +
    +
    +
    +

    Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy)

    + Source: R/draws.R +
    extract_data_nmar_as_na.Rd
    +
    + +
    +

    Set to NA outcome values that would be MNAR if they were missing +(i.e. which occur after an ICE handled using a reference-based imputation strategy)

    +
    + +
    +

    Usage

    + 
    extract_data_nmar_as_na(longdata)
    +
    + +
    +

    Arguments

    + + +
    longdata
    +

    R6 longdata object containing all relevant input data information.

    + +
    +
    +

    Value

    +

    A data.frame containing longdata$get_data(longdata$ids), but MNAR outcome +values are set to NA.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/extract_draws.html b/v1.3.1/reference/extract_draws.html new file mode 100644 index 000000000..046e6989e --- /dev/null +++ b/v1.3.1/reference/extract_draws.html @@ -0,0 +1,99 @@ + +Extract draws from a stanfit object — extract_draws • rbmi + Skip to contents + + +
    +
    +
    +

    Extract draws from a stanfit object

    + Source: R/mcmc.R +
    extract_draws.Rd
    +
    + +
    +

    Extract draws from a stanfit object and convert them into lists.

    +

    The function rstan::extract() returns the draws for a given parameter as an array. This function +calls rstan::extract() to extract the draws from a stanfit object +and then convert the arrays into lists.

    +
    + +
    +

    Usage

    + 
    extract_draws(stan_fit)
    +
    + +
    +

    Arguments

    + + +
    stan_fit
    +

    A stanfit object.

    + +
    +
    +

    Value

    +

    A named list of length 2 containing:

    • beta: a list of length equal to the number of draws containing +the draws from the posterior distribution of the regression coefficients.

      • +

    • sigma: a list of length equal to the number of draws containing +the draws from the posterior distribution of the covariance matrices. Each element +of the list is a list with length equal to 1 if same_cov = TRUE or equal to the +number of groups if same_cov = FALSE.

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/extract_imputed_df.html b/v1.3.1/reference/extract_imputed_df.html new file mode 100644 index 000000000..d3f33f556 --- /dev/null +++ b/v1.3.1/reference/extract_imputed_df.html @@ -0,0 +1,117 @@ + +Extract imputed dataset — extract_imputed_df • rbmi + Skip to contents + + +
    +
    +
    +

    Extract imputed dataset

    + Source: R/analyse.R +
    extract_imputed_df.Rd
    +
    + +
    +

    Takes an imputation object as generated by imputation_df() and uses +this to extract a completed dataset from a longdata object as created +by longDataConstructor(). Also applies a delta transformation +if a data.frame is provided to the delta argument. See analyse() for +details on the structure of this data.frame.

    +

    Subject IDs in the returned data.frame are scrambled i.e. are not the original +values.

    +
    + +
    +

    Usage

    + 
    extract_imputed_df(imputation, ld, delta = NULL, idmap = FALSE)
    +
    + +
    +

    Arguments

    + + +
    imputation
    +

    An imputation object as generated by imputation_df().

    + + +
    ld
    +

    A longdata object as generated by longDataConstructor().

    + + +
    delta
    +

    Either NULL or a data.frame. Is used to offset outcome values in the imputed dataset.

    + + +
    idmap
    +

    Logical. If TRUE an attribute called "idmap" is attached to +the return object which contains a list that maps the old subject ids +the new subject ids.

    + +
    +
    +

    Value

    +

    A data.frame.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/extract_imputed_dfs.html b/v1.3.1/reference/extract_imputed_dfs.html new file mode 100644 index 000000000..e5126deef --- /dev/null +++ b/v1.3.1/reference/extract_imputed_dfs.html @@ -0,0 +1,124 @@ + +Extract imputed datasets — extract_imputed_dfs • rbmi + Skip to contents + + +
    +
    +
    +

    Extract imputed datasets

    + Source: R/analyse.R +
    extract_imputed_dfs.Rd
    +
    + +
    +

    Extracts the imputed datasets contained within an imputations object generated +by impute().

    +
    + +
    +

    Usage

    + 
    extract_imputed_dfs(
+  imputations,
+  index = seq_along(imputations$imputations),
+  delta = NULL,
+  idmap = FALSE
+)
    +
    + +
    +

    Arguments

    + + +
    imputations
    +

    An imputations object as created by impute().

    + + +
    index
    +

    The indexes of the imputed datasets to return. By default, +all datasets within the imputations object will be returned.

    + + +
    delta
    +

    A data.frame containing the delta transformation to be +applied to the imputed dataset. See analyse() for details on the +format and specification of this data.frame.

    + + +
    idmap
    +

    Logical. The subject IDs in the imputed data.frame's are +replaced with new IDs to ensure they are unique. Setting this argument to +TRUE attaches an attribute, called idmap, to the returned data.frame's +that will provide a map from the new subject IDs to the old subject IDs.

    + +
    +
    +

    Value

    +

    A list of data.frames equal in length to the index argument.

    +
    +
    +

    See also

    +

    delta_template() for creating delta data.frames.

    +

    analyse().

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+extract_imputed_dfs(imputeObj)
+extract_imputed_dfs(imputeObj, c(1:3))
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/extract_params.html b/v1.3.1/reference/extract_params.html new file mode 100644 index 000000000..64208155a --- /dev/null +++ b/v1.3.1/reference/extract_params.html @@ -0,0 +1,84 @@ + +Extract parameters from a MMRM model — extract_params • rbmi + Skip to contents + + +
    +
    +
    +

    Extract parameters from a MMRM model

    + Source: R/mmrm.R +
    extract_params.Rd
    +
    + +
    +

    Extracts the beta and sigma coefficients from an MMRM model created +by mmrm::mmrm().

    +
    + +
    +

    Usage

    + 
    extract_params(fit)
    +
    + +
    +

    Arguments

    + + +
    fit
    +

    an object created by mmrm::mmrm()

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/figures/logo.png b/v1.3.1/reference/figures/logo.png new file mode 100644 index 000000000..08fbb4fcd Binary files /dev/null and b/v1.3.1/reference/figures/logo.png differ diff --git a/v1.3.1/reference/fit_mcmc.html b/v1.3.1/reference/fit_mcmc.html new file mode 100644 index 000000000..f19155417 --- /dev/null +++ b/v1.3.1/reference/fit_mcmc.html @@ -0,0 +1,145 @@ + +Fit the base imputation model using a Bayesian approach — fit_mcmc • rbmi + Skip to contents + + +
    +
    +
    +

    Fit the base imputation model using a Bayesian approach

    + Source: R/mcmc.R +
    fit_mcmc.Rd
    +
    + +
    +

    fit_mcmc() fits the base imputation model using a Bayesian approach. +This is done through a MCMC method that is implemented in stan +and is run by using the function rstan::sampling(). +The function returns the draws from the posterior distribution of the model parameters +and the stanfit object. Additionally it performs multiple diagnostics checks of the chain +and returns warnings in case of any detected issues.

    +
    + +
    +

    Usage

    + 
    fit_mcmc(designmat, outcome, group, subjid, visit, method, quiet = FALSE)
    +
    + +
    +

    Arguments

    + + +
    designmat
    +

    The design matrix of the fixed effects.

    + + +
    outcome
    +

    The response variable. Must be numeric.

    + + +
    group
    +

    Character vector containing the group variable.

    + + +
    subjid
    +

    Character vector containing the subjects IDs.

    + + +
    visit
    +

    Character vector containing the visit variable.

    + + +
    method
    +

    A method object as generated by method_bayes().

    + + +
    quiet
    +

    Specify whether the stan sampling log should be printed to the console.

    + +
    +
    +

    Value

    +

    A named list composed by the following:

    • samples: a named list containing the draws for each parameter. It corresponds to the output of extract_draws().

      • +

    • fit: a stanfit object.

      • +
    +
    +

    Details

    +

    The Bayesian model assumes a multivariate normal likelihood function and weakly-informative +priors for the model parameters: in particular, uniform priors are assumed for the regression +coefficients and inverse-Wishart priors for the covariance matrices. +The chain is initialized using the REML parameter estimates from MMRM as starting values.

    +

    The function performs the following steps:

    1. Fit MMRM using a REML approach.

      2. +

    2. Prepare the input data for the MCMC fit as described in the data{} +block of the Stan file. See prepare_stan_data() for details.

      3. +

    3. Run the MCMC according the input arguments and using as starting values the REML parameter estimates +estimated at point 1.

      4. +

    4. Performs diagnostics checks of the MCMC. See check_mcmc() for details.

      5. +

    5. Extract the draws from the model fit.

      6. +

    The chains perform method$n_samples draws by keeping one every method$burn_between iterations. Additionally +the first method$burn_in iterations are discarded. The total number of iterations will +then be method$burn_in + method$burn_between*method$n_samples. +The purpose of method$burn_in is to ensure that the samples are drawn from the stationary +distribution of the Markov Chain. +The method$burn_between aims to keep the draws uncorrelated each from other.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/fit_mmrm.html b/v1.3.1/reference/fit_mmrm.html new file mode 100644 index 000000000..b1230dbd0 --- /dev/null +++ b/v1.3.1/reference/fit_mmrm.html @@ -0,0 +1,132 @@ + +Fit a MMRM model — fit_mmrm • rbmi + Skip to contents + + +
    +
    +
    +

    Fit a MMRM model

    + Source: R/mmrm.R +
    fit_mmrm.Rd
    +
    + +
    +

    Fits a MMRM model allowing for different covariance structures using mmrm::mmrm(). +Returns a list of key model parameters beta, sigma and an additional element failed +indicating whether or not the fit failed to converge. If the fit did fail to converge +beta and sigma will not be present.

    +
    + +
    +

    Usage

    + 
    fit_mmrm(
+  designmat,
+  outcome,
+  subjid,
+  visit,
+  group,
+  cov_struct = c("us", "ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", "toeph"),
+  REML = TRUE,
+  same_cov = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    designmat
    +

    a data.frame or matrix containing the covariates to use in the MMRM model. +Dummy variables must already be expanded out, i.e. via stats::model.matrix(). Cannot contain +any missing values

    + + +
    outcome
    +

    a numeric vector. The outcome value to be regressed on in the MMRM model.

    + + +
    subjid
    +

    a character / factor vector. The subject identifier used to link separate visits +that belong to the same subject.

    + + +
    visit
    +

    a character / factor vector. Indicates which visit the outcome value occurred on.

    + + +
    group
    +

    a character / factor vector. Indicates which treatment group the patient belongs to.

    + + +
    cov_struct
    +

    a character value. Specifies which covariance structure to use. Must be one of "us" (default), +"ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", or "toeph")

    + + +
    REML
    +

    logical. Specifies whether restricted maximum likelihood should be used

    + + +
    same_cov
    +

    logical. Used to specify if a shared or individual covariance matrix should be +used per group

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/generate_data_single.html b/v1.3.1/reference/generate_data_single.html new file mode 100644 index 000000000..1596e5ac3 --- /dev/null +++ b/v1.3.1/reference/generate_data_single.html @@ -0,0 +1,119 @@ + +Generate data for a single group — generate_data_single • rbmi + Skip to contents + + +
    +
    +
    +

    Generate data for a single group

    + Source: R/simulate_data.R +
    generate_data_single.Rd
    +
    + +
    +

    Generate data for a single group

    +
    + +
    +

    Usage

    + 
    generate_data_single(pars_group, strategy_fun = NULL, distr_pars_ref = NULL)
    +
    + +
    +

    Arguments

    + + +
    pars_group
    +

    A simul_pars object as generated by set_simul_pars(). It specifies +the simulation parameters of the given group.

    + + +
    strategy_fun
    +

    Function implementing trajectories after the intercurrent event (ICE). +Must be one of getStrategies(). See getStrategies() for details. If NULL then post-ICE +outcomes are untouched.

    + + +
    distr_pars_ref
    +

    Optional. Named list containing the simulation parameters of the +reference arm. It contains the following elements:

    • mu: Numeric vector indicating the mean outcome trajectory assuming no ICEs. It should +include the outcome at baseline.

      • +

    • sigma Covariance matrix of the outcome trajectory assuming no ICEs. +If NULL, then these parameters are inherited from pars_group.

      • +
    + +
    +
    +

    Value

    +

    A data.frame containing the simulated data. It includes the following variables:

    • id: Factor variable that specifies the id of each subject.

      • +

    • visit: Factor variable that specifies the visit of each assessment. Visit 0 denotes +the baseline visit.

      • +

    • group: Factor variable that specifies which treatment group each subject belongs to.

      • +

    • outcome_bl: Numeric variable that specifies the baseline outcome.

      • +

    • outcome_noICE: Numeric variable that specifies the longitudinal outcome assuming +no ICEs.

      • +

    • ind_ice1: Binary variable that takes value 1 if the corresponding visit is +affected by ICE1 and 0 otherwise.

      • +

    • dropout_ice1: Binary variable that takes value 1 if the corresponding visit is +affected by the drop-out following ICE1 and 0 otherwise.

      • +

    • ind_ice2: Binary variable that takes value 1 if the corresponding visit is affected +by ICE2.

      • +

    • outcome: Numeric variable that specifies the longitudinal outcome including ICE1, ICE2 +and the intermittent missing values.

      • +
    +
    +

    See also

    +

    simulate_data().

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/getStrategies.html b/v1.3.1/reference/getStrategies.html new file mode 100644 index 000000000..e9e5a2b25 --- /dev/null +++ b/v1.3.1/reference/getStrategies.html @@ -0,0 +1,116 @@ + +Get imputation strategies — getStrategies • rbmi + Skip to contents + + +
    +
    +
    +

    Get imputation strategies

    + Source: R/strategies.R +
    getStrategies.Rd
    +
    + +
    +

    Returns a list defining the imputation strategies to be used to create the +multivariate normal distribution parameters by merging those of the source +group and reference group per patient.

    +
    + +
    +

    Usage

    + 
    getStrategies(...)
    +
    + +
    +

    Arguments

    + + +
    ...
    +

    User defined methods to be added to the return list. Input must +be a function.

    + +
    +
    +

    Details

    +

    By default Jump to Reference (JR), Copy Reference (CR), Copy Increments in +Reference (CIR), Last Mean Carried Forward (LMCF) and Missing at Random (MAR) +are defined.

    +

    The user can define their own strategy functions (or overwrite the pre-defined ones) +by specifying a named input to the function i.e. NEW = function(...) .... +Only exception is MAR which cannot be overwritten.

    +

    All user defined functions must take 3 inputs: pars_group, pars_ref and +index_mar. pars_group and pars_ref are both lists with elements mu +and sigma representing the multivariate normal distribution parameters for +the subject's current group and reference group respectively. index_mar will be +a logical vector specifying which visits the subject met the MAR assumption +at. The function must return a list with elements mu and sigma. See the implementation +of strategy_JR() for an example.

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+getStrategies()
+getStrategies(
+    NEW = function(pars_group, pars_ref, index_mar) code ,
+    JR = function(pars_group, pars_ref, index_mar)  more_code
+)
+} # }
+
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_ESS.html b/v1.3.1/reference/get_ESS.html new file mode 100644 index 000000000..98b3a00fc --- /dev/null +++ b/v1.3.1/reference/get_ESS.html @@ -0,0 +1,85 @@ + +Extract the Effective Sample Size (ESS) from a stanfit object — get_ESS • rbmi + Skip to contents + + +
    +
    +
    +

    Extract the Effective Sample Size (ESS) from a stanfit object

    + Source: R/mcmc.R +
    get_ESS.Rd
    +
    + +
    +

    Extract the Effective Sample Size (ESS) from a stanfit object

    +
    + +
    +

    Usage

    + 
    get_ESS(stan_fit)
    +
    + +
    +

    Arguments

    + + +
    stan_fit
    +

    A stanfit object.

    + +
    +
    +

    Value

    +

    A named vector containing the ESS for each parameter of the model.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_bootstrap_stack.html b/v1.3.1/reference/get_bootstrap_stack.html new file mode 100644 index 000000000..5aa5dfa8d --- /dev/null +++ b/v1.3.1/reference/get_bootstrap_stack.html @@ -0,0 +1,92 @@ + +Creates a stack object populated with bootstrapped samples — get_bootstrap_stack • rbmi + Skip to contents + + +
    +
    +
    +

    Creates a stack object populated with bootstrapped samples

    + Source: R/stack.R +
    get_bootstrap_stack.Rd
    +
    + +
    +

    Function creates a Stack() object and populated the stack with bootstrap +samples based upon method$n_samples

    +
    + +
    +

    Usage

    + 
    get_bootstrap_stack(longdata, method, stack = Stack$new())
    +
    + +
    +

    Arguments

    + + +
    longdata
    +

    A longDataConstructor() object

    + + +
    method
    +

    A method object

    + + +
    stack
    +

    A Stack() object (this is only exposed for unit testing purposes)

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_conditional_parameters.html b/v1.3.1/reference/get_conditional_parameters.html new file mode 100644 index 000000000..13e7b1240 --- /dev/null +++ b/v1.3.1/reference/get_conditional_parameters.html @@ -0,0 +1,95 @@ + +Derive conditional multivariate normal parameters — get_conditional_parameters • rbmi + Skip to contents + + +
    +
    +
    +

    Derive conditional multivariate normal parameters

    + Source: R/impute.R +
    get_conditional_parameters.Rd
    +
    + +
    +

    Takes parameters for a multivariate normal distribution and observed values +to calculate the conditional distribution for the unobserved values.

    +
    + +
    +

    Usage

    + 
    get_conditional_parameters(pars, values)
    +
    + +
    +

    Arguments

    + + +
    pars
    +

    a list with elements mu and sigma defining the mean vector and +covariance matrix respectively.

    + + +
    values
    +

    a vector of observed values to condition on, must be same length as pars$mu. +Missing values must be represented by an NA.

    + +
    +
    +

    Value

    +

    A list with the conditional distribution parameters:

    • mu - The conditional mean vector.

      • +

    • sigma - The conditional covariance matrix.

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_delta_template.html b/v1.3.1/reference/get_delta_template.html new file mode 100644 index 000000000..4fb3613a4 --- /dev/null +++ b/v1.3.1/reference/get_delta_template.html @@ -0,0 +1,87 @@ + +Get delta utility variables — get_delta_template • rbmi + Skip to contents + + +
    +
    +
    +

    Get delta utility variables

    + Source: R/delta.R +
    get_delta_template.Rd
    +
    + +
    +

    This function creates the default delta template (1 row per subject per visit) +and extracts all the utility information that users need to define their own logic +for defining delta. See delta_template() for full details.

    +
    + +
    +

    Usage

    + 
    get_delta_template(imputations)
    +
    + +
    +

    Arguments

    + + +
    imputations
    +

    an imputations object created by impute().

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_draws_mle.html b/v1.3.1/reference/get_draws_mle.html new file mode 100644 index 000000000..c1a494ff3 --- /dev/null +++ b/v1.3.1/reference/get_draws_mle.html @@ -0,0 +1,162 @@ + +Fit the base imputation model on bootstrap samples — get_draws_mle • rbmi + Skip to contents + + +
    +
    +
    +

    Fit the base imputation model on bootstrap samples

    + Source: R/draws.R +
    get_draws_mle.Rd
    +
    + +
    +

    Fit the base imputation model using a ML/REML approach on a given number of bootstrap samples as +specified by method$n_samples. Returns the parameter estimates from the model fit.

    +
    + +
    +

    Usage

    + 
    get_draws_mle(
+  longdata,
+  method,
+  sample_stack,
+  n_target_samples,
+  first_sample_orig,
+  use_samp_ids,
+  failure_limit = 0,
+  ncores = 1,
+  quiet = FALSE
+)
    +
    + +
    +

    Arguments

    + + +
    longdata
    +

    R6 longdata object containing all relevant input data information.

    + + +
    method
    +

    A method object as generated by either +method_approxbayes() or method_condmean() with argument type = "bootstrap".

    + + +
    sample_stack
    +

    A stack object containing the subject ids to be used on each mmrm iteration.

    + + +
    n_target_samples
    +

    Number of samples needed to be created

    + + +
    first_sample_orig
    +

    Logical. If TRUE the function returns method$n_samples + 1 samples where +the first sample contains the parameter estimates from the original dataset and method$n_samples +samples contain the parameter estimates from bootstrap samples. +If FALSE the function returns method$n_samples samples containing the parameter estimates from +bootstrap samples.

    + + +
    use_samp_ids
    +

    Logical. If TRUE, the sampled subject ids are returned. Otherwise +the subject ids from the original dataset are returned. These values are used to tell impute() +what subjects should be used to derive the imputed dataset.

    + + +
    failure_limit
    +

    Number of failed samples that are allowed before throwing an error

    + + +
    ncores
    +

    Number of processes to parallelise the job over

    + + +
    quiet
    +

    Logical, If TRUE will suppress printing of progress information that is printed to +the console.

    + +
    +
    +

    Value

    +

    A draws object which is a named list containing the following:

    • data: R6 longdata object containing all relevant input data information.

      • +

    • method: A method object as generated by either method_bayes(), +method_approxbayes() or method_condmean().

      • +

    • samples: list containing the estimated parameters of interest. +Each element of samples is a named list containing the following:

      • ids: vector of characters containing the ids of the subjects included in the original dataset.

        • +

      • beta: numeric vector of estimated regression coefficients.

        • +

      • sigma: list of estimated covariance matrices (one for each level of vars$group).

        • +

      • theta: numeric vector of transformed covariances.

        • +

      • failed: Logical. TRUE if the model fit failed.

        • +

      • ids_samp: vector of characters containing the ids of the subjects included in the given sample.

        • +
      • +

    • fit: if method_bayes() is chosen, returns the MCMC Stan fit object. Otherwise NULL.

      • +

    • n_failures: absolute number of failures of the model fit. +Relevant only for method_condmean(type = "bootstrap"), method_approxbayes() and method_bmlmi().

      • +

    • formula: fixed effects formula object used for the model specification.

      • +
    +
    +

    Details

    +

    This function takes a Stack object which contains multiple lists of patient ids. The function +takes this Stack and pulls a set ids and then constructs a dataset just consisting of these +patients (i.e. potentially a bootstrap or a jackknife sample).

    +

    The function then fits a MMRM model to this dataset to create a sample object. The function +repeats this process until n_target_samples have been reached. If more than failure_limit +samples fail to converge then the function throws an error.

    +

    After reaching the desired number of samples the function generates and returns a draws object.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_ests_bmlmi.html b/v1.3.1/reference/get_ests_bmlmi.html new file mode 100644 index 000000000..87c94a2db --- /dev/null +++ b/v1.3.1/reference/get_ests_bmlmi.html @@ -0,0 +1,107 @@ + +Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi • rbmi + Skip to contents + + +
    +
    +
    +

    Von Hippel and Bartlett pooling of BMLMI method

    + Source: R/pool.R +
    get_ests_bmlmi.Rd
    +
    + +
    +

    Compute pooled point estimates, standard error and degrees of freedom +according to the Von Hippel and Bartlett formula for Bootstrapped Maximum Likelihood +Multiple Imputation (BMLMI).

    +
    + +
    +

    Usage

    + 
    get_ests_bmlmi(ests, D)
    +
    + +
    +

    Arguments

    + + +
    ests
    +

    numeric vector containing estimates from the analysis of the imputed datasets.

    + + +
    D
    +

    numeric representing the number of imputations between each bootstrap sample in the BMLMI method.

    + +
    +
    +

    Value

    +

    a list containing point estimate, standard error and degrees of freedom.

    +
    +
    +

    Details

    +

    ests must be provided in the following order: the firsts D elements are related to analyses from +random imputation of one bootstrap sample. The second set of D elements (i.e. from D+1 to 2*D) +are related to the second bootstrap sample and so on.

    +
    +
    +

    References

    +

    Von Hippel, Paul T and Bartlett, Jonathan W8. +Maximum likelihood multiple imputation: Faster imputations and consistent standard errors +without posterior draws. 2021

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_example_data.html b/v1.3.1/reference/get_example_data.html new file mode 100644 index 000000000..912d9b644 --- /dev/null +++ b/v1.3.1/reference/get_example_data.html @@ -0,0 +1,108 @@ + +Simulate a realistic example dataset — get_example_data • rbmi + Skip to contents + + +
    +
    +
    +

    Simulate a realistic example dataset

    + Source: R/simulate_data.R +
    get_example_data.Rd
    +
    + +
    +

    Simulate a realistic example dataset using simulate_data() with hard-coded +values of all the input arguments.

    +
    + +
    +

    Usage

    + 
    get_example_data()
    +
    + +
    +

    Details

    +

    get_example_data() simulates a 1:1 randomized trial of +an active drug (intervention) versus placebo (control) with 100 subjects per +group and 6 post-baseline assessments (bi-monthly visits until 12 months). +One intercurrent event corresponding to treatment discontinuation is also simulated. +Specifically, data are simulated under the following assumptions:

    • The mean outcome trajectory in the placebo group increases linearly from +50 at baseline (visit 0) to 60 at visit 6, i.e. the slope is 10 points/year.

      • +

    • The mean outcome trajectory in the intervention group is identical to the +placebo group up to visit 2. From visit 2 onward, the slope decreases by 50% to 5 points/year.

      • +

    • The covariance structure of the baseline and follow-up values in both groups +is implied by a random intercept and slope model with a standard deviation of 5 +for both the intercept and the slope, and a correlation of 0.25. +In addition, an independent residual error with standard deviation 2.5 is added +to each assessment.

      • +

    • The probability of study drug discontinuation after each visit is calculated +according to a logistic model which depends on the observed outcome at that visit. +Specifically, a visit-wise discontinuation probability of 2% and 3% in the control +and intervention group, respectively, is specified in case the observed outcome is +equal to 50 (the mean value at baseline). The odds of a discontinuation is simulated +to increase by +10% for each +1 point increase of the observed outcome.

      • +

    • Study drug discontinuation is simulated to have no effect on the mean trajectory in +the placebo group. In the intervention group, subjects who discontinue follow +the slope of the mean trajectory from the placebo group from that time point onward. +This is compatible with a copy increments in reference (CIR) assumption.

      • +

    • Study drop-out at the study drug discontinuation visit occurs with a probability +of 50% leading to missing outcome data from that time point onward.

      • +
    +
    +

    See also

    +

    simulate_data(), set_simul_pars()

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_jackknife_stack.html b/v1.3.1/reference/get_jackknife_stack.html new file mode 100644 index 000000000..38e61ffc5 --- /dev/null +++ b/v1.3.1/reference/get_jackknife_stack.html @@ -0,0 +1,92 @@ + +Creates a stack object populated with jackknife samples — get_jackknife_stack • rbmi + Skip to contents + + +
    +
    +
    +

    Creates a stack object populated with jackknife samples

    + Source: R/stack.R +
    get_jackknife_stack.Rd
    +
    + +
    +

    Function creates a Stack() object and populated the stack with jackknife +samples based upon

    +
    + +
    +

    Usage

    + 
    get_jackknife_stack(longdata, method, stack = Stack$new())
    +
    + +
    +

    Arguments

    + + +
    longdata
    +

    A longDataConstructor() object

    + + +
    method
    +

    A method object

    + + +
    stack
    +

    A Stack() object (this is only exposed for unit testing purposes)

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_mmrm_sample.html b/v1.3.1/reference/get_mmrm_sample.html new file mode 100644 index 000000000..b21c5ee47 --- /dev/null +++ b/v1.3.1/reference/get_mmrm_sample.html @@ -0,0 +1,102 @@ + +Fit MMRM and returns parameter estimates — get_mmrm_sample • rbmi + Skip to contents + + +
    +
    +
    +

    Fit MMRM and returns parameter estimates

    + Source: R/draws.R +
    get_mmrm_sample.Rd
    +
    + +
    +

    get_mmrm_sample fits the base imputation model using a ML/REML approach. +Returns the parameter estimates from the fit.

    +
    + +
    +

    Usage

    + 
    get_mmrm_sample(ids, longdata, method)
    +
    + +
    +

    Arguments

    + + +
    ids
    +

    vector of characters containing the ids of the subjects.

    + + +
    longdata
    +

    R6 longdata object containing all relevant input data information.

    + + +
    method
    +

    A method object as generated by either +method_approxbayes() or method_condmean().

    + +
    +
    +

    Value

    +

    A named list of class sample_single. It contains the following:

    • ids vector of characters containing the ids of the subjects included in the original dataset.

      • +

    • beta numeric vector of estimated regression coefficients.

      • +

    • sigma list of estimated covariance matrices (one for each level of vars$group).

      • +

    • theta numeric vector of transformed covariances.

      • +

    • failed logical. TRUE if the model fit failed.

      • +

    • ids_samp vector of characters containing the ids of the subjects included in the given sample.

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_pattern_groups.html b/v1.3.1/reference/get_pattern_groups.html new file mode 100644 index 000000000..b93f28683 --- /dev/null +++ b/v1.3.1/reference/get_pattern_groups.html @@ -0,0 +1,92 @@ + +Determine patients missingness group — get_pattern_groups • rbmi + Skip to contents + + +
    +
    +
    +

    Determine patients missingness group

    + Source: R/mcmc.R +
    get_pattern_groups.Rd
    +
    + +
    +

    Takes a design matrix with multiple rows per subject and returns a dataset +with 1 row per subject with a new column pgroup indicating which group +the patient belongs to (based upon their missingness pattern and treatment group)

    +
    + +
    +

    Usage

    + 
    get_pattern_groups(ddat)
    +
    + +
    +

    Arguments

    + + +
    ddat
    +

    a data.frame with columns subjid, visit, group, is_avail

    + +
    +
    +

    Details

    + +

    • The column is_avail must be a character or numeric 0 or 1

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_pattern_groups_unique.html b/v1.3.1/reference/get_pattern_groups_unique.html new file mode 100644 index 000000000..19a520eea --- /dev/null +++ b/v1.3.1/reference/get_pattern_groups_unique.html @@ -0,0 +1,93 @@ + +Get Pattern Summary — get_pattern_groups_unique • rbmi + Skip to contents + + +
    +
    +
    +

    Get Pattern Summary

    + Source: R/mcmc.R +
    get_pattern_groups_unique.Rd
    +
    + +
    +

    Takes a dataset of pattern information and creates a summary dataset of it +with just 1 row per pattern

    +
    + +
    +

    Usage

    + 
    get_pattern_groups_unique(patterns)
    +
    + +
    +

    Arguments

    + + +
    patterns
    +

    A data.frame with the columns pgroup, pattern and group

    + +
    +
    +

    Details

    + +

    • The column pgroup must be a numeric vector indicating which pattern group the patient belongs to

      • +

    • The column pattern must be a character string of 0's or 1's. It must be identical for all +rows within the same pgroup

      • +

    • The column group must be a character / numeric vector indicating which covariance group the observation +belongs to. It must be identical within the same pgroup

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_pool_components.html b/v1.3.1/reference/get_pool_components.html new file mode 100644 index 000000000..87adb9f66 --- /dev/null +++ b/v1.3.1/reference/get_pool_components.html @@ -0,0 +1,85 @@ + +Expected Pool Components — get_pool_components • rbmi + Skip to contents + + +
    +
    +
    +

    Expected Pool Components

    + Source: R/pool.R +
    get_pool_components.Rd
    +
    + +
    +

    Returns the elements expected to be contained in the analyse object +depending on what analysis method was specified.

    +
    + +
    +

    Usage

    + 
    get_pool_components(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    Character name of the analysis method, must one of +either "rubin", "jackknife", "bootstrap" or "bmlmi".

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_session_hash.html b/v1.3.1/reference/get_session_hash.html new file mode 100644 index 000000000..b98c08de1 --- /dev/null +++ b/v1.3.1/reference/get_session_hash.html @@ -0,0 +1,72 @@ + +Get session hash — get_session_hash • rbmi + Skip to contents + + +
    +
    +
    +

    Get session hash

    + Source: R/utilities.R +
    get_session_hash.Rd
    +
    + +
    +

    Gets a unique string based on the current R version and relevant packages.

    +
    + +
    +

    Usage

    + 
    get_session_hash()
    +
    + + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_stan_model.html b/v1.3.1/reference/get_stan_model.html new file mode 100644 index 000000000..616467122 --- /dev/null +++ b/v1.3.1/reference/get_stan_model.html @@ -0,0 +1,72 @@ + +Get Compiled Stan Object — get_stan_model • rbmi + Skip to contents + + +
    +
    +
    +

    Get Compiled Stan Object

    + Source: R/utilities.R +
    get_stan_model.Rd
    +
    + +
    +

    Gets a compiled Stan object that can be used with rstan::sampling()

    +
    + +
    +

    Usage

    + 
    get_stan_model()
    +
    + + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/get_visit_distribution_parameters.html b/v1.3.1/reference/get_visit_distribution_parameters.html new file mode 100644 index 000000000..20e4c4e5f --- /dev/null +++ b/v1.3.1/reference/get_visit_distribution_parameters.html @@ -0,0 +1,105 @@ + +Derive visit distribution parameters — get_visit_distribution_parameters • rbmi + Skip to contents + + +
    +
    +
    +

    Derive visit distribution parameters

    + Source: R/impute.R +
    get_visit_distribution_parameters.Rd
    +
    + +
    +

    Takes patient level data and beta coefficients and expands them +to get a patient specific estimate for the visit distribution parameters +mu and sigma. Returns the values in a specific format +which is expected by downstream functions in the imputation process +(namely list(list(mu = ..., sigma = ...), list(mu = ..., sigma = ...))).

    +
    + +
    +

    Usage

    + 
    get_visit_distribution_parameters(dat, beta, sigma)
    +
    + +
    +

    Arguments

    + + +
    dat
    +

    Patient level dataset, must be 1 row per visit. Column order must +be in the same order as beta. The number of columns must match the length of beta

    + + +
    beta
    +

    List of model beta coefficients. There should be 1 element for each sample +e.g. if there were 3 samples and the models each had 4 beta coefficients then this argument +should be of the form list( c(1,2,3,4) , c(5,6,7,8), c(9,10,11,12)). +All elements of beta must be the same length and must be the same length and order as dat.

    + + +
    sigma
    +

    List of sigma. Must have the same number of entries as beta.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/has_class.html b/v1.3.1/reference/has_class.html new file mode 100644 index 000000000..782c240cd --- /dev/null +++ b/v1.3.1/reference/has_class.html @@ -0,0 +1,96 @@ + +Does object have a class ? — has_class • rbmi + Skip to contents + + +
    +
    +
    +

    Does object have a class ?

    + Source: R/utilities.R +
    has_class.Rd
    +
    + +
    +

    Utility function to see if an object has a particular class. +Useful when we don't know how many other classes the object may +have.

    +
    + +
    +

    Usage

    + 
    has_class(x, cls)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    the object we want to check the class of.

    + + +
    cls
    +

    the class we want to know if it has or not.

    + +
    +
    +

    Value

    +

    TRUE if the object has the class. +FALSE if the object does not have the class.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/ife.html b/v1.3.1/reference/ife.html new file mode 100644 index 000000000..4aa421402 --- /dev/null +++ b/v1.3.1/reference/ife.html @@ -0,0 +1,98 @@ + +if else — ife • rbmi + Skip to contents + + +
    +
    +
    +

    if else

    + Source: R/utilities.R +
    ife.Rd
    +
    + +
    +

    A wrapper around if() else() to prevent unexpected +interactions between ifelse() and factor variables

    +
    + +
    +

    Usage

    + 
    ife(x, a, b)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    True / False

    + + +
    a
    +

    value to return if True

    + + +
    b
    +

    value to return if False

    + +
    +
    +

    Details

    +

    By default ifelse() will convert factor variables to their +numeric values which is often undesirable. This connivance +function avoids that problem

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/imputation_df.html b/v1.3.1/reference/imputation_df.html new file mode 100644 index 000000000..158f5eadf --- /dev/null +++ b/v1.3.1/reference/imputation_df.html @@ -0,0 +1,81 @@ + +Create a valid imputation_df object — imputation_df • rbmi + Skip to contents + + +
    +
    +
    +

    Create a valid imputation_df object

    + Source: R/dataclasses.R +
    imputation_df.Rd
    +
    + +
    +

    Create a valid imputation_df object

    +
    + +
    +

    Usage

    + 
    imputation_df(...)
    +
    + +
    +

    Arguments

    + + +
    ...
    +

    a list of imputation_single.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/imputation_list_df.html b/v1.3.1/reference/imputation_list_df.html new file mode 100644 index 000000000..433c3ab2c --- /dev/null +++ b/v1.3.1/reference/imputation_list_df.html @@ -0,0 +1,81 @@ + +List of imputations_df — imputation_list_df • rbmi + Skip to contents + + +
    +
    +
    +

    List of imputations_df

    + Source: R/dataclasses.R +
    imputation_list_df.Rd
    +
    + +
    +

    A container for multiple imputation_df's

    +
    + +
    +

    Usage

    + 
    imputation_list_df(...)
    +
    + +
    +

    Arguments

    + + +
    ...
    +

    objects of class imputation_df

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/imputation_list_single.html b/v1.3.1/reference/imputation_list_single.html new file mode 100644 index 000000000..5a95c4b9a --- /dev/null +++ b/v1.3.1/reference/imputation_list_single.html @@ -0,0 +1,92 @@ + +A collection of imputation_singles() grouped by a single subjid ID — imputation_list_single • rbmi + Skip to contents + + +
    +
    +
    +

    A collection of imputation_singles() grouped by a single subjid ID

    + Source: R/dataclasses.R +
    imputation_list_single.Rd
    +
    + +
    +

    A collection of imputation_singles() grouped by a single subjid ID

    +
    + +
    +

    Usage

    + 
    imputation_list_single(imputations, D = 1)
    +
    + +
    +

    Arguments

    + + +
    imputations
    +

    a list of imputation_single() objects ordered so that repetitions +are grouped sequentially

    + + +
    D
    +

    the number of repetitions that were performed which determines how many columns +the imputation matrix should have

    +

    This is a constructor function to create a imputation_list_single object +which contains a matrix of imputation_single() objects grouped by a single id. The matrix +is split so that it has D columns (i.e. for non-bmlmi methods this will always be 1)

    +

    The id attribute is determined by extracting the id attribute from the contributing +imputation_single() objects. An error is throw if multiple id are detected

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/imputation_single.html b/v1.3.1/reference/imputation_single.html new file mode 100644 index 000000000..b18e33d38 --- /dev/null +++ b/v1.3.1/reference/imputation_single.html @@ -0,0 +1,85 @@ + +Create a valid imputation_single object — imputation_single • rbmi + Skip to contents + + +
    +
    +
    +

    Create a valid imputation_single object

    + Source: R/dataclasses.R +
    imputation_single.Rd
    +
    + +
    +

    Create a valid imputation_single object

    +
    + +
    +

    Usage

    + 
    imputation_single(id, values)
    +
    + +
    +

    Arguments

    + + +
    id
    +

    a character string specifying the subject id.

    + + +
    values
    +

    a numeric vector indicating the imputed values.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/impute.html b/v1.3.1/reference/impute.html new file mode 100644 index 000000000..6c79925e5 --- /dev/null +++ b/v1.3.1/reference/impute.html @@ -0,0 +1,202 @@ + +Create imputed datasets — impute • rbmi + Skip to contents + + +
    +
    +
    +

    Create imputed datasets

    + Source: R/impute.R +
    impute.Rd
    +
    + +
    +

    impute() creates imputed datasets based upon the data and options specified in +the call to draws(). One imputed dataset is created per each "sample" created by +draws().

    +
    + +
    +

    Usage

    + 
    impute(
+  draws,
+  references = NULL,
+  update_strategy = NULL,
+  strategies = getStrategies()
+)
+
+# S3 method for class 'random'
+impute(
+  draws,
+  references = NULL,
+  update_strategy = NULL,
+  strategies = getStrategies()
+)
+
+# S3 method for class 'condmean'
+impute(
+  draws,
+  references = NULL,
+  update_strategy = NULL,
+  strategies = getStrategies()
+)
    +
    + +
    +

    Arguments

    + + +
    draws
    +

    A draws object created by draws().

    + + +
    references
    +

    A named vector. Identifies the references to be used for reference-based +imputation methods. Should be of the form c("Group1" = "Reference1", "Group2" = "Reference2"). +If NULL (default), the references are assumed to be of the form +c("Group1" = "Group1", "Group2" = "Group2"). This argument cannot be NULL if +an imputation strategy (as defined by data_ice[[vars$strategy]] in the call to draws) other than MAR is set.

    + + +
    update_strategy
    +

    An optional data.frame. Updates the imputation method that was +originally set via the data_ice option in draws(). See the details section for more +information.

    + + +
    strategies
    +

    A named list of functions. Defines the imputation functions to be used. +The names of the list should mirror the values specified in strategy column of data_ice. +Default = getStrategies(). See getStrategies() for more details.

    + +
    +
    +

    Details

    +

    impute() uses the imputation model parameter estimates, as generated by draws(), to +first calculate the marginal (multivariate normal) distribution of a subject's longitudinal +outcome variable +depending on their covariate values. +For subjects with intercurrent events (ICEs) handled using non-MAR methods, this marginal distribution +is then updated depending on the time of the first visit affected by the ICE, +the chosen imputation strategy and the chosen reference group as described in Carpenter, Roger, and Kenward (2013) . +The subject's imputation distribution used for imputing missing values is then defined as +their marginal distribution conditional on their observed outcome values. +One dataset is being generated per set of parameter estimates provided by draws().

    +

    The exact manner in how missing values are imputed from this conditional imputation distribution depends +on the method object that was provided to draws(), in particular:

    • Bayes & Approximate Bayes: each imputed dataset contains 1 row per subject & visit +from the original dataset with missing values imputed by taking a single random sample +from the conditional imputation distribution.

      • +

    • Conditional Mean: each imputed dataset contains 1 row per subject & visit from the +bootstrapped or jackknife dataset that was used to generate the corresponding parameter +estimates in draws(). Missing values are imputed by using the mean of the conditional +imputation distribution. Please note that the first imputed dataset refers to the conditional +mean imputation on the original dataset whereas all subsequent imputed datasets refer to +conditional mean imputations for bootstrap or jackknife samples, respectively, of the original data.

      • +

    • Bootstrapped Maximum Likelihood MI (BMLMI): it performs D random imputations of each bootstrapped +dataset that was used to generate the corresponding parameter estimates in draws(). A total number of +B*D imputed datasets is provided, where B is the number of bootstrapped datasets. Missing values +are imputed by taking a random sample from the conditional imputation distribution.

      • +

    The update_strategy argument can be used to update the imputation strategy that was +originally set via the data_ice option in draws(). This avoids having to re-run the draws() +function when changing the imputation strategy in certain circumstances (as detailed below). +The data.frame provided to update_strategy argument must contain two columns, +one for the subject ID and another for the imputation strategy, whose names are the same as +those defined in the vars argument as specified in the call to draws(). Please note that this +argument only allows you to update the imputation strategy and not other arguments such as the +time of the first visit affected by the ICE. +A key limitation of this functionality is +that one can only switch between a MAR and a non-MAR strategy (or vice versa) for subjects without +observed post-ICE data. The reason for this is that such a change would affect whether the post-ICE data is included +in the base imputation model or not (as explained in the help to draws()). +As an example, if a subject had their ICE on "Visit 2" +but had observed/known values for "Visit 3" then the function will throw an error +if one tries to switch the strategy from MAR to a non-MAR strategy. In contrast, switching from +a non-MAR to a MAR strategy, whilst valid, will raise a warning as not all usable data +will have been utilised in the imputation model.

    +
    +
    +

    References

    +

    James R Carpenter, James H Roger, and Michael G Kenward. Analysis of longitudinal trials with protocol deviation: +a framework for relevant, +accessible assumptions, and inference via multiple imputation. Journal of Biopharmaceutical Statistics, +23(6):1352–1371, 2013. [Section 4.2 and 4.3]

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+
+impute(
+    draws = drawobj,
+    references = c("Trt" = "Placebo", "Placebo" = "Placebo")
+)
+
+new_strategy <- data.frame(
+  subjid = c("Pt1", "Pt2"),
+  strategy = c("MAR", "JR")
+)
+
+impute(
+    draws = drawobj,
+    references = c("Trt" = "Placebo", "Placebo" = "Placebo"),
+    update_strategy = new_strategy
+)
+} # }
+
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/impute_data_individual.html b/v1.3.1/reference/impute_data_individual.html new file mode 100644 index 000000000..df9693083 --- /dev/null +++ b/v1.3.1/reference/impute_data_individual.html @@ -0,0 +1,144 @@ + +Impute data for a single subject — impute_data_individual • rbmi + Skip to contents + + +
    +
    +
    +

    Impute data for a single subject

    + Source: R/impute.R +
    impute_data_individual.Rd
    +
    + +
    +

    This function performs the imputation for a single subject at a time implementing the +process as detailed in impute().

    +
    + +
    +

    Usage

    + 
    impute_data_individual(
+  id,
+  index,
+  beta,
+  sigma,
+  data,
+  references,
+  strategies,
+  condmean,
+  n_imputations = 1
+)
    +
    + +
    +

    Arguments

    + + +
    id
    +

    Character string identifying the subject.

    + + +
    index
    +

    The sample indexes which the subject belongs to e.g c(1,1,1,2,2,4).

    + + +
    beta
    +

    A list of beta coefficients for each sample, i.e. beta[[1]] is the set of +beta coefficients for the first sample.

    + + +
    sigma
    +

    A list of the sigma coefficients for each sample split by group i.e. +sigma[[1]][["A"]] would give the sigma coefficients for group A for the first sample.

    + + +
    data
    +

    A longdata object created by longDataConstructor()

    + + +
    references
    +

    A named vector. Identifies the references to be used when generating the +imputed values. Should be of the form c("Group" = "Reference", "Group" = "Reference").

    + + +
    strategies
    +

    A named list of functions. Defines the imputation functions to be used. +The names of the list should mirror the values specified in method column of data_ice. +Default = getStrategies(). See getStrategies() for more details.

    + + +
    condmean
    +

    Logical. If TRUE will impute using the conditional mean values, if FALSE +will impute by taking a random draw from the multivariate normal distribution.

    + + +
    n_imputations
    +

    When condmean = FALSE numeric representing the number of random +imputations to be performed for each sample. +Default is 1 (one random imputation per sample).

    + +
    +
    +

    Details

    +

    Note that this function performs all of the required imputations for a subject at the +same time. I.e. if a subject is included in samples 1,3,5,9 then all imputations (using +sample-dependent imputation model parameters) are performed in one step in order to avoid +having to look up a subjects's covariates and expanding them to a design matrix multiple times +(which would be more computationally expensive). +The function also supports subject belonging to the same sample multiple times, +i.e. 1,1,2,3,5,5, as will typically occur for bootstrapped datasets.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/impute_internal.html b/v1.3.1/reference/impute_internal.html new file mode 100644 index 000000000..2372ef76d --- /dev/null +++ b/v1.3.1/reference/impute_internal.html @@ -0,0 +1,115 @@ + +Create imputed datasets — impute_internal • rbmi + Skip to contents + + +
    +
    +
    +

    Create imputed datasets

    + Source: R/impute.R +
    impute_internal.Rd
    +
    + +
    +

    This is the work horse function that implements most of the functionality of impute. +See the user level function impute() for further details.

    +
    + +
    +

    Usage

    + 
    impute_internal(
+  draws,
+  references = NULL,
+  update_strategy,
+  strategies,
+  condmean
+)
    +
    + +
    +

    Arguments

    + + +
    draws
    +

    A draws object created by draws().

    + + +
    references
    +

    A named vector. Identifies the references to be used for reference-based +imputation methods. Should be of the form c("Group1" = "Reference1", "Group2" = "Reference2"). +If NULL (default), the references are assumed to be of the form +c("Group1" = "Group1", "Group2" = "Group2"). This argument cannot be NULL if +an imputation strategy (as defined by data_ice[[vars$strategy]] in the call to draws) other than MAR is set.

    + + +
    update_strategy
    +

    An optional data.frame. Updates the imputation method that was +originally set via the data_ice option in draws(). See the details section for more +information.

    + + +
    strategies
    +

    A named list of functions. Defines the imputation functions to be used. +The names of the list should mirror the values specified in strategy column of data_ice. +Default = getStrategies(). See getStrategies() for more details.

    + + +
    condmean
    +

    logical. If TRUE will impute using the conditional mean values, if values +will impute by taking a random draw from the multivariate normal distribution.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/impute_outcome.html b/v1.3.1/reference/impute_outcome.html new file mode 100644 index 000000000..a67bc3f26 --- /dev/null +++ b/v1.3.1/reference/impute_outcome.html @@ -0,0 +1,92 @@ + +Sample outcome value — impute_outcome • rbmi + Skip to contents + + +
    +
    +
    +

    Sample outcome value

    + Source: R/impute.R +
    impute_outcome.Rd
    +
    + +
    +

    Draws a random sample from a multivariate normal distribution.

    +
    + +
    +

    Usage

    + 
    impute_outcome(conditional_parameters, n_imputations = 1, condmean = FALSE)
    +
    + +
    +

    Arguments

    + + +
    conditional_parameters
    +

    a list with elements mu and sigma which +contain the mean vector and covariance matrix to sample from.

    + + +
    n_imputations
    +

    numeric representing the number of random samples from the multivariate +normal distribution to be performed. Default is 1.

    + + +
    condmean
    +

    should conditional mean imputation be performed (as opposed to random +sampling)

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/index.html b/v1.3.1/reference/index.html new file mode 100644 index 000000000..d4eb6b721 --- /dev/null +++ b/v1.3.1/reference/index.html @@ -0,0 +1,876 @@ + +Package index • rbmi + Skip to contents + + +
    +
    +
    +

    Package index

    +
    + +
    +

    All functions

    + + + + +
    + + + + +
    + + QR_decomp() + +
    +
    QR decomposition
    +
    + + Stack + +
    +
    R6 Class for a FIFO stack
    +
    + + add_class() + +
    +
    Add a class
    +
    + + adjust_trajectories() + +
    +
    Adjust trajectories due to the intercurrent event (ICE)
    +
    + + adjust_trajectories_single() + +
    +
    Adjust trajectory of a subject's outcome due to the intercurrent event (ICE)
    +
    + + analyse() + +
    +
    Analyse Multiple Imputed Datasets
    +
    + + ancova() + +
    +
    Analysis of Covariance
    +
    + + ancova_single() + +
    +
    Implements an Analysis of Covariance (ANCOVA)
    +
    + + antidepressant_data + +
    +
    Antidepressant trial data
    +
    + + apply_delta() + +
    +
    Applies delta adjustment
    +
    + + as_analysis() + +
    +
    Construct an analysis object
    +
    + + as_ascii_table() + +
    +
    as_ascii_table
    +
    + + as_class() + +
    +
    Set Class
    +
    + + as_cropped_char() + +
    +
    as_cropped_char
    +
    + + as_dataframe() + +
    +
    Convert object to dataframe
    +
    + + as_draws() + +
    +
    Creates a draws object
    +
    + + as_imputation() + +
    +
    Create an imputation object
    +
    + + as_indices() + +
    +
    Convert indicator to index
    +
    + + as_mmrm_df() + +
    +
    Creates a "MMRM" ready dataset
    +
    + + as_mmrm_formula() + +
    +
    Create MMRM formula
    +
    + + as_model_df() + +
    +
    Expand data.frame into a design matrix
    +
    + + as_simple_formula() + +
    +
    Creates a simple formula object from a string
    +
    + + as_stan_array() + +
    +
    As array
    +
    + + as_strata() + +
    +
    Create vector of Stratas
    +
    + + assert_variables_exist() + +
    +
    Assert that all variables exist within a dataset
    +
    + + char2fct() + +
    +
    Convert character variables to factor
    +
    + + check_ESS() + +
    +
    Diagnostics of the MCMC based on ESS
    +
    + + check_hmc_diagn() + +
    +
    Diagnostics of the MCMC based on HMC-related measures.
    +
    + + check_mcmc() + +
    +
    Diagnostics of the MCMC
    +
    + + compute_sigma() + +
    +
    Compute covariance matrix for some reference-based methods (JR, CIR)
    +
    + + convert_to_imputation_list_df() + +
    +
    Convert list of imputation_list_single() objects to an imputation_list_df() object (i.e. a list of imputation_df() objects's)
    +
    + + d_lagscale() + +
    +
    Calculate delta from a lagged scale coefficient
    +
    + + delta_template() + +
    +
    Create a delta data.frame template
    +
    + + draws() + +
    +
    Fit the base imputation model and get parameter estimates
    +
    + + eval_mmrm() + +
    +
    Evaluate a call to mmrm
    +
    + + expand() fill_locf() expand_locf() + +
    +
    Expand and fill in missing data.frame rows
    +
    + + extract_covariates() + +
    +
    Extract Variables from string vector
    +
    + + extract_data_nmar_as_na() + +
    +
    Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy)
    +
    + + extract_draws() + +
    +
    Extract draws from a stanfit object
    +
    + + extract_imputed_df() + +
    +
    Extract imputed dataset
    +
    + + extract_imputed_dfs() + +
    +
    Extract imputed datasets
    +
    + + extract_params() + +
    +
    Extract parameters from a MMRM model
    +
    + + fit_mcmc() + +
    +
    Fit the base imputation model using a Bayesian approach
    +
    + + fit_mmrm() + +
    +
    Fit a MMRM model
    +
    + + generate_data_single() + +
    +
    Generate data for a single group
    +
    + + getStrategies() + +
    +
    Get imputation strategies
    +
    + + get_ESS() + +
    +
    Extract the Effective Sample Size (ESS) from a stanfit object
    +
    + + get_bootstrap_stack() + +
    +
    Creates a stack object populated with bootstrapped samples
    +
    + + get_conditional_parameters() + +
    +
    Derive conditional multivariate normal parameters
    +
    + + get_delta_template() + +
    +
    Get delta utility variables
    +
    + + get_draws_mle() + +
    +
    Fit the base imputation model on bootstrap samples
    +
    + + get_ests_bmlmi() + +
    +
    Von Hippel and Bartlett pooling of BMLMI method
    +
    + + get_example_data() + +
    +
    Simulate a realistic example dataset
    +
    + + get_jackknife_stack() + +
    +
    Creates a stack object populated with jackknife samples
    +
    + + get_mmrm_sample() + +
    +
    Fit MMRM and returns parameter estimates
    +
    + + get_pattern_groups() + +
    +
    Determine patients missingness group
    +
    + + get_pattern_groups_unique() + +
    +
    Get Pattern Summary
    +
    + + get_pool_components() + +
    +
    Expected Pool Components
    +
    + + get_visit_distribution_parameters() + +
    +
    Derive visit distribution parameters
    +
    + + has_class() + +
    +
    Does object have a class ?
    +
    + + ife() + +
    +
    if else
    +
    + + imputation_df() + +
    +
    Create a valid imputation_df object
    +
    + + imputation_list_df() + +
    +
    List of imputations_df
    +
    + + imputation_list_single() + +
    +
    A collection of imputation_singles() grouped by a single subjid ID
    +
    + + imputation_single() + +
    +
    Create a valid imputation_single object
    +
    + + impute() + +
    +
    Create imputed datasets
    +
    + + impute_data_individual() + +
    +
    Impute data for a single subject
    +
    + + impute_internal() + +
    +
    Create imputed datasets
    +
    + + impute_outcome() + +
    +
    Sample outcome value
    +
    + + invert() + +
    +
    invert
    +
    + + invert_indexes() + +
    +
    Invert and derive indexes
    +
    + + is_absent() + +
    +
    Is value absent
    +
    + + is_char_fact() + +
    +
    Is character or factor
    +
    + + is_char_one() + +
    +
    Is single character
    +
    + + is_in_rbmi_development() + +
    +
    Is package in development mode?
    +
    + + is_num_char_fact() + +
    +
    Is character, factor or numeric
    +
    + + locf() + +
    +
    Last Observation Carried Forward
    +
    + + longDataConstructor + +
    +
    R6 Class for Storing / Accessing & Sampling Longitudinal Data
    +
    + + ls_design_equal() ls_design_counterfactual() ls_design_proportional() + +
    +
    Calculate design vector for the lsmeans
    +
    + + lsmeans() + +
    +
    Least Square Means
    +
    + + make_rbmi_cluster() + +
    +
    Create a rbmi ready cluster
    +
    + + method_bayes() method_approxbayes() method_condmean() method_bmlmi() + +
    +
    Set the multiple imputation methodology
    +
    + + par_lapply() + +
    +
    Parallelise Lapply
    +
    + + parametric_ci() + +
    +
    Calculate parametric confidence intervals
    +
    + + pool() as.data.frame(<pool>) print(<pool>) + +
    +
    Pool analysis results obtained from the imputed datasets
    +
    + + pool_bootstrap_normal() + +
    +
    Bootstrap Pooling via normal approximation
    +
    + + pool_bootstrap_percentile() + +
    +
    Bootstrap Pooling via Percentiles
    +
    + + pool_internal() + +
    +
    Internal Pool Methods
    +
    + + prepare_stan_data() + +
    +
    Prepare input data to run the Stan model
    +
    + + print(<analysis>) + +
    +
    Print analysis object
    +
    + + print(<draws>) + +
    +
    Print draws object
    +
    + + print(<imputation>) + +
    +
    Print imputation object
    +
    + + progressLogger + +
    +
    R6 Class for printing current sampling progress
    +
    + + pval_percentile() + +
    +
    P-value of percentile bootstrap
    +
    + + random_effects_expr() + +
    +
    Construct random effects formula
    +
    + + set_options() + +
    +
    rbmi settings
    +
    + + record() + +
    +
    Capture all Output
    +
    + + recursive_reduce() + +
    +
    recursive_reduce
    +
    + + remove_if_all_missing() + +
    +
    Remove subjects from dataset if they have no observed values
    +
    + + rubin_df() + +
    +
    Barnard and Rubin degrees of freedom adjustment
    +
    + + rubin_rules() + +
    +
    Combine estimates using Rubin's rules
    +
    + + sample_ids() + +
    +
    Sample Patient Ids
    +
    + + sample_list() + +
    +
    Create and validate a sample_list object
    +
    + + sample_mvnorm() + +
    +
    Sample random values from the multivariate normal distribution
    +
    + + sample_single() + +
    +
    Create object of sample_single class
    +
    + + scalerConstructor + +
    +
    R6 Class for scaling (and un-scaling) design matrices
    +
    + + set_simul_pars() + +
    +
    Set simulation parameters of a study group.
    +
    + + set_vars() + +
    +
    Set key variables
    +
    + + simulate_data() + +
    +
    Generate data
    +
    + + simulate_dropout() + +
    +
    Simulate drop-out
    +
    + + simulate_ice() + +
    +
    Simulate intercurrent event
    +
    + + simulate_test_data() as_vcov() + +
    +
    Create simulated datasets
    +
    + + sort_by() + +
    +
    Sort data.frame
    +
    + + split_dim() + +
    +
    Transform array into list of arrays
    +
    + + split_imputations() + +
    +
    Split a flat list of imputation_single() into multiple imputation_df()'s by ID
    +
    + + str_contains() + +
    +
    Does a string contain a substring
    +
    + + strategy_MAR() strategy_JR() strategy_CR() strategy_CIR() strategy_LMCF() + +
    +
    Strategies
    +
    + + string_pad() + +
    +
    string_pad
    +
    + + transpose_imputations() + +
    +
    Transpose imputations
    +
    + + transpose_results() + +
    +
    Transpose results object
    +
    + + transpose_samples() + +
    +
    Transpose samples
    +
    + + validate() + +
    +
    Generic validation method
    +
    + + validate(<analysis>) + +
    +
    Validate analysis objects
    +
    + + validate(<draws>) + +
    +
    Validate draws object
    +
    + + validate(<is_mar>) + +
    +
    Validate is_mar for a given subject
    +
    + + validate(<ivars>) + +
    +
    Validate inputs for vars
    +
    + + validate(<references>) + +
    +
    Validate user supplied references
    +
    + + validate(<sample_list>) + +
    +
    Validate sample_list object
    +
    + + validate(<sample_single>) + +
    +
    Validate sample_single object
    +
    + + validate(<simul_pars>) + +
    +
    Validate a simul_pars object
    +
    + + validate(<stan_data>) + +
    +
    Validate a stan_data object
    +
    + + validate_analyse_pars() + +
    +
    Validate analysis results
    +
    + + validate_datalong() validate_datalong_varExists() validate_datalong_types() validate_datalong_notMissing() validate_datalong_complete() validate_datalong_unifromStrata() validate_dataice() + +
    +
    Validate a longdata object
    +
    + + validate_strategies() + +
    +
    Validate user specified strategies
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/invert.html b/v1.3.1/reference/invert.html new file mode 100644 index 000000000..45114891c --- /dev/null +++ b/v1.3.1/reference/invert.html @@ -0,0 +1,84 @@ + +invert — invert • rbmi + Skip to contents + + +
    +
    +
    +

    invert

    + Source: R/as_ascii_table.R +
    invert.Rd
    +
    + +
    +

    Utility function used to replicated purrr::transpose. Turns a list inside +out.

    +
    + +
    +

    Usage

    + 
    invert(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    list

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/invert_indexes.html b/v1.3.1/reference/invert_indexes.html new file mode 100644 index 000000000..70f51df30 --- /dev/null +++ b/v1.3.1/reference/invert_indexes.html @@ -0,0 +1,95 @@ + +Invert and derive indexes — invert_indexes • rbmi + Skip to contents + + +
    +
    +
    +

    Invert and derive indexes

    + Source: R/impute.R +
    invert_indexes.Rd
    +
    + +
    +

    Takes a list of elements and creates a new list +containing 1 entry per unique element value containing +the indexes of which original elements it occurred in.

    +
    + +
    +

    Usage

    + 
    invert_indexes(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    list of elements to invert and calculate index from (see details).

    + +
    +
    +

    Details

    +

    This functions purpose is best illustrated by an example:

    +

    input:

    +

    list( c("A", "B", "C"), c("A", "A", "B"))}

    +

    becomes:

    +

    list( "A" = c(1,2,2), "B" = c(1,2), "C" = 1 )

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/is_absent.html b/v1.3.1/reference/is_absent.html new file mode 100644 index 000000000..287f20b1d --- /dev/null +++ b/v1.3.1/reference/is_absent.html @@ -0,0 +1,95 @@ + +Is value absent — is_absent • rbmi + Skip to contents + + +
    +
    +
    +

    Is value absent

    + Source: R/utilities.R +
    is_absent.Rd
    +
    + +
    +

    Returns true if a value is either NULL, NA or "". +In the case of a vector all values must be NULL/NA/"" +for x to be regarded as absent.

    +
    + +
    +

    Usage

    + 
    is_absent(x, na = TRUE, blank = TRUE)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a value to check if it is absent or not

    + + +
    na
    +

    do NAs count as absent

    + + +
    blank
    +

    do blanks i.e. "" count as absent

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/is_char_fact.html b/v1.3.1/reference/is_char_fact.html new file mode 100644 index 000000000..ab92b0e12 --- /dev/null +++ b/v1.3.1/reference/is_char_fact.html @@ -0,0 +1,81 @@ + +Is character or factor — is_char_fact • rbmi + Skip to contents + + +
    +
    +
    +

    Is character or factor

    + Source: R/utilities.R +
    is_char_fact.Rd
    +
    + +
    +

    returns true if x is character or factor vector

    +
    + +
    +

    Usage

    + 
    is_char_fact(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a character or factor vector

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/is_char_one.html b/v1.3.1/reference/is_char_one.html new file mode 100644 index 000000000..18fa6d422 --- /dev/null +++ b/v1.3.1/reference/is_char_one.html @@ -0,0 +1,81 @@ + +Is single character — is_char_one • rbmi + Skip to contents + + +
    +
    +
    +

    Is single character

    + Source: R/utilities.R +
    is_char_one.Rd
    +
    + +
    +

    returns true if x is a length 1 character vector

    +
    + +
    +

    Usage

    + 
    is_char_one(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a character vector

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/is_in_rbmi_development.html b/v1.3.1/reference/is_in_rbmi_development.html new file mode 100644 index 000000000..c03268a77 --- /dev/null +++ b/v1.3.1/reference/is_in_rbmi_development.html @@ -0,0 +1,85 @@ + +Is package in development mode? — is_in_rbmi_development • rbmi + Skip to contents + + +
    +
    +
    +

    Is package in development mode?

    + Source: R/parallel.R +
    is_in_rbmi_development.Rd
    +
    + +
    +

    Returns TRUE if the package is being developed on i.e. you have a local copy of the +source code which you are actively editing +Returns FALSE otherwise

    +
    + +
    +

    Usage

    + 
    is_in_rbmi_development()
    +
    + +
    +

    Details

    +

    Main use of this function is in parallel processing to indicate whether the sub-processes +need to load the current development version of the code or whether they should load +the main installed package on the system

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/is_num_char_fact.html b/v1.3.1/reference/is_num_char_fact.html new file mode 100644 index 000000000..c825480e7 --- /dev/null +++ b/v1.3.1/reference/is_num_char_fact.html @@ -0,0 +1,81 @@ + +Is character, factor or numeric — is_num_char_fact • rbmi + Skip to contents + + +
    +
    +
    +

    Is character, factor or numeric

    + Source: R/utilities.R +
    is_num_char_fact.Rd
    +
    + +
    +

    returns true if x is a character, numeric or factor vector

    +
    + +
    +

    Usage

    + 
    is_num_char_fact(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a character, numeric or factor vector

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/locf.html b/v1.3.1/reference/locf.html new file mode 100644 index 000000000..f7707a316 --- /dev/null +++ b/v1.3.1/reference/locf.html @@ -0,0 +1,88 @@ + +Last Observation Carried Forward — locf • rbmi + Skip to contents + + +
    +
    +
    +

    Last Observation Carried Forward

    + Source: R/expand.R +
    locf.Rd
    +
    + +
    +

    Returns a vector after applied last observation carried forward imputation.

    +
    + +
    +

    Usage

    + 
    locf(x)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a vector.

    + +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+locf(c(NA, 1, 2, 3, NA, 4)) # Returns c(NA, 1, 2, 3, 3, 4)
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/longDataConstructor.html b/v1.3.1/reference/longDataConstructor.html new file mode 100644 index 000000000..1688d58e7 --- /dev/null +++ b/v1.3.1/reference/longDataConstructor.html @@ -0,0 +1,453 @@ + +R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor • rbmi + Skip to contents + + +
    +
    +
    +

    R6 Class for Storing / Accessing & Sampling Longitudinal Data

    + Source: R/longData.R +
    longDataConstructor.Rd
    +
    + +
    +

    A longdata object allows for efficient storage and recall of longitudinal datasets for use in +bootstrap sampling. The object works by de-constructing the data into lists based upon subject id +thus enabling efficient lookup.

    +
    + + +
    +

    Details

    +

    The object also handles multiple other operations specific to rbmi such as defining whether an +outcome value is MAR / Missing or not as well as tracking which imputation strategy is assigned +to each subject.

    +

    It is recognised that this objects functionality is fairly overloaded and is hoped that this can +be split out into more area specific objects / functions in the future. Further additions of functionality +to this object should be avoided if possible.

    +
    +
    +

    Public fields

    +

    data
    +

    The original dataset passed to the constructor (sorted by id and visit)

    + + +
    vars
    +

    The vars object (list of key variables) passed to the constructor

    + + +
    visits
    +

    A character vector containing the distinct visit levels

    + + +
    ids
    +

    A character vector containing the unique ids of each subject in self$data

    + + +
    formula
    +

    A formula expressing how the design matrix for the data should be constructed

    + + +
    strata
    +

    A numeric vector indicating which strata each corresponding value of +self$ids belongs to. +If no stratification variable is defined this will default to 1 for all subjects +(i.e. same group). +This field is only used as part of the self$sample_ids() function to enable +stratified bootstrap +sampling

    + + +
    ice_visit_index
    +

    A list indexed by subject storing the index number of the first visit +affected by the ICE. If there is no ICE then it is set equal to the number of visits plus 1.

    + + +
    values
    +

    A list indexed by subject storing a numeric vector of the +original (unimputed) outcome values

    + + +
    group
    +

    A list indexed by subject storing a single character +indicating which imputation group the subject belongs to as defined +by self$data[id, self$ivars$group] +It is used +to determine what reference group should be used when imputing the subjects data.

    + + +
    is_mar
    +

    A list indexed by subject storing logical values indicating +if the subjects outcome values are MAR or not. +This list is defaulted to TRUE for all subjects & outcomes and is then +modified by calls to self$set_strategies(). +Note that this does not indicate which values are missing, this variable +is True for outcome values that either occurred before the ICE visit +or are post the ICE visit and have an imputation strategy of MAR

    + + +
    strategies
    +

    A list indexed by subject storing a single character +value indicating the imputation +strategy assigned to that subject. This list is defaulted to "MAR" +for all subjects and is then +modified by calls to either self$set_strategies() or self$update_strategies()

    + + +
    strategy_lock
    +

    A list indexed by subject storing a single +logical value indicating whether a +patients imputation strategy is locked or not. If a strategy is +locked it means that it can't change +from MAR to non-MAR. Strategies can be changed from non-MAR to MAR though +this will trigger a warning. +Strategies are locked if the patient is assigned a MAR strategy and +has non-missing after their ICE date. This list is populated by a call to +self$set_strategies().

    + + +
    indexes
    +

    A list indexed by subject storing a numeric vector of +indexes which specify which rows in the +original dataset belong to this subject i.e. to recover the full data +for subject "pt3" you can use +self$data[self$indexes[["pt3"]],]. This may seem redundant over filtering +the data directly +however it enables efficient bootstrap sampling of the data i.e.

    +

    indexes <- unlist(self$indexes[c("pt3", "pt3")])
+self$data[indexes,]

    +

    This list is populated during the object initialisation.

    + + +
    is_missing
    +

    A list indexed by subject storing a logical vector +indicating whether the corresponding +outcome of a subject is missing. This list is populated during the +object initialisation.

    + + +
    is_post_ice
    +

    A list indexed by subject storing a logical vector +indicating whether the corresponding +outcome of a subject is post the date of their ICE. If no ICE data has +been provided this defaults to False +for all observations. This list is populated by a call to self$set_strategies().

    + + +

    +
    +
    +

    Methods

    + +
    +

    Public methods

    + +

    +

    Method get_data()

    +

    Returns a data.frame based upon required subject IDs. Replaces missing +values with new ones if provided.

    +

    Usage

    +

    longDataConstructor$get_data(
+  obj = NULL,
+  nmar.rm = FALSE,
+  na.rm = FALSE,
+  idmap = FALSE
+)

    +
    + +
    +

    Arguments

    +

    obj
    +

    Either NULL, a character vector of subjects IDs or a +imputation list object. See details.

    + + +
    nmar.rm
    +

    Logical value. If TRUE will remove observations that are +not regarded as MAR (as determined from self$is_mar).

    + + +
    na.rm
    +

    Logical value. If TRUE will remove outcome values that are +missing (as determined from self$is_missing).

    + + +
    idmap
    +

    Logical value. If TRUE will add an attribute idmap which +contains a mapping from the new subject ids to the old subject ids. See details.

    + + +

    +
    +
    +

    Details

    +

    If obj is NULL then the full original dataset is returned.

    +

    If obj is a character vector then a new dataset consisting of just those subjects is +returned; if the character vector contains duplicate entries then that subject will be +returned multiple times.

    +

    If obj is an imputation_df object (as created by imputation_df()) then the +subject ids specified in the object will be returned and missing values will be filled +in by those specified in the imputation list object. i.e.

    +

    obj <- imputation_df(
+  imputation_single( id = "pt1", values = c(1,2,3)),
+  imputation_single( id = "pt1", values = c(4,5,6)),
+  imputation_single( id = "pt3", values = c(7,8))
+)
+longdata$get_data(obj)

    +

    Will return a data.frame consisting of all observations for pt1 twice and all of the +observations for pt3 once. The first set of observations for pt1 will have missing +values filled in with c(1,2,3) and the second set will be filled in by c(4,5,6). The +length of the values must be equal to sum(self$is_missing[[id]]).

    +

    If obj is not NULL then all subject IDs will be scrambled in order to ensure that they +are unique +i.e. If the pt2 is requested twice then this process guarantees that each set of observations +be have a unique subject ID number. The idmap attribute (if requested) can be used +to map from the new ids back to the old ids.

    +
    + +
    +

    Returns

    +

    A data.frame.

    +
    + +

    +

    Method add_subject()

    +

    This function decomposes a patient data from self$data and populates +all the corresponding lists i.e. self$is_missing, self$values, self$group, etc. +This function is only called upon the objects initialization.

    +

    Usage

    +

    longDataConstructor$add_subject(id)

    +
    + +
    +

    Arguments

    +

    id
    +

    Character subject id that exists within self$data.

    + + +

    +
    + +

    +

    Method validate_ids()

    +

    Throws an error if any element of ids is not within the source data self$data.

    +

    Usage

    +

    longDataConstructor$validate_ids(ids)

    +
    + +
    +

    Arguments

    +

    ids
    +

    A character vector of ids.

    + + +

    +
    +
    +

    Returns

    +

    TRUE

    +
    + +

    +

    Method sample_ids()

    +

    Performs random stratified sampling of patient ids (with replacement) +Each patient has an equal weight of being picked within their strata (i.e is not dependent on +how many non-missing visits they had).

    +

    Usage

    +

    longDataConstructor$sample_ids()

    +
    + +
    +

    Returns

    +

    Character vector of ids.

    +
    + +

    +

    Method extract_by_id()

    +

    Returns a list of key information for a given subject. Is a convenience wrapper +to save having to manually grab each element.

    +

    Usage

    +

    longDataConstructor$extract_by_id(id)

    +
    + +
    +

    Arguments

    +

    id
    +

    Character subject id that exists within self$data.

    + + +

    +
    + +

    +

    Method update_strategies()

    +

    Convenience function to run self$set_strategies(dat_ice, update=TRUE) +kept for legacy reasons.

    +

    Usage

    +

    longDataConstructor$update_strategies(dat_ice)

    +
    + +
    +

    Arguments

    +

    dat_ice
    +

    A data.frame containing ICE information see impute() for the format of this dataframe.

    + + +

    +
    + +

    +

    Method set_strategies()

    +

    Updates the self$strategies, self$is_mar, self$is_post_ice variables based upon the provided ICE +information.

    +

    Usage

    +

    longDataConstructor$set_strategies(dat_ice = NULL, update = FALSE)

    +
    + +
    +

    Arguments

    +

    dat_ice
    +

    a data.frame containing ICE information. See details.

    + + +
    update
    +

    Logical, indicates that the ICE data should be used as an update. See details.

    + + +

    +
    +
    +

    Details

    +

    See draws() for the specification of dat_ice if update=FALSE. +See impute() for the format of dat_ice if update=TRUE. +If update=TRUE this function ensures that MAR strategies cannot be changed to non-MAR in the presence +of post-ICE observations.

    +
    + + +

    +

    Method check_has_data_at_each_visit()

    +

    Ensures that all visits have at least 1 observed "MAR" observation. Throws +an error if this criteria is not met. This is to ensure that the initial +MMRM can be resolved.

    +

    Usage

    +

    longDataConstructor$check_has_data_at_each_visit()

    +
    + + +

    +

    Method set_strata()

    +

    Populates the self$strata variable. If the user has specified stratification variables +The first visit is used to determine the value of those variables. If no stratification variables +have been specified then everyone is defined as being in strata 1.

    +

    Usage

    +

    longDataConstructor$set_strata()

    +
    + + +

    +

    Method new()

    +

    Constructor function.

    +

    Usage

    +

    longDataConstructor$new(data, vars)

    +
    + +
    +

    Arguments

    +

    data
    +

    longitudinal dataset.

    + + +
    vars
    +

    an ivars object created by set_vars().

    + + +

    +
    + +

    +

    Method clone()

    +

    The objects of this class are cloneable with this method.

    +

    Usage

    +

    longDataConstructor$clone(deep = FALSE)

    +
    + +
    +

    Arguments

    +

    deep
    +

    Whether to make a deep clone.

    + + +

    +
    + +
    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/ls_design.html b/v1.3.1/reference/ls_design.html new file mode 100644 index 000000000..5ec8b194b --- /dev/null +++ b/v1.3.1/reference/ls_design.html @@ -0,0 +1,108 @@ + +Calculate design vector for the lsmeans — ls_design • rbmi + Skip to contents + + +
    +
    +
    +

    Calculate design vector for the lsmeans

    + Source: R/lsmeans.R +
    ls_design.Rd
    +
    + +
    +

    Calculates the design vector as required to generate the lsmean +and standard error. ls_design_equal calculates it by +applying an equal weight per covariate combination whilst +ls_design_proportional applies weighting proportional +to the frequency in which the covariate combination occurred +in the actual dataset.

    +
    + +
    +

    Usage

    + 
    ls_design_equal(data, frm, fix)
+
+ls_design_counterfactual(data, frm, fix)
+
+ls_design_proportional(data, frm, fix)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    A data.frame

    + + +
    frm
    +

    Formula used to fit the original model

    + + +
    fix
    +

    A named list of variables with fixed values

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/lsmeans.html b/v1.3.1/reference/lsmeans.html new file mode 100644 index 000000000..2a35c4d16 --- /dev/null +++ b/v1.3.1/reference/lsmeans.html @@ -0,0 +1,180 @@ + +Least Square Means — lsmeans • rbmi + Skip to contents + + +
    +
    +
    +

    Least Square Means

    + Source: R/lsmeans.R +
    lsmeans.Rd
    +
    + +
    +

    Estimates the least square means from a linear model. The exact implementation +/ interpretation depends on the weighting scheme; see the weighting section for more +information.

    +
    + +
    +

    Usage

    + 
    lsmeans(
+  model,
+  ...,
+  .weights = c("counterfactual", "equal", "proportional_em", "proportional")
+)
    +
    + +
    +

    Arguments

    + + +
    model
    +

    A model created by lm.

    + + +
    ...
    +

    Fixes specific variables to specific values i.e. +trt = 1 or age = 50. The name of the argument must be the name +of the variable within the dataset.

    + + +
    .weights
    +

    Character, either "counterfactual" (default), "equal", +"proportional_em" or "proportional". +Specifies the weighting strategy to be used when calculating the lsmeans. +See the weighting section for more details.

    + +
    +
    +

    Weighting

    + + +
    +

    Counterfactual

    + + +

    For weights = "counterfactual" (the default) the lsmeans are obtained by +taking the average of the predicted values for each patient after assigning all patients +to each arm in turn. +This approach is equivalent to standardization or g-computation. +In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", counterfactual = "<treatment>")

    +

    Note that to ensure backwards compatibility with previous versions of rbmi +weights = "proportional" is an alias for weights = "counterfactual". +To get results consistent with emmeans's weights = "proportional" +please use weights = "proportional_em".

    +
    + +
    +

    Equal

    + + +

    For weights = "equal" the lsmeans are obtained by taking the model fitted +value of a hypothetical patient whose covariates are defined as follows:

    • Continuous covariates are set to mean(X)

      • +

    • Dummy categorical variables are set to 1/N where N is the number of levels

      • +

    • Continuous * continuous interactions are set to mean(X) * mean(Y)

      • +

    • Continuous * categorical interactions are set to mean(X) * 1/N

      • +

    • Dummy categorical * categorical interactions are set to 1/N * 1/M

      • +

    In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", weights = "equal")

    +
    + +
    +

    Proportional

    + + +

    For weights = "proportional_em" the lsmeans are obtained as per weights = "equal" +except instead of weighting each observation equally they are weighted by the proportion +in which the given combination of categorical values occurred in the data. +In comparison to emmeans this approach is equivalent to:

    +

    emmeans::emmeans(model, specs = "<treatment>", weights = "proportional")

    +

    Note that this is not to be confused with weights = "proportional" which is an alias +for weights = "counterfactual".

    +
    + +
    +
    +

    Fixing

    + + + +

    Regardless of the weighting scheme any named arguments passed via ... will +fix the value of the covariate to the specified value. +For example, lsmeans(model, trt = "A") will fix the dummy variable trtA to 1 +for all patients (real or hypothetical) when calculating the lsmeans.

    +

    See the references for similar implementations as done in SAS and +in R via the emmeans package.

    +
    +
    +

    References

    +

    https://CRAN.R-project.org/package=emmeans

    +

    https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.3/statug/statug_glm_details41.htm

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+mod <- lm(Sepal.Length ~ Species + Petal.Length, data = iris)
+lsmeans(mod)
+lsmeans(mod, Species = "virginica")
+lsmeans(mod, Species = "versicolor")
+lsmeans(mod, Species = "versicolor", Petal.Length = 1)
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/make_rbmi_cluster.html b/v1.3.1/reference/make_rbmi_cluster.html new file mode 100644 index 000000000..49cda2c23 --- /dev/null +++ b/v1.3.1/reference/make_rbmi_cluster.html @@ -0,0 +1,114 @@ + +Create a rbmi ready cluster — make_rbmi_cluster • rbmi + Skip to contents + + +
    +
    +
    +

    Create a rbmi ready cluster

    + Source: R/parallel.R +
    make_rbmi_cluster.Rd
    +
    + +
    +

    Create a rbmi ready cluster

    +
    + +
    +

    Usage

    + 
    make_rbmi_cluster(ncores = 1, objects = NULL, packages = NULL)
    +
    + +
    +

    Arguments

    + + +
    ncores
    +

    Number of parallel processes to use or an existing cluster to make use of

    + + +
    objects
    +

    a named list of objects to export into the sub-processes

    + + +
    packages
    +

    a character vector of libraries to load in the sub-processes

    +

    This function is a wrapper around parallel::makePSOCKcluster() but takes +care of configuring rbmi to be used in the sub-processes as well as loading +user defined objects and libraries and setting the seed for reproducibility.

    +

    If ncores is 1 this function will return NULL.

    +

    If ncores is a cluster created via parallel::makeCluster() then this function +just takes care of inserting the relevant rbmi objects into the existing cluster.

    + +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+# Basic usage
+make_rbmi_cluster(5)
+
+# User objects + libraries
+VALUE <- 5
+myfun <- function(x) {
+    x + day(VALUE) # From lubridate::day()
+}
+make_rbmi_cluster(5, list(VALUE = VALUE, myfun = myfun), c("lubridate"))
+
+# Using a already created cluster
+cl <- parallel::makeCluster(5)
+make_rbmi_cluster(cl)
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/method.html b/v1.3.1/reference/method.html new file mode 100644 index 000000000..221fa1602 --- /dev/null +++ b/v1.3.1/reference/method.html @@ -0,0 +1,212 @@ + +Set the multiple imputation methodology — method • rbmi + Skip to contents + + +
    +
    +
    +

    Set the multiple imputation methodology

    + Source: R/methods.R +
    method.Rd
    +
    + +
    +

    These functions determine what methods rbmi should use when creating +the imputation models, generating imputed values and pooling the results.

    +
    + +
    +

    Usage

    + 
    method_bayes(
+  burn_in = 200,
+  burn_between = 50,
+  same_cov = TRUE,
+  n_samples = 20,
+  seed = NULL
+)
+
+method_approxbayes(
+  covariance = c("us", "ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", "toeph"),
+  threshold = 0.01,
+  same_cov = TRUE,
+  REML = TRUE,
+  n_samples = 20
+)
+
+method_condmean(
+  covariance = c("us", "ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", "toeph"),
+  threshold = 0.01,
+  same_cov = TRUE,
+  REML = TRUE,
+  n_samples = NULL,
+  type = c("bootstrap", "jackknife")
+)
+
+method_bmlmi(
+  covariance = c("us", "ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", "toeph"),
+  threshold = 0.01,
+  same_cov = TRUE,
+  REML = TRUE,
+  B = 20,
+  D = 2
+)
    +
    + +
    +

    Arguments

    + + +
    burn_in
    +

    a numeric that specifies how many observations should be discarded +prior to extracting actual samples. Note that the sampler +is initialized at the maximum likelihood estimates and a weakly informative +prior is used thus in theory this value should not need to be that high.

    + + +
    burn_between
    +

    a numeric that specifies the "thinning" rate i.e. how many +observations should be discarded between each sample. This is used to prevent +issues associated with autocorrelation between the samples.

    + + +
    same_cov
    +

    a logical, if TRUE the imputation model will be fitted using a single +shared covariance matrix for all observations. If FALSE a separate covariance +matrix will be fit for each group as determined by the group argument of +set_vars().

    + + +
    n_samples
    +

    a numeric that determines how many imputed datasets are generated. +In the case of method_condmean(type = "jackknife") this argument +must be set to NULL. See details.

    + + +
    seed
    +

    deprecated. Please use set.seed() instead.

    + + +
    covariance
    +

    a character string that specifies the structure of the covariance +matrix to be used in the imputation model. Must be one of "us" (default), "ad", +"adh", "ar1", "ar1h", "cs", "csh", "toep", or "toeph"). See details.

    + + +
    threshold
    +

    a numeric between 0 and 1, specifies the proportion of bootstrap +datasets that can fail to produce valid samples before an error is thrown. +See details.

    + + +
    REML
    +

    a logical indicating whether to use REML estimation rather than maximum +likelihood.

    + + +
    type
    +

    a character string that specifies the resampling method used to perform inference +when a conditional mean imputation approach (set via method_condmean()) is used. +Must be one of "bootstrap" or "jackknife".

    + + +
    B
    +

    a numeric that determines the number of bootstrap samples for method_bmlmi.

    + + +
    D
    +

    a numeric that determines the number of random imputations for each bootstrap sample. +Needed for method_bmlmi().

    + +
    +
    +

    Details

    +

    In the case of method_condmean(type = "bootstrap") there will be n_samples + 1 +imputation models and datasets generated as the first sample will be based on +the original dataset whilst the other n_samples samples will be +bootstrapped datasets. Likewise, for method_condmean(type = "jackknife") there will +be length(unique(data$subjid)) + 1 imputation models and datasets generated. In both cases this is +represented by n + 1 being displayed in the print message.

    +

    The user is able to specify different covariance structures using the the covariance +argument. Currently supported structures include:

    • Unstructured ("us") (default)

      • +

    • Ante-dependence ("ad")

      • +

    • Heterogeneous ante-dependence ("adh")

      • +

    • First-order auto-regressive ("ar1")

      • +

    • Heterogeneous first-order auto-regressive ("ar1h")

      • +

    • Compound symmetry ("cs")

      • +

    • Heterogeneous compound symmetry ("csh")

      • +

    • Toeplitz ("toep")

      • +

    • Heterogeneous Toeplitz ("toeph")

      • +

    For full details please see mmrm::cov_types().

    +

    Note that at present Bayesian methods only support unstructured.

    +

    In the case of method_condmean(type = "bootstrap"), method_approxbayes() and method_bmlmi() repeated +bootstrap samples of the original dataset are taken with an MMRM fitted to each sample. +Due to the randomness of these sampled datasets, as well as limitations in the optimisers +used to fit the models, it is not uncommon that estimates for a particular dataset can't +be generated. In these instances rbmi is designed to throw out that bootstrapped dataset +and try again with another. However to ensure that these errors are due to chance and +not due to some underlying misspecification in the data and/or model a tolerance limit +is set on how many samples can be discarded. Once the tolerance limit has been reached +an error will be thrown and the process aborted. The tolerance limit is defined as +ceiling(threshold * n_samples). Note that for the jackknife method estimates need to be +generated for all leave-one-out datasets and as such an error will be thrown if +any of them fail to fit.

    +

    Please note that at the time of writing (September 2021) Stan is unable to produce +reproducible samples across different operating systems even when the same seed is used. +As such care must be taken when using Stan across different machines. For more information +on this limitation please consult the Stan documentation +https://mc-stan.org/docs/2_27/reference-manual/reproducibility-chapter.html

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/par_lapply.html b/v1.3.1/reference/par_lapply.html new file mode 100644 index 000000000..9c05fc43f --- /dev/null +++ b/v1.3.1/reference/par_lapply.html @@ -0,0 +1,96 @@ + +Parallelise Lapply — par_lapply • rbmi + Skip to contents + + +
    +
    +
    +

    Parallelise Lapply

    + Source: R/parallel.R +
    par_lapply.Rd
    +
    + +
    +

    Simple wrapper around lapply and parallel::clusterApplyLB to abstract away +the logic of deciding which one to use

    +
    + +
    +

    Usage

    + 
    par_lapply(cl, fun, x, ...)
    +
    + +
    +

    Arguments

    + + +
    cl
    +

    Cluster created by parallel::makeCluster() or NULL

    + + +
    fun
    +

    Function to be run

    + + +
    x
    +

    object to be looped over

    + + +
    ...
    +

    extra arguements passed to fun

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/parametric_ci.html b/v1.3.1/reference/parametric_ci.html new file mode 100644 index 000000000..d2d07bac8 --- /dev/null +++ b/v1.3.1/reference/parametric_ci.html @@ -0,0 +1,110 @@ + +Calculate parametric confidence intervals — parametric_ci • rbmi + Skip to contents + + +
    +
    +
    +

    Calculate parametric confidence intervals

    + Source: R/pool.R +
    parametric_ci.Rd
    +
    + +
    +

    Calculates confidence intervals based upon a parametric +distribution.

    +
    + +
    +

    Usage

    + 
    parametric_ci(point, se, alpha, alternative, qfun, pfun, ...)
    +
    + +
    +

    Arguments

    + + +
    point
    +

    The point estimate.

    + + +
    se
    +

    The standard error of the point estimate. If using a non-"normal" +distribution this should be set to 1.

    + + +
    alpha
    +

    The type 1 error rate, should be a value between 0 and 1.

    + + +
    alternative
    +

    a character string specifying the alternative hypothesis, +must be one of "two.sided" (default), "greater" or "less".

    + + +
    qfun
    +

    The quantile function for the assumed distribution i.e. qnorm.

    + + +
    pfun
    +

    The CDF function for the assumed distribution i.e. pnorm.

    + + +
    ...
    +

    additional arguments passed on qfun and pfun i.e. df = 102.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/pool.html b/v1.3.1/reference/pool.html new file mode 100644 index 000000000..330f23bdf --- /dev/null +++ b/v1.3.1/reference/pool.html @@ -0,0 +1,143 @@ + +Pool analysis results obtained from the imputed datasets — pool • rbmi + Skip to contents + + +
    +
    +
    +

    Pool analysis results obtained from the imputed datasets

    + Source: R/pool.R +
    pool.Rd
    +
    + +
    +

    Pool analysis results obtained from the imputed datasets

    +
    + +
    +

    Usage

    + 
    pool(
+  results,
+  conf.level = 0.95,
+  alternative = c("two.sided", "less", "greater"),
+  type = c("percentile", "normal")
+)
+
+# S3 method for class 'pool'
+as.data.frame(x, ...)
+
+# S3 method for class 'pool'
+print(x, ...)
    +
    + +
    +

    Arguments

    + + +
    results
    +

    an analysis object created by analyse().

    + + +
    conf.level
    +

    confidence level of the returned confidence interval. +Must be a single number between 0 and 1. Default is 0.95.

    + + +
    alternative
    +

    a character string specifying the alternative hypothesis, +must be one of "two.sided" (default), "greater" or "less".

    + + +
    type
    +

    a character string of either "percentile" (default) or +"normal". Determines what method should be used to calculate the bootstrap confidence +intervals. See details. +Only used if method_condmean(type = "bootstrap") was specified +in the original call to draws().

    + + +
    x
    +

    a pool object generated by pool().

    + + +
    ...
    +

    not used.

    + +
    +
    +

    Details

    +

    The calculation used to generate the point estimate, standard errors and +confidence interval depends upon the method specified in the original +call to draws(); In particular:

    • method_approxbayes() & method_bayes() both use Rubin's rules to pool estimates +and variances across multiple imputed datasets, and the Barnard-Rubin rule to pool +degree's of freedom; see Little & Rubin (2002).

      • +

    • method_condmean(type = "bootstrap") uses percentile or normal approximation; +see Efron & Tibshirani (1994). Note that for the percentile bootstrap, no standard error is +calculated, i.e. the standard errors will be NA in the object / data.frame.

      • +

    • method_condmean(type = "jackknife") uses the standard jackknife variance formula; +see Efron & Tibshirani (1994).

      • +

    • method_bmlmi uses pooling procedure for Bootstrapped Maximum Likelihood MI (BMLMI). +See Von Hippel & Bartlett (2021).

      • +
    +
    +

    References

    +

    Bradley Efron and Robert J Tibshirani. An introduction to the bootstrap. CRC +press, 1994. [Section 11]

    +

    Roderick J. A. Little and Donald B. Rubin. Statistical Analysis with Missing +Data, Second Edition. John Wiley & Sons, Hoboken, New Jersey, 2002. [Section 5.4]

    +

    Von Hippel, Paul T and Bartlett, Jonathan W. +Maximum likelihood multiple imputation: Faster imputations and consistent standard +errors without posterior draws. 2021.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/pool_bootstrap_normal.html b/v1.3.1/reference/pool_bootstrap_normal.html new file mode 100644 index 000000000..b05065405 --- /dev/null +++ b/v1.3.1/reference/pool_bootstrap_normal.html @@ -0,0 +1,99 @@ + +Bootstrap Pooling via normal approximation — pool_bootstrap_normal • rbmi + Skip to contents + + +
    +
    +
    +

    Bootstrap Pooling via normal approximation

    + Source: R/pool.R +
    pool_bootstrap_normal.Rd
    +
    + +
    +

    Get point estimate, confidence interval and p-value using +the normal approximation.

    +
    + +
    +

    Usage

    + 
    pool_bootstrap_normal(est, conf.level, alternative)
    +
    + +
    +

    Arguments

    + + +
    est
    +

    a numeric vector of point estimates from each bootstrap sample.

    + + +
    conf.level
    +

    confidence level of the returned confidence interval. +Must be a single number between 0 and 1. Default is 0.95.

    + + +
    alternative
    +

    a character string specifying the alternative hypothesis, +must be one of "two.sided" (default), "greater" or "less".

    + +
    +
    +

    Details

    +

    The point estimate is taken to be the first element of est. The remaining +n-1 values of est are then used to generate the confidence intervals.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/pool_bootstrap_percentile.html b/v1.3.1/reference/pool_bootstrap_percentile.html new file mode 100644 index 000000000..d4c262969 --- /dev/null +++ b/v1.3.1/reference/pool_bootstrap_percentile.html @@ -0,0 +1,102 @@ + +Bootstrap Pooling via Percentiles — pool_bootstrap_percentile • rbmi + Skip to contents + + +
    +
    +
    +

    Bootstrap Pooling via Percentiles

    + Source: R/pool.R +
    pool_bootstrap_percentile.Rd
    +
    + +
    +

    Get point estimate, confidence interval and p-value using +percentiles. Note that quantile "type=6" is used, +see stats::quantile() for details.

    +
    + +
    +

    Usage

    + 
    pool_bootstrap_percentile(est, conf.level, alternative)
    +
    + +
    +

    Arguments

    + + +
    est
    +

    a numeric vector of point estimates from each bootstrap sample.

    + + +
    conf.level
    +

    confidence level of the returned confidence interval. +Must be a single number between 0 and 1. Default is 0.95.

    + + +
    alternative
    +

    a character string specifying the alternative hypothesis, +must be one of "two.sided" (default), "greater" or "less".

    + +
    +
    +

    Details

    +

    The point estimate is taken to be the first element of est. The remaining +n-1 values of est are then used to generate the confidence intervals.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/pool_internal.html b/v1.3.1/reference/pool_internal.html new file mode 100644 index 000000000..9652b83b7 --- /dev/null +++ b/v1.3.1/reference/pool_internal.html @@ -0,0 +1,125 @@ + +Internal Pool Methods — pool_internal • rbmi + Skip to contents + + +
    +
    +
    +

    Internal Pool Methods

    + Source: R/pool.R +
    pool_internal.Rd
    +
    + +
    +

    Dispatches pool methods based upon results object class. See +pool() for details.

    +
    + +
    +

    Usage

    + 
    pool_internal(results, conf.level, alternative, type, D)
+
+# S3 method for class 'jackknife'
+pool_internal(results, conf.level, alternative, type, D)
+
+# S3 method for class 'bootstrap'
+pool_internal(
+  results,
+  conf.level,
+  alternative,
+  type = c("percentile", "normal"),
+  D
+)
+
+# S3 method for class 'bmlmi'
+pool_internal(results, conf.level, alternative, type, D)
+
+# S3 method for class 'rubin'
+pool_internal(results, conf.level, alternative, type, D)
    +
    + +
    +

    Arguments

    + + +
    results
    +

    a list of results i.e. the x$results element of an +analyse object created by analyse()).

    + + +
    conf.level
    +

    confidence level of the returned confidence interval. +Must be a single number between 0 and 1. Default is 0.95.

    + + +
    alternative
    +

    a character string specifying the alternative hypothesis, +must be one of "two.sided" (default), "greater" or "less".

    + + +
    type
    +

    a character string of either "percentile" (default) or +"normal". Determines what method should be used to calculate the bootstrap confidence +intervals. See details. +Only used if method_condmean(type = "bootstrap") was specified +in the original call to draws().

    + + +
    D
    +

    numeric representing the number of imputations between each bootstrap sample in the BMLMI method.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/prepare_stan_data.html b/v1.3.1/reference/prepare_stan_data.html new file mode 100644 index 000000000..e760b6443 --- /dev/null +++ b/v1.3.1/reference/prepare_stan_data.html @@ -0,0 +1,121 @@ + +Prepare input data to run the Stan model — prepare_stan_data • rbmi + Skip to contents + + +
    +
    +
    +

    Prepare input data to run the Stan model

    + Source: R/mcmc.R +
    prepare_stan_data.Rd
    +
    + +
    +

    Prepare input data to run the Stan model. +Creates / calculates all the required inputs as required by the data{} block of the MMRM Stan program.

    +
    + +
    +

    Usage

    + 
    prepare_stan_data(ddat, subjid, visit, outcome, group)
    +
    + +
    +

    Arguments

    + + +
    ddat
    +

    A design matrix

    + + +
    subjid
    +

    Character vector containing the subjects IDs.

    + + +
    visit
    +

    Vector containing the visits.

    + + +
    outcome
    +

    Numeric vector containing the outcome variable.

    + + +
    group
    +

    Vector containing the group variable.

    + +
    +
    +

    Value

    +

    A stan_data object. A named list as per data{} block of the related Stan file. In particular it returns:

    • N - The number of rows in the design matrix

      • +

    • P - The number of columns in the design matrix

      • +

    • G - The number of distinct covariance matrix groups (i.e. length(unique(group)))

      • +

    • n_visit - The number of unique outcome visits

      • +

    • n_pat - The total number of pattern groups (as defined by missingness patterns & covariance group)

      • +

    • pat_G - Index for which Sigma each pattern group should use

      • +

    • pat_n_pt - number of patients within each pattern group

      • +

    • pat_n_visit - number of non-missing visits in each pattern group

      • +

    • pat_sigma_index - rows/cols from Sigma to subset on for the pattern group (padded by 0's)

      • +

    • y - The outcome variable

      • +

    • Q - design matrix (after QR decomposition)

      • +

    • R - R matrix from the QR decomposition of the design matrix

      • +
    +
    +

    Details

    + +

    • The group argument determines which covariance matrix group the subject belongs to. If you +want all subjects to use a shared covariance matrix then set group to "1" for everyone.

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/print.analysis.html b/v1.3.1/reference/print.analysis.html new file mode 100644 index 000000000..ee3f1096e --- /dev/null +++ b/v1.3.1/reference/print.analysis.html @@ -0,0 +1,86 @@ + +Print analysis object — print.analysis • rbmi + Skip to contents + + +
    +
    +
    +

    Print analysis object

    + Source: R/analyse.R +
    print.analysis.Rd
    +
    + +
    +

    Print analysis object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'analysis'
+print(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    An analysis object generated by analyse().

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/print.draws.html b/v1.3.1/reference/print.draws.html new file mode 100644 index 000000000..9ab7d0e8e --- /dev/null +++ b/v1.3.1/reference/print.draws.html @@ -0,0 +1,86 @@ + +Print draws object — print.draws • rbmi + Skip to contents + + +
    +
    +
    +

    Print draws object

    + Source: R/draws.R +
    print.draws.Rd
    +
    + +
    +

    Print draws object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'draws'
+print(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    A draws object generated by draws().

    + + +
    ...
    +

    not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/print.imputation.html b/v1.3.1/reference/print.imputation.html new file mode 100644 index 000000000..4f5a89be6 --- /dev/null +++ b/v1.3.1/reference/print.imputation.html @@ -0,0 +1,86 @@ + +Print imputation object — print.imputation • rbmi + Skip to contents + + +
    +
    +
    +

    Print imputation object

    + Source: R/impute.R +
    print.imputation.Rd
    +
    + +
    +

    Print imputation object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'imputation'
+print(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    An imputation object generated by impute().

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/progressLogger.html b/v1.3.1/reference/progressLogger.html new file mode 100644 index 000000000..66424d711 --- /dev/null +++ b/v1.3.1/reference/progressLogger.html @@ -0,0 +1,188 @@ + +R6 Class for printing current sampling progress — progressLogger • rbmi + Skip to contents + + +
    +
    +
    +

    R6 Class for printing current sampling progress

    + Source: R/draws.R +
    progressLogger.Rd
    +
    + +
    +

    Object is initalised with total number of iterations that are expected to occur. +User can then update the object with the add method to indicate how many more iterations +have just occurred. +Every time step * 100 % of iterations have occurred a message is printed to the console. +Use the quiet argument to prevent the object from printing anything at all

    +
    + + +
    +

    Public fields

    +

    step
    +

    real, percentage of iterations to allow before printing the +progress to the console

    + + +
    step_current
    +

    integer, the total number of iterations completed since +progress was last printed to the console

    + + +
    n
    +

    integer, the current number of completed iterations

    + + +
    n_max
    +

    integer, total number of expected iterations to be completed +acts as the denominator for calculating progress percentages

    + + +
    quiet
    +

    logical holds whether or not to print anything

    + + +

    +
    +
    +

    Methods

    + +
    +

    Public methods

    + +

    +

    Method new()

    +

    Create progressLogger object

    +

    Usage

    +

    progressLogger$new(n_max, quiet = FALSE, step = 0.1)

    +
    + +
    +

    Arguments

    +

    n_max
    +

    integer, sets field n_max

    + + +
    quiet
    +

    logical, sets field quiet

    + + +
    step
    +

    real, sets field step

    + + +

    +
    + +

    +

    Method add()

    +

    Records that n more iterations have been completed +this will add that number to the current step count (step_current) and will +print a progress message to the log if the step limit (step) has been reached. +This function will do nothing if quiet has been set to TRUE

    +

    Usage

    +

    progressLogger$add(n)

    +
    + +
    +

    Arguments

    +

    n
    +

    the number of successfully complete iterations since add() was last called

    + + +

    +
    + +

    +

    Method print_progress()

    +

    method to print the current state of progress

    +

    Usage

    +

    progressLogger$print_progress()

    +
    + + +

    +

    Method clone()

    +

    The objects of this class are cloneable with this method.

    +

    Usage

    +

    progressLogger$clone(deep = FALSE)

    +
    + +
    +

    Arguments

    +

    deep
    +

    Whether to make a deep clone.

    + + +

    +
    + +
    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/pval_percentile.html b/v1.3.1/reference/pval_percentile.html new file mode 100644 index 000000000..a2f23d2fb --- /dev/null +++ b/v1.3.1/reference/pval_percentile.html @@ -0,0 +1,96 @@ + +P-value of percentile bootstrap — pval_percentile • rbmi + Skip to contents + + +
    +
    +
    +

    P-value of percentile bootstrap

    + Source: R/pool.R +
    pval_percentile.Rd
    +
    + +
    +

    Determines the (not necessarily unique) quantile (type=6) of "est" which gives a value of 0 +From this, derive the p-value corresponding to the percentile bootstrap via inversion.

    +
    + +
    +

    Usage

    + 
    pval_percentile(est)
    +
    + +
    +

    Arguments

    + + +
    est
    +

    a numeric vector of point estimates from each bootstrap sample.

    + +
    +
    +

    Value

    +

    A named numeric vector of length 2 containing the p-value for H_0: theta=0 vs H_A: theta>0 +("pval_greater") and the p-value for H_0: theta=0 vs H_A: theta<0 ("pval_less").

    +
    +
    +

    Details

    +

    The p-value for H_0: theta=0 vs H_A: theta>0 is the value alpha for which q_alpha = 0. +If there is at least one estimate equal to zero it returns the largest alpha such that q_alpha = 0. +If all bootstrap estimates are > 0 it returns 0; if all bootstrap estimates are < 0 it returns 1. Analogous +reasoning is applied for the p-value for H_0: theta=0 vs H_A: theta<0.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/random_effects_expr.html b/v1.3.1/reference/random_effects_expr.html new file mode 100644 index 000000000..c4061891f --- /dev/null +++ b/v1.3.1/reference/random_effects_expr.html @@ -0,0 +1,101 @@ + +Construct random effects formula — random_effects_expr • rbmi + Skip to contents + + +
    +
    +
    +

    Construct random effects formula

    + Source: R/mmrm.R +
    random_effects_expr.Rd
    +
    + +
    +

    Constructs a character representation of the random effects formula +for fitting a MMRM for subject by visit in the format required for mmrm::mmrm().

    +
    + +
    +

    Usage

    + 
    random_effects_expr(
+  cov_struct = c("us", "ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", "toeph"),
+  cov_by_group = FALSE
+)
    +
    + +
    +

    Arguments

    + + +
    cov_struct
    +

    Character - The covariance structure to be used, must be one of "us" (default), +"ad", "adh", "ar1", "ar1h", "cs", "csh", "toep", or "toeph")

    + + +
    cov_by_group
    +

    Boolean - Whenever or not to use separate covariances per each group level

    + +
    +
    +

    Details

    +

    For example assuming the user specified a covariance structure of "us" and that no groups +were provided this will return

    +

    us(visit | subjid)

    +

    If cov_by_group is set to FALSE then this indicates that separate covariance matrices +are required per group and as such the following will be returned:

    +

    us( visit | group / subjid )

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/rbmi-package.html b/v1.3.1/reference/rbmi-package.html new file mode 100644 index 000000000..ea594d24a --- /dev/null +++ b/v1.3.1/reference/rbmi-package.html @@ -0,0 +1,114 @@ + +rbmi: Reference Based Multiple Imputation — rbmi-package • rbmi + Skip to contents + + +
    +
    +
    +

    rbmi: Reference Based Multiple Imputation

    + Source: R/rbmi.R +
    rbmi-package.Rd
    +
    + +
    +

    The rbmi package is used to perform reference based multiple imputation. The package +provides implementations for common, patient-specific imputation strategies whilst allowing the user to +select between various standard Bayesian and frequentist approaches.

    +

    The package is designed around 4 core functions:

    • draws() - Fits multiple imputation models

      • +

    • impute() - Imputes multiple datasets

      • +

    • analyse() - Analyses multiple datasets

      • +

    • pool() - Pools multiple results into a single statistic

      • +

    To learn more about rbmi, please see the quickstart vignette:

    +

    vignette(topic= "quickstart", package = "rbmi")

    +
    + + +
    +

    See also

    +

    Useful links:

    +
    +
    +

    Author

    +

    Maintainer: Craig Gower-Page craig.gower-page@roche.com

    +

    Authors:

    Other contributors:

    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/rbmi-settings.html b/v1.3.1/reference/rbmi-settings.html new file mode 100644 index 000000000..6101aea52 --- /dev/null +++ b/v1.3.1/reference/rbmi-settings.html @@ -0,0 +1,112 @@ + +rbmi settings — rbmi-settings • rbmi + Skip to contents + + +
    +
    +
    +

    rbmi settings

    + Source: R/utilities.R +
    rbmi-settings.Rd
    +
    + +
    +

    Define settings that modify the behaviour of the rbmi package

    +

    Each of the following are the name of options that can be set via:

    +

    options(<option_name> = <value>)

    +

    rbmi.cache_dir

    + + +

    Default = tools::R_user_dir("rbmi", which = "cache")

    +

    Directory to store compiled Stan model in. If not set, a temporary directory is used for +the given R session. Can also be set via the environment variable RBMI_CACHE_DIR.

    +
    + +
    + +
    +

    Usage

    + 
    set_options()
    +
    + + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+options(rbmi.cache_dir = "some/directory/path")
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/record.html b/v1.3.1/reference/record.html new file mode 100644 index 000000000..55e7fcfdc --- /dev/null +++ b/v1.3.1/reference/record.html @@ -0,0 +1,107 @@ + +Capture all Output — record • rbmi + Skip to contents + + +
    +
    +
    +

    Capture all Output

    + Source: R/utilities.R +
    record.Rd
    +
    + +
    +

    This function silences all warnings, errors & messages and instead returns a list +containing the results (if it didn't error) + the warning and error messages as +character vectors.

    +
    + +
    +

    Usage

    + 
    record(expr)
    +
    + +
    +

    Arguments

    + + +
    expr
    +

    An expression to be executed

    + +
    +
    +

    Value

    +

    A list containing

    • results - The object returned by expr or list() if an error was thrown

      • +

    • warnings - NULL or a character vector if warnings were thrown

      • +

    • errors - NULL or a string if an error was thrown

      • +

    • messages - NULL or a character vector if messages were produced

      • +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+record({
+  x <- 1
+  y <- 2
+  warning("something went wrong")
+  message("O nearly done")
+  x + y
+})
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/recursive_reduce.html b/v1.3.1/reference/recursive_reduce.html new file mode 100644 index 000000000..5907d61f2 --- /dev/null +++ b/v1.3.1/reference/recursive_reduce.html @@ -0,0 +1,89 @@ + +recursive_reduce — recursive_reduce • rbmi + Skip to contents + + +
    +
    +
    +

    recursive_reduce

    + Source: R/as_ascii_table.R +
    recursive_reduce.Rd
    +
    + +
    +

    Utility function used to replicated purrr::reduce. Recursively applies a +function to a list of elements until only 1 element remains

    +
    + +
    +

    Usage

    + 
    recursive_reduce(.l, .f)
    +
    + +
    +

    Arguments

    + + +
    .l
    +

    list of values to apply a function to

    + + +
    .f
    +

    function to apply to each each element of the list in turn +i.e. .l[[1]] <- .f( .l[[1]] , .l[[2]]) ; .l[[1]] <- .f( .l[[1]] , .l[[3]])

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/remove_if_all_missing.html b/v1.3.1/reference/remove_if_all_missing.html new file mode 100644 index 000000000..e2fa00ec0 --- /dev/null +++ b/v1.3.1/reference/remove_if_all_missing.html @@ -0,0 +1,87 @@ + +Remove subjects from dataset if they have no observed values — remove_if_all_missing • rbmi + Skip to contents + + +
    +
    +
    +

    Remove subjects from dataset if they have no observed values

    + Source: R/mcmc.R +
    remove_if_all_missing.Rd
    +
    + +
    +

    This function takes a data.frame with variables visit, outcome & subjid. +It then removes all rows for a given subjid if they don't have any non-missing +values for outcome.

    +
    + +
    +

    Usage

    + 
    remove_if_all_missing(dat)
    +
    + +
    +

    Arguments

    + + +
    dat
    +

    a data.frame

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/rubin_df.html b/v1.3.1/reference/rubin_df.html new file mode 100644 index 000000000..cfc5d3116 --- /dev/null +++ b/v1.3.1/reference/rubin_df.html @@ -0,0 +1,108 @@ + +Barnard and Rubin degrees of freedom adjustment — rubin_df • rbmi + Skip to contents + + +
    +
    +
    +

    Barnard and Rubin degrees of freedom adjustment

    + Source: R/pool.R +
    rubin_df.Rd
    +
    + +
    +

    Compute degrees of freedom according to the Barnard-Rubin formula.

    +
    + +
    +

    Usage

    + 
    rubin_df(v_com, var_b, var_t, M)
    +
    + +
    +

    Arguments

    + + +
    v_com
    +

    Positive number representing the degrees of freedom in the complete-data analysis.

    + + +
    var_b
    +

    Between-variance of point estimate across multiply imputed datasets.

    + + +
    var_t
    +

    Total-variance of point estimate according to Rubin's rules.

    + + +
    M
    +

    Number of imputations.

    + +
    +
    +

    Value

    +

    Degrees of freedom according to Barnard-Rubin formula. See Barnard-Rubin (1999).

    +
    +
    +

    Details

    +

    The computation takes into account limit cases where there is no missing data +(i.e. the between-variance var_b is zero) or where the complete-data degrees of freedom is +set to Inf. Moreover, if v_com is given as NA, the function returns Inf.

    +
    +
    +

    References

    +

    Barnard, J. and Rubin, D.B. (1999). +Small sample degrees of freedom with multiple imputation. Biometrika, 86, 948-955.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/rubin_rules.html b/v1.3.1/reference/rubin_rules.html new file mode 100644 index 000000000..96444d60d --- /dev/null +++ b/v1.3.1/reference/rubin_rules.html @@ -0,0 +1,116 @@ + +Combine estimates using Rubin's rules — rubin_rules • rbmi + Skip to contents + + +
    +
    +
    +

    Combine estimates using Rubin's rules

    + Source: R/pool.R +
    rubin_rules.Rd
    +
    + +
    +

    Pool together the results from M complete-data analyses according to Rubin's rules. See details.

    +
    + +
    +

    Usage

    + 
    rubin_rules(ests, ses, v_com)
    +
    + +
    +

    Arguments

    + + +
    ests
    +

    Numeric vector containing the point estimates from the complete-data analyses.

    + + +
    ses
    +

    Numeric vector containing the standard errors from the complete-data analyses.

    + + +
    v_com
    +

    Positive number representing the degrees of freedom in the complete-data analysis.

    + +
    +
    +

    Value

    +

    A list containing:

    • est_point: the pooled point estimate according to Little-Rubin (2002).

      • +

    • var_t: total variance according to Little-Rubin (2002).

      • +

    • df: degrees of freedom according to Barnard-Rubin (1999).

      • +
    +
    +

    Details

    +

    rubin_rules applies Rubin's rules (Rubin, 1987) for pooling together +the results from a multiple imputation procedure. The pooled point estimate est_point is +is the average across the point estimates from the complete-data analyses (given by the input argument ests). +The total variance var_t is the sum of two terms representing the within-variance +and the between-variance (see Little-Rubin (2002)). The function +also returns df, the estimated pooled degrees of freedom according to Barnard-Rubin (1999) +that can be used for inference based on the t-distribution.

    +
    +
    +

    References

    +

    Barnard, J. and Rubin, D.B. (1999). +Small sample degrees of freedom with multiple imputation. Biometrika, 86, 948-955

    +

    Roderick J. A. Little and Donald B. Rubin. Statistical Analysis with Missing +Data, Second Edition. John Wiley & Sons, Hoboken, New Jersey, 2002. [Section 5.4]

    +
    +
    +

    See also

    +

    rubin_df() for the degrees of freedom estimation.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/sample_ids.html b/v1.3.1/reference/sample_ids.html new file mode 100644 index 000000000..0359d587b --- /dev/null +++ b/v1.3.1/reference/sample_ids.html @@ -0,0 +1,96 @@ + +Sample Patient Ids — sample_ids • rbmi + Skip to contents + + +
    +
    +
    +

    Sample Patient Ids

    + Source: R/bootstrap.R +
    sample_ids.Rd
    +
    + +
    +

    Performs a stratified bootstrap sample of IDS +ensuring the return vector is the same length as the input vector

    +
    + +
    +

    Usage

    + 
    sample_ids(ids, strata = rep(1, length(ids)))
    +
    + +
    +

    Arguments

    + + +
    ids
    +

    vector to sample from

    + + +
    strata
    +

    strata indicator, ids are sampled within each strata +ensuring the that the numbers of each strata are maintained

    + +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+sample_ids( c("a", "b", "c", "d"), strata = c(1,1,2,2))
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/sample_list.html b/v1.3.1/reference/sample_list.html new file mode 100644 index 000000000..e9ba0ffc7 --- /dev/null +++ b/v1.3.1/reference/sample_list.html @@ -0,0 +1,84 @@ + +Create and validate a sample_list object — sample_list • rbmi + Skip to contents + + +
    +
    +
    +

    Create and validate a sample_list object

    + Source: R/dataclasses.R +
    sample_list.Rd
    +
    + +
    +

    Given a list of sample_single objects generate by sample_single(), +creates a sample_list objects and validate it.

    +
    + +
    +

    Usage

    + 
    sample_list(...)
    +
    + +
    +

    Arguments

    + + +
    ...
    +

    A list of sample_single objects.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/sample_mvnorm.html b/v1.3.1/reference/sample_mvnorm.html new file mode 100644 index 000000000..eb1d171f3 --- /dev/null +++ b/v1.3.1/reference/sample_mvnorm.html @@ -0,0 +1,89 @@ + +Sample random values from the multivariate normal distribution — sample_mvnorm • rbmi + Skip to contents + + +
    +
    +
    +

    Sample random values from the multivariate normal distribution

    + Source: R/utilities.R +
    sample_mvnorm.Rd
    +
    + +
    +

    Sample random values from the multivariate normal distribution

    +
    + +
    +

    Usage

    + 
    sample_mvnorm(mu, sigma)
    +
    + +
    +

    Arguments

    + + +
    mu
    +

    mean vector

    + + +
    sigma
    +

    covariance matrix

    +

    Samples multivariate normal variables by multiplying +univariate random normal variables by the cholesky +decomposition of the covariance matrix.

    +

    If mu is length 1 then just uses rnorm instead.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/sample_single.html b/v1.3.1/reference/sample_single.html new file mode 100644 index 000000000..1c4f615b4 --- /dev/null +++ b/v1.3.1/reference/sample_single.html @@ -0,0 +1,120 @@ + +Create object of sample_single class — sample_single • rbmi + Skip to contents + + +
    +
    +
    +

    Create object of sample_single class

    + Source: R/dataclasses.R +
    sample_single.Rd
    +
    + +
    +

    Creates an object of class sample_single which is a named list +containing the input parameters and validate them.

    +
    + +
    +

    Usage

    + 
    sample_single(
+  ids,
+  beta = NA,
+  sigma = NA,
+  theta = NA,
+  failed = any(is.na(beta)),
+  ids_samp = ids
+)
    +
    + +
    +

    Arguments

    + + +
    ids
    +

    Vector of characters containing the ids of the subjects included in the original dataset.

    + + +
    beta
    +

    Numeric vector of estimated regression coefficients.

    + + +
    sigma
    +

    List of estimated covariance matrices (one for each level of vars$group).

    + + +
    theta
    +

    Numeric vector of transformed covariances.

    + + +
    failed
    +

    Logical. TRUE if the model fit failed.

    + + +
    ids_samp
    +

    Vector of characters containing the ids of the subjects included in the given sample.

    + +
    +
    +

    Value

    +

    A named list of class sample_single. It contains the following:

    • ids vector of characters containing the ids of the subjects included in the original dataset.

      • +

    • beta numeric vector of estimated regression coefficients.

      • +

    • sigma list of estimated covariance matrices (one for each level of vars$group).

      • +

    • theta numeric vector of transformed covariances.

      • +

    • failed logical. TRUE if the model fit failed.

      • +

    • ids_samp vector of characters containing the ids of the subjects included in the given sample.

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/scalerConstructor.html b/v1.3.1/reference/scalerConstructor.html new file mode 100644 index 000000000..ffa559a93 --- /dev/null +++ b/v1.3.1/reference/scalerConstructor.html @@ -0,0 +1,218 @@ + +R6 Class for scaling (and un-scaling) design matrices — scalerConstructor • rbmi + Skip to contents + + +
    +
    +
    +

    R6 Class for scaling (and un-scaling) design matrices

    + Source: R/scaling.R +
    scalerConstructor.Rd
    +
    + +
    +

    Scales a design matrix so that all non-categorical columns have a mean +of 0 and an standard deviation of 1.

    +
    + + +
    +

    Details

    +

    The object initialisation +is used to determine the relevant mean and SD's to scale by and then +the scaling (and un-scaling) itself is performed by the relevant object +methods.

    +

    Un-scaling is done on linear model Beta and Sigma coefficients. For this purpose +the first column on the dataset to be scaled is assumed to be the outcome variable +with all other variables assumed to be post-transformation predictor variables (i.e. +all dummy variables have already been expanded).

    +
    +
    +

    Public fields

    +

    centre
    +

    Vector of column means. The first value is the outcome +variable, all other variables are the predictors.

    + + +
    scales
    +

    Vector of column standard deviations. The first value is the outcome +variable, all other variables are the predictors.

    + + +

    +
    +
    +

    Methods

    + +
    +

    Public methods

    + +

    +

    Method new()

    +

    Uses dat to determine the relevant column means and standard deviations to use +when scaling and un-scaling future datasets. Implicitly assumes that new datasets +have the same column order as dat

    +

    Usage

    +

    scalerConstructor$new(dat)

    +
    + +
    +

    Arguments

    +

    dat
    +

    A data.frame or matrix. All columns must be numeric (i.e dummy variables, +must have already been expanded out).

    + + +

    +
    +
    +

    Details

    +

    Categorical columns (as determined by those who's values are entirely 1 or 0) +will not be scaled. This is achieved by setting the corresponding values of centre +to 0 and scale to 1.

    +
    + + +

    +

    Method scale()

    +

    Scales a dataset so that all continuous variables have a mean of 0 and a +standard deviation of 1.

    +

    Usage

    +

    scalerConstructor$scale(dat)

    +
    + +
    +

    Arguments

    +

    dat
    +

    A data.frame or matrix whose columns are all numeric (i.e. dummy +variables have all been expanded out) and whose columns are in the same +order as the dataset used in the initialization function.

    + + +

    +
    + +

    +

    Method unscale_sigma()

    +

    Unscales a sigma value (or matrix) as estimated by a linear model +using a design matrix scaled by this object. This function only +works if the first column of the initialisation data.frame was the outcome +variable.

    +

    Usage

    +

    scalerConstructor$unscale_sigma(sigma)

    +
    + +
    +

    Arguments

    +

    sigma
    +

    A numeric value or matrix.

    + + +

    +
    +
    +

    Returns

    +

    A numeric value or matrix

    +
    + +

    +

    Method unscale_beta()

    +

    Unscales a beta value (or vector) as estimated by a linear model +using a design matrix scaled by this object. This function only +works if the first column of the initialization data.frame was the outcome +variable.

    +

    Usage

    +

    scalerConstructor$unscale_beta(beta)

    +
    + +
    +

    Arguments

    +

    beta
    +

    A numeric vector of beta coefficients as estimated from a linear model.

    + + +

    +
    +
    +

    Returns

    +

    A numeric vector.

    +
    + +

    +

    Method clone()

    +

    The objects of this class are cloneable with this method.

    +

    Usage

    +

    scalerConstructor$clone(deep = FALSE)

    +
    + +
    +

    Arguments

    +

    deep
    +

    Whether to make a deep clone.

    + + +

    +
    + +
    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/set_simul_pars.html b/v1.3.1/reference/set_simul_pars.html new file mode 100644 index 000000000..95e8dc3a2 --- /dev/null +++ b/v1.3.1/reference/set_simul_pars.html @@ -0,0 +1,165 @@ + +Set simulation parameters of a study group. — set_simul_pars • rbmi + Skip to contents + + +
    +
    +
    +

    Set simulation parameters of a study group.

    + Source: R/simulate_data.R +
    set_simul_pars.Rd
    +
    + +
    +

    This function provides input arguments for each study group needed to +simulate data with simulate_data(). simulate_data() generates data for a two-arms +clinical trial with longitudinal continuous outcomes and two intercurrent events (ICEs). +ICE1 may be thought of as a discontinuation from study treatment due to study drug or +condition related (SDCR) reasons. ICE2 may be thought of as discontinuation from study +treatment due to uninformative study drop-out, i.e. due to not study drug or +condition related (NSDRC) reasons and outcome data after ICE2 is always missing.

    +
    + +
    +

    Usage

    + 
    set_simul_pars(
+  mu,
+  sigma,
+  n,
+  prob_ice1 = 0,
+  or_outcome_ice1 = 1,
+  prob_post_ice1_dropout = 0,
+  prob_ice2 = 0,
+  prob_miss = 0
+)
    +
    + +
    +

    Arguments

    + + +
    mu
    +

    Numeric vector describing the mean outcome trajectory at each visit (including +baseline) assuming no ICEs.

    + + +
    sigma
    +

    Covariance matrix of the outcome trajectory assuming no ICEs.

    + + +
    n
    +

    Number of subjects belonging to the group.

    + + +
    prob_ice1
    +

    Numeric vector that specifies the probability of experiencing ICE1 +(discontinuation from study treatment due to SDCR reasons) after each visit for a subject +with observed outcome at that visit equal to the mean at baseline (mu[1]). +If a single numeric is provided, then the same probability is applied to each visit.

    + + +
    or_outcome_ice1
    +

    Numeric value that specifies the odds ratio of experiencing ICE1 after +each visit corresponding to a +1 higher value of the observed outcome at that visit.

    + + +
    prob_post_ice1_dropout
    +

    Numeric value that specifies the probability of study +drop-out following ICE1. If a subject is simulated to drop-out after ICE1, all outcomes after +ICE1 are set to missing.

    + + +
    prob_ice2
    +

    Numeric that specifies an additional probability that a post-baseline +visit is affected by study drop-out. Outcome data at the subject's first simulated visit +affected by study drop-out and all subsequent visits are set to missing. This generates +a second intercurrent event ICE2, which may be thought as treatment discontinuation due to +NSDRC reasons with subsequent drop-out. +If for a subject, both ICE1 and ICE2 are simulated to occur, +then it is assumed that only the earlier of them counts. +In case both ICEs are simulated to occur at the same time, it is assumed that ICE1 counts. +This means that a single subject can experience either ICE1 or ICE2, but not both of them.

    + + +
    prob_miss
    +

    Numeric value that specifies an additional probability for a given +post-baseline observation to be missing. This can be used to produce +"intermittent" missing values which are not associated with any ICE.

    + +
    +
    +

    Value

    +

    A simul_pars object which is a named list containing the simulation parameters.

    +
    +
    +

    Details

    +

    For the details, please see simulate_data().

    +
    +
    +

    See also

    +

    simulate_data()

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/set_vars.html b/v1.3.1/reference/set_vars.html new file mode 100644 index 000000000..10f695898 --- /dev/null +++ b/v1.3.1/reference/set_vars.html @@ -0,0 +1,155 @@ + +Set key variables — set_vars • rbmi + Skip to contents + + +
    +
    +
    +

    Set key variables

    + Source: R/utilities.R +
    set_vars.Rd
    +
    + +
    +

    This function is used to define the names of key variables within the data.frame's +that are provided as input arguments to draws() and ancova().

    +
    + +
    +

    Usage

    + 
    set_vars(
+  subjid = "subjid",
+  visit = "visit",
+  outcome = "outcome",
+  group = "group",
+  covariates = character(0),
+  strata = group,
+  strategy = "strategy"
+)
    +
    + +
    +

    Arguments

    + + +
    subjid
    +

    The name of the "Subject ID" variable. A length 1 character vector.

    + + +
    visit
    +

    The name of the "Visit" variable. A length 1 character vector.

    + + +
    outcome
    +

    The name of the "Outcome" variable. A length 1 character vector.

    + + +
    group
    +

    The name of the "Group" variable. A length 1 character vector.

    + + +
    covariates
    +

    The name of any covariates to be used in the context of modeling. +See details.

    + + +
    strata
    +

    The name of the any stratification variable to be used in the context of bootstrap +sampling. See details.

    + + +
    strategy
    +

    The name of the "strategy" variable. A length 1 character vector.

    + +
    +
    +

    Details

    +

    In both draws() and ancova() the covariates argument can be specified to indicate +which variables should be included in the imputation and analysis models respectively. If you wish +to include interaction terms these need to be manually specified i.e. +covariates = c("group*visit", "age*sex"). Please note that the use of the I() function to +inhibit the interpretation/conversion of objects is not supported.

    +

    Currently strata is only used by draws() in combination with method_condmean(type = "bootstrap") +and method_approxbayes() in order to allow for the specification of stratified bootstrap sampling. +By default strata is set equal to the value of group as it is assumed most users will want to +preserve the group size between samples. See draws() for more details.

    +

    Likewise, currently the strategy argument is only used by draws() to specify the name of the +strategy variable within the data_ice data.frame. See draws() for more details.

    +
    +
    +

    See also

    +

    draws()

    +

    ancova()

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+
+# Using CDISC variable names as an example
+set_vars(
+    subjid = "usubjid",
+    visit = "avisit",
+    outcome = "aval",
+    group = "arm",
+    covariates = c("bwt", "bht", "arm * avisit"),
+    strategy = "strat"
+)
+
+} # }
+
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/simulate_data.html b/v1.3.1/reference/simulate_data.html new file mode 100644 index 000000000..8b7f70de6 --- /dev/null +++ b/v1.3.1/reference/simulate_data.html @@ -0,0 +1,181 @@ + +Generate data — simulate_data • rbmi + Skip to contents + + +
    +
    +
    +

    Generate data

    + Source: R/simulate_data.R +
    simulate_data.Rd
    +
    + +
    +

    Generate data for a two-arms clinical trial with longitudinal continuous +outcome and two intercurrent events (ICEs). +ICE1 may be thought of as a discontinuation from study treatment due to study drug or +condition related (SDCR) reasons. +ICE2 may be thought of as discontinuation from study treatment due to uninformative +study drop-out, i.e. due to not study drug or +condition related (NSDRC) reasons and outcome data after ICE2 is always missing.

    +
    + +
    +

    Usage

    + 
    simulate_data(pars_c, pars_t, post_ice1_traj, strategies = getStrategies())
    +
    + +
    +

    Arguments

    + + +
    pars_c
    +

    A simul_pars object as generated by set_simul_pars(). It specifies +the simulation parameters of the control arm.

    + + +
    pars_t
    +

    A simul_pars object as generated by set_simul_pars(). It specifies +the simulation parameters of the treatment arm.

    + + +
    post_ice1_traj
    +

    A string which specifies how observed outcomes occurring after +ICE1 are simulated. +Must target a function included in strategies. Possible choices are: Missing At +Random "MAR", Jump to Reference "JR", +Copy Reference "CR", Copy Increments in Reference "CIR", Last Mean Carried +Forward "LMCF". User-defined strategies +could also be added. See getStrategies() for details.

    + + +
    strategies
    +

    A named list of functions. Default equal to getStrategies(). +See getStrategies() for details.

    + +
    +
    +

    Value

    +

    A data.frame containing the simulated data. It includes the following variables:

    • id: Factor variable that specifies the id of each subject.

      • +

    • visit: Factor variable that specifies the visit of each assessment. Visit 0 denotes +the baseline visit.

      • +

    • group: Factor variable that specifies which treatment group each subject belongs to.

      • +

    • outcome_bl: Numeric variable that specifies the baseline outcome.

      • +

    • outcome_noICE: Numeric variable that specifies the longitudinal outcome assuming +no ICEs.

      • +

    • ind_ice1: Binary variable that takes value 1 if the corresponding visit is +affected by ICE1 and 0 otherwise.

      • +

    • dropout_ice1: Binary variable that takes value 1 if the corresponding visit is +affected by the drop-out following ICE1 and 0 otherwise.

      • +

    • ind_ice2: Binary variable that takes value 1 if the corresponding visit is affected +by ICE2.

      • +

    • outcome: Numeric variable that specifies the longitudinal outcome including ICE1, ICE2 +and the intermittent missing values.

      • +
    +
    +

    Details

    +

    The data generation works as follows:

    • Generate outcome data for all visits (including baseline) from a multivariate +normal distribution with parameters pars_c$mu and pars_c$sigma +for the control arm and parameters pars_t$mu and pars_t$sigma for the treatment +arm, respectively. +Note that for a randomized trial, outcomes have the same distribution at baseline +in both treatment groups, i.e. one should set +pars_c$mu[1]=pars_t$mu[1] and pars_c$sigma[1,1]=pars_t$sigma[1,1].

      • +

    • Simulate whether ICE1 (study treatment discontinuation due to SDCR reasons) occurs +after each visit according to parameters pars_c$prob_ice1 and pars_c$or_outcome_ice1 +for the control arm and pars_t$prob_ice1 and pars_t$or_outcome_ice1 for the +treatment arm, respectively.

      • +

    • Simulate drop-out following ICE1 according to pars_c$prob_post_ice1_dropout and +pars_t$prob_post_ice1_dropout.

      • +

    • Simulate an additional uninformative study drop-out with probabilities pars_c$prob_ice2 +and pars_t$prob_ice2 at each visit. This generates a second intercurrent event ICE2, which +may be thought as treatment discontinuation due to NSDRC reasons with subsequent drop-out. +The simulated time of drop-out is the subject's first visit which is affected by +drop-out and data from this visit and all subsequent visits are consequently set to missing. +If for a subject, both ICE1 and ICE2 are simulated to occur, +then it is assumed that only the earlier of them counts. +In case both ICEs are simulated to occur at the same time, it is assumed that ICE1 counts. +This means that a single subject can experience either ICE1 or ICE2, but not both of them.

      • +

    • Adjust trajectories after ICE1 according to the given assumption expressed with +the post_ice1_traj argument. Note that only post-ICE1 outcomes in the intervention arm can be +adjusted. Post-ICE1 outcomes from the control arm are not adjusted.

      • +

    • Simulate additional intermittent missing outcome data as per arguments pars_c$prob_miss +and pars_t$prob_miss.

      • +

    The probability of the ICE after each visit is modeled according to the following +logistic regression model: +~ 1 + I(visit == 0) + ... + I(visit == n_visits-1) + I((x-alpha)) where:

    • n_visits is the number of visits (including baseline).

      • +

    • alpha is the baseline outcome mean. +The term I((x-alpha)) specifies the dependency of the probability of the ICE on +the current outcome value. +The corresponding regression coefficients of the logistic model are defined as follows: +The intercept is set to 0, the coefficients corresponding to discontinuation after +each visit for a subject with outcome equal to +the mean at baseline are set according to parameters pars_c$prob_ice1 (pars_t$prob_ice1), +and the regression coefficient associated with the covariate I((x-alpha)) is set +to log(pars_c$or_outcome_ice1) (log(pars_t$or_outcome_ice1)).

      • +

    Please note that the baseline outcome cannot be missing nor be affected by any ICEs.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/simulate_dropout.html b/v1.3.1/reference/simulate_dropout.html new file mode 100644 index 000000000..cb07abd30 --- /dev/null +++ b/v1.3.1/reference/simulate_dropout.html @@ -0,0 +1,108 @@ + +Simulate drop-out — simulate_dropout • rbmi + Skip to contents + + +
    +
    +
    +

    Simulate drop-out

    + Source: R/simulate_data.R +
    simulate_dropout.Rd
    +
    + +
    +

    Simulate drop-out

    +
    + +
    +

    Usage

    + 
    simulate_dropout(prob_dropout, ids, subset = rep(1, length(ids)))
    +
    + +
    +

    Arguments

    + + +
    prob_dropout
    +

    Numeric that specifies the probability that a post-baseline visit is +affected by study drop-out.

    + + +
    ids
    +

    Factor variable that specifies the id of each subject.

    + + +
    subset
    +

    Binary variable that specifies the subset that could be affected by drop-out. +I.e. subset is a binary vector +of length equal to the length of ids that takes value 1 if the corresponding visit could +be affected by drop-out and 0 otherwise.

    + +
    +
    +

    Value

    +

    A binary vector of length equal to the length of ids that takes value 1 if the +corresponding outcome is +affected by study drop-out.

    +
    +
    +

    Details

    +

    subset can be used to specify outcome values that cannot be affected by the +drop-out. By default +subset will be set to 1 for all the values except the values corresponding to the +baseline outcome, since baseline is supposed to not be affected by drop-out. +Even if subset is specified by the user, the values corresponding to the baseline +outcome are still hard-coded to be 0.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/simulate_ice.html b/v1.3.1/reference/simulate_ice.html new file mode 100644 index 000000000..16bcbc097 --- /dev/null +++ b/v1.3.1/reference/simulate_ice.html @@ -0,0 +1,124 @@ + +Simulate intercurrent event — simulate_ice • rbmi + Skip to contents + + +
    +
    +
    +

    Simulate intercurrent event

    + Source: R/simulate_data.R +
    simulate_ice.Rd
    +
    + +
    +

    Simulate intercurrent event

    +
    + +
    +

    Usage

    + 
    simulate_ice(outcome, visits, ids, prob_ice, or_outcome_ice, baseline_mean)
    +
    + +
    +

    Arguments

    + + +
    outcome
    +

    Numeric variable that specifies the longitudinal outcome for a single group.

    + + +
    visits
    +

    Factor variable that specifies the visit of each assessment.

    + + +
    ids
    +

    Factor variable that specifies the id of each subject.

    + + +
    prob_ice
    +

    Numeric vector that specifies for each visit the probability of experiencing +the ICE after the current visit for a subject with outcome equal to the mean at baseline. +If a single numeric is provided, then the same probability is applied to each visit.

    + + +
    or_outcome_ice
    +

    Numeric value that specifies the odds ratio of the ICE corresponding to +a +1 higher value of the outcome at the visit.

    + + +
    baseline_mean
    +

    Mean outcome value at baseline.

    + +
    +
    +

    Value

    +

    A binary variable that takes value 1 if the corresponding outcome is affected +by the ICE and 0 otherwise.

    +
    +
    +

    Details

    +

    The probability of the ICE after each visit is modeled according to the following +logistic regression model: +~ 1 + I(visit == 0) + ... + I(visit == n_visits-1) + I((x-alpha)) where:

    • n_visits is the number of visits (including baseline).

      • +

    • alpha is the baseline outcome mean set via argument baseline_mean. +The term I((x-alpha)) specifies the dependency of the probability of the ICE on the current +outcome value. +The corresponding regression coefficients of the logistic model are defined as follows: +The intercept is set to 0, the coefficients corresponding to discontinuation after each visit +for a subject with outcome equal to +the mean at baseline are set according to parameter or_outcome_ice, +and the regression coefficient associated with the covariate I((x-alpha)) is set to +log(or_outcome_ice).

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/simulate_test_data.html b/v1.3.1/reference/simulate_test_data.html new file mode 100644 index 000000000..0228b0814 --- /dev/null +++ b/v1.3.1/reference/simulate_test_data.html @@ -0,0 +1,133 @@ + +Create simulated datasets — simulate_test_data • rbmi + Skip to contents + + +
    +
    +
    +

    Create simulated datasets

    + Source: R/simulate.R +
    simulate_test_data.Rd
    +
    + +
    +

    Creates a longitudinal dataset in the format that rbmi was +designed to analyse.

    +
    + +
    +

    Usage

    + 
    simulate_test_data(
+  n = 200,
+  sd = c(3, 5, 7),
+  cor = c(0.1, 0.7, 0.4),
+  mu = list(int = 10, age = 3, sex = 2, trt = c(0, 4, 8), visit = c(0, 1, 2))
+)
+
+as_vcov(sd, cor)
    +
    + +
    +

    Arguments

    + + +
    n
    +

    the number of subjects to sample. Total number of observations returned +is thus n * length(sd)

    + + +
    sd
    +

    the standard deviations for the outcome at each visit. +i.e. the square root of the diagonal of the covariance matrix for the outcome

    + + +
    cor
    +

    the correlation coefficients between the outcome values at each visit. +See details.

    + + +
    mu
    +

    the coefficients to use to construct the mean outcome value at each visit. Must +be a named list with elements int, age, sex, trt & visit. See details.

    + +
    +
    +

    Details

    +

    The number of visits is determined by the size of the variance covariance matrix. +i.e. if 3 standard deviation values are provided then 3 visits per patient will be +created.

    +

    The covariates in the simulated dataset are produced as follows:

    • Patients age is sampled at random from a N(0,1) distribution

      • +

    • Patients sex is sampled at random with a 50/50 split

      • +

    • Patients group is sampled at random but fixed so that each group has n/2 patients

      • +

    • The outcome variable is sampled from a multivariate normal distribution, see below +for details

      • +

    The mean for the outcome variable is derived as:

    +

    outcome = Intercept + age + sex + visit + treatment

    +

    The coefficients for the intercept, age and sex are taken from mu$int, +mu$age and mu$sex respectively, all of which must be a length 1 numeric.

    +

    Treatment and visit coefficients are taken from mu$trt and mu$visit respectively +and must either be of length 1 (i.e. a constant affect across all visits) or equal to the +number of visits (as determined by the length of sd). I.e. if you wanted a treatment +slope of 5 and a visit slope of 1 you could specify:

    +

    mu = list(..., "trt" = c(0,5,10), "visit" = c(0,1,2))

    +

    The correlation matrix is constructed from cor as follows. +Let cor = c(a, b, c, d, e, f) then the correlation matrix would be:

    +

    1  a  b  d
+a  1  c  e
+b  c  1  f
+d  e  f  1

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/sort_by.html b/v1.3.1/reference/sort_by.html new file mode 100644 index 000000000..2e716e305 --- /dev/null +++ b/v1.3.1/reference/sort_by.html @@ -0,0 +1,98 @@ + +Sort data.frame — sort_by • rbmi + Skip to contents + + +
    +
    +
    +

    Sort data.frame

    + Source: R/utilities.R +
    sort_by.Rd
    +
    + +
    +

    Sorts a data.frame (ascending by default) based upon variables within the dataset

    +
    + +
    +

    Usage

    + 
    sort_by(df, vars = NULL, decreasing = FALSE)
    +
    + +
    +

    Arguments

    + + +
    df
    +

    data.frame

    + + +
    vars
    +

    character vector of variables

    + + +
    decreasing
    +

    logical whether sort order should be in descending or ascending (default) order. +Can be either a single logical value (in which case it is applied to +all variables) or a vector which is the same length as vars

    + +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+sort_by(iris, c("Sepal.Length", "Sepal.Width"), decreasing = c(TRUE, FALSE))
+} # }
+
    +
    +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/split_dim.html b/v1.3.1/reference/split_dim.html new file mode 100644 index 000000000..79611f752 --- /dev/null +++ b/v1.3.1/reference/split_dim.html @@ -0,0 +1,118 @@ + +Transform array into list of arrays — split_dim • rbmi + Skip to contents + + +
    +
    +
    +

    Transform array into list of arrays

    + Source: R/mcmc.R +
    split_dim.Rd
    +
    + +
    +

    Transform an array into list of arrays where the listing +is performed on a given dimension.

    +
    + +
    +

    Usage

    + 
    split_dim(a, n)
    +
    + +
    +

    Arguments

    + + +
    a
    +

    Array with number of dimensions at least 2.

    + + +
    n
    +

    Positive integer. Dimension of a to be listed.

    + +
    +
    +

    Value

    +

    A list of length n of arrays with number of dimensions equal to the +number of dimensions of a minus 1.

    +
    +
    +

    Details

    +

    For example, if a is a 3 dimensional array and n = 1, +split_dim(a,n) returns a list of 2 dimensional arrays (i.e. +a list of matrices) where each element of the list is a[i, , ], where +i takes values from 1 to the length of the first dimension of the array.

    +

    Example:

    +

    inputs: +a <- array( c(1,2,3,4,5,6,7,8,9,10,11,12), dim = c(3,2,2)), +which means that:

    +

    a[1,,]     a[2,,]     a[3,,]
+
+[,1] [,2]  [,1] [,2]  [,1] [,2]
+---------  ---------  ---------
+ 1    7     2    8     3    9
+ 4    10    5    11    6    12

    +

    n <- 1

    +

    output of res <- split_dim(a,n) is a list of 3 elements:

    +

    res[[1]]   res[[2]]   res[[3]]
+
+[,1] [,2]  [,1] [,2]  [,1] [,2]
+---------  ---------  ---------
+ 1    7     2    8     3    9
+ 4    10    5    11    6    12

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/split_imputations.html b/v1.3.1/reference/split_imputations.html new file mode 100644 index 000000000..df97a1783 --- /dev/null +++ b/v1.3.1/reference/split_imputations.html @@ -0,0 +1,121 @@ + +Split a flat list of imputation_single() into multiple imputation_df()'s by ID — split_imputations • rbmi + Skip to contents + + +
    +
    +
    +

    Split a flat list of imputation_single() into multiple imputation_df()'s by ID

    + Source: R/impute.R +
    split_imputations.Rd
    +
    + +
    +

    Split a flat list of imputation_single() into multiple imputation_df()'s by ID

    +
    + +
    +

    Usage

    + 
    split_imputations(list_of_singles, split_ids)
    +
    + +
    +

    Arguments

    + + +
    list_of_singles
    +

    A list of imputation_single()'s

    + + +
    split_ids
    +

    A list with 1 element per required split. Each element +must contain a vector of "ID"'s which correspond to the imputation_single() ID's +that are required within that sample. The total number of ID's must by equal to the +length of list_of_singles

    + +
    +
    +

    Details

    +

    This function converts a list of imputations from being structured per patient +to being structured per sample i.e. it converts

    +

    obj <- list(
+    imputation_single("Ben", numeric(0)),
+    imputation_single("Ben", numeric(0)),
+    imputation_single("Ben", numeric(0)),
+    imputation_single("Harry", c(1, 2)),
+    imputation_single("Phil", c(3, 4)),
+    imputation_single("Phil", c(5, 6)),
+    imputation_single("Tom", c(7, 8, 9))
+)
+
+index <- list(
+    c("Ben", "Harry", "Phil", "Tom"),
+    c("Ben", "Ben", "Phil")
+)

    +

    Into:

    +

    output <- list(
+    imputation_df(
+        imputation_single(id = "Ben", values = numeric(0)),
+        imputation_single(id = "Harry", values = c(1, 2)),
+        imputation_single(id = "Phil", values = c(3, 4)),
+        imputation_single(id = "Tom", values = c(7, 8, 9))
+    ),
+    imputation_df(
+        imputation_single(id = "Ben", values = numeric(0)),
+        imputation_single(id = "Ben", values = numeric(0)),
+        imputation_single(id = "Phil", values = c(5, 6))
+    )
+)

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/str_contains.html b/v1.3.1/reference/str_contains.html new file mode 100644 index 000000000..686bd8cca --- /dev/null +++ b/v1.3.1/reference/str_contains.html @@ -0,0 +1,99 @@ + +Does a string contain a substring — str_contains • rbmi + Skip to contents + + +
    +
    +
    +

    Does a string contain a substring

    + Source: R/utilities.R +
    str_contains.Rd
    +
    + +
    +

    Returns a vector of TRUE/FALSE for each element of x +if it contains any element in subs

    +

    i.e.

    +

    str_contains( c("ben", "tom", "harry"), c("e", "y"))
+[1] TRUE FALSE TRUE

    +
    + +
    +

    Usage

    + 
    str_contains(x, subs)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    character vector

    + + +
    subs
    +

    a character vector of substrings to look for

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/strategies.html b/v1.3.1/reference/strategies.html new file mode 100644 index 000000000..c73b610ec --- /dev/null +++ b/v1.3.1/reference/strategies.html @@ -0,0 +1,125 @@ + +Strategies — strategies • rbmi + Skip to contents + + +
    +
    +
    +

    Strategies

    + Source: R/strategies.R +
    strategies.Rd
    +
    + +
    +

    These functions are used to implement various reference based imputation +strategies by combining a subjects own distribution with that of +a reference distribution based upon which of their visits failed to meet +the Missing-at-Random (MAR) assumption.

    +
    + +
    +

    Usage

    + 
    strategy_MAR(pars_group, pars_ref, index_mar)
+
+strategy_JR(pars_group, pars_ref, index_mar)
+
+strategy_CR(pars_group, pars_ref, index_mar)
+
+strategy_CIR(pars_group, pars_ref, index_mar)
+
+strategy_LMCF(pars_group, pars_ref, index_mar)
    +
    + +
    +

    Arguments

    + + +
    pars_group
    +

    A list of parameters for the subject's group. See details.

    + + +
    pars_ref
    +

    A list of parameters for the subject's reference group. See details.

    + + +
    index_mar
    +

    A logical vector indicating which visits meet the MAR assumption +for the subject. I.e. this identifies the observations after a non-MAR +intercurrent event (ICE).

    + +
    +
    +

    Details

    +

    pars_group and pars_ref both must be a list containing elements mu and sigma. +mu must be a numeric vector and sigma must be a square matrix symmetric covariance +matrix with dimensions equal to the length of mu and index_mar. e.g.

    +

    list(
+    mu = c(1,2,3),
+    sigma = matrix(c(4,3,2,3,5,4,2,4,6), nrow = 3, ncol = 3)
+)

    +

    Users can define their own strategy functions and include them via the strategies +argument to impute() using getStrategies(). That being said the following +strategies are available "out the box":

    • Missing at Random (MAR)

      • +

    • Jump to Reference (JR)

      • +

    • Copy Reference (CR)

      • +

    • Copy Increments in Reference (CIR)

      • +

    • Last Mean Carried Forward (LMCF)

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/string_pad.html b/v1.3.1/reference/string_pad.html new file mode 100644 index 000000000..5d9d16bb4 --- /dev/null +++ b/v1.3.1/reference/string_pad.html @@ -0,0 +1,88 @@ + +string_pad — string_pad • rbmi + Skip to contents + + +
    +
    +
    +

    string_pad

    + Source: R/as_ascii_table.R +
    string_pad.Rd
    +
    + +
    +

    Utility function used to replicate str_pad. Adds white space to either end +of a string to get it to equal the desired length

    +
    + +
    +

    Usage

    + 
    string_pad(x, width)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    string

    + + +
    width
    +

    desired length

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/transpose_imputations.html b/v1.3.1/reference/transpose_imputations.html new file mode 100644 index 000000000..3781a471b --- /dev/null +++ b/v1.3.1/reference/transpose_imputations.html @@ -0,0 +1,106 @@ + +Transpose imputations — transpose_imputations • rbmi + Skip to contents + + +
    +
    +
    +

    Transpose imputations

    + Source: R/longData.R +
    transpose_imputations.Rd
    +
    + +
    +

    Takes an imputation_df object and transposes it e.g.

    +

    list(
+    list(id = "a", values = c(1,2,3)),
+    list(id = "b", values = c(4,5,6)
+    )
+)

    +
    + +
    +

    Usage

    + 
    transpose_imputations(imputations)
    +
    + +
    +

    Arguments

    + + +
    imputations
    +

    An imputation_df object created by imputation_df()

    + +
    +
    +

    Details

    +

    becomes

    +

    list(
+    ids = c("a", "b"),
+    values = c(1,2,3,4,5,6)
+)

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/transpose_results.html b/v1.3.1/reference/transpose_results.html new file mode 100644 index 000000000..5d6ecce64 --- /dev/null +++ b/v1.3.1/reference/transpose_results.html @@ -0,0 +1,126 @@ + +Transpose results object — transpose_results • rbmi + Skip to contents + + +
    +
    +
    +

    Transpose results object

    + Source: R/pool.R +
    transpose_results.Rd
    +
    + +
    +

    Transposes a Results object (as created by analyse()) in order to group +the same estimates together into vectors.

    +
    + +
    +

    Usage

    + 
    transpose_results(results, components)
    +
    + +
    +

    Arguments

    + + +
    results
    +

    A list of results.

    + + +
    components
    +

    a character vector of components to extract +(i.e. "est", "se").

    + +
    +
    +

    Details

    +

    Essentially this function takes an object of the format:

    +

    x <- list(
+    list(
+        "trt1" = list(
+            est = 1,
+            se  = 2
+        ),
+        "trt2" = list(
+            est = 3,
+            se  = 4
+        )
+    ),
+    list(
+        "trt1" = list(
+            est = 5,
+            se  = 6
+        ),
+        "trt2" = list(
+            est = 7,
+            se  = 8
+        )
+    )
+)

    +

    and produces:

    +

    list(
+    trt1 = list(
+        est = c(1,5),
+        se = c(2,6)
+    ),
+    trt2 = list(
+        est = c(3,7),
+        se = c(4,8)
+    )
+)

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/transpose_samples.html b/v1.3.1/reference/transpose_samples.html new file mode 100644 index 000000000..1863b39c9 --- /dev/null +++ b/v1.3.1/reference/transpose_samples.html @@ -0,0 +1,84 @@ + +Transpose samples — transpose_samples • rbmi + Skip to contents + + +
    +
    +
    +

    Transpose samples

    + Source: R/impute.R +
    transpose_samples.Rd
    +
    + +
    +

    Transposes samples generated by draws() so that they are grouped +by subjid instead of by sample number.

    +
    + +
    +

    Usage

    + 
    transpose_samples(samples)
    +
    + +
    +

    Arguments

    + + +
    samples
    +

    A list of samples generated by draws().

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.analysis.html b/v1.3.1/reference/validate.analysis.html new file mode 100644 index 000000000..16a8445f8 --- /dev/null +++ b/v1.3.1/reference/validate.analysis.html @@ -0,0 +1,86 @@ + +Validate analysis objects — validate.analysis • rbmi + Skip to contents + + +
    +
    +
    +

    Validate analysis objects

    + Source: R/analyse.R +
    validate.analysis.Rd
    +
    + +
    +

    Validates the return object of the analyse() function.

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'analysis'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    An analysis results object (of class "jackknife", "bootstrap", "rubin").

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.draws.html b/v1.3.1/reference/validate.draws.html new file mode 100644 index 000000000..e458911c1 --- /dev/null +++ b/v1.3.1/reference/validate.draws.html @@ -0,0 +1,86 @@ + +Validate draws object — validate.draws • rbmi + Skip to contents + + +
    +
    +
    +

    Validate draws object

    + Source: R/draws.R +
    validate.draws.Rd
    +
    + +
    +

    Validate draws object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'draws'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    A draws object generated by as_draws().

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.html b/v1.3.1/reference/validate.html new file mode 100644 index 000000000..e78d7ae10 --- /dev/null +++ b/v1.3.1/reference/validate.html @@ -0,0 +1,91 @@ + +Generic validation method — validate • rbmi + Skip to contents + + +
    +
    +
    +

    Generic validation method

    + Source: R/validate.R +
    validate.Rd
    +
    + +
    +

    This function is used to perform assertions that an object +conforms to its expected structure and no basic assumptions +have been violated. Will throw an error if checks do not pass.

    +
    + +
    +

    Usage

    + 
    validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    object to be validated.

    + + +
    ...
    +

    additional arguments to pass to the specific validation method.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.is_mar.html b/v1.3.1/reference/validate.is_mar.html new file mode 100644 index 000000000..47df46dc9 --- /dev/null +++ b/v1.3.1/reference/validate.is_mar.html @@ -0,0 +1,96 @@ + +Validate is_mar for a given subject — validate.is_mar • rbmi + Skip to contents + + +
    +
    +
    +

    Validate is_mar for a given subject

    + Source: R/longData.R +
    validate.is_mar.Rd
    +
    + +
    +

    Checks that the longitudinal data for a patient is divided in MAR +followed by non-MAR data; a non-MAR observation followed by a MAR +observation is not allowed.

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'is_mar'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    Object of class is_mar. Logical vector indicating whether observations are MAR.

    + + +
    ...
    +

    Not used.

    + +
    +
    +

    Value

    +

    Will error if there is an issue otherwise will return TRUE.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.ivars.html b/v1.3.1/reference/validate.ivars.html new file mode 100644 index 000000000..684e5eecf --- /dev/null +++ b/v1.3.1/reference/validate.ivars.html @@ -0,0 +1,89 @@ + +Validate inputs for vars — validate.ivars • rbmi + Skip to contents + + +
    +
    +
    +

    Validate inputs for vars

    + Source: R/utilities.R +
    validate.ivars.Rd
    +
    + +
    +

    Checks that the required variable names are defined within vars and +are of appropriate datatypes

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'ivars'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    named list indicating the names of key variables in the source dataset

    + + +
    ...
    +

    not used

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.references.html b/v1.3.1/reference/validate.references.html new file mode 100644 index 000000000..6b0752495 --- /dev/null +++ b/v1.3.1/reference/validate.references.html @@ -0,0 +1,97 @@ + +Validate user supplied references — validate.references • rbmi + Skip to contents + + +
    +
    +
    +

    Validate user supplied references

    + Source: R/impute.R +
    validate.references.Rd
    +
    + +
    +

    Checks to ensure that the user specified references are +expect values (i.e. those found within the source data).

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'references'
+validate(x, control, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    named character vector.

    + + +
    control
    +

    factor variable (should be the group variable from the source dataset).

    + + +
    ...
    +

    Not used.

    + +
    +
    +

    Value

    +

    Will error if there is an issue otherwise will return TRUE.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.sample_list.html b/v1.3.1/reference/validate.sample_list.html new file mode 100644 index 000000000..f3bd95e7a --- /dev/null +++ b/v1.3.1/reference/validate.sample_list.html @@ -0,0 +1,86 @@ + +Validate sample_list object — validate.sample_list • rbmi + Skip to contents + + +
    +
    +
    +

    Validate sample_list object

    + Source: R/dataclasses.R +
    validate.sample_list.Rd
    +
    + +
    +

    Validate sample_list object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'sample_list'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    A sample_list object generated by sample_list().

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.sample_single.html b/v1.3.1/reference/validate.sample_single.html new file mode 100644 index 000000000..116ce4ed6 --- /dev/null +++ b/v1.3.1/reference/validate.sample_single.html @@ -0,0 +1,86 @@ + +Validate sample_single object — validate.sample_single • rbmi + Skip to contents + + +
    +
    +
    +

    Validate sample_single object

    + Source: R/dataclasses.R +
    validate.sample_single.Rd
    +
    + +
    +

    Validate sample_single object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'sample_single'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    A sample_single object generated by sample_single().

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.simul_pars.html b/v1.3.1/reference/validate.simul_pars.html new file mode 100644 index 000000000..9b6b9c462 --- /dev/null +++ b/v1.3.1/reference/validate.simul_pars.html @@ -0,0 +1,86 @@ + +Validate a simul_pars object — validate.simul_pars • rbmi + Skip to contents + + +
    +
    +
    +

    Validate a simul_pars object

    + Source: R/simulate_data.R +
    validate.simul_pars.Rd
    +
    + +
    +

    Validate a simul_pars object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'simul_pars'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    An simul_pars object as generated by set_simul_pars().

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate.stan_data.html b/v1.3.1/reference/validate.stan_data.html new file mode 100644 index 000000000..c9e2ff7b1 --- /dev/null +++ b/v1.3.1/reference/validate.stan_data.html @@ -0,0 +1,86 @@ + +Validate a stan_data object — validate.stan_data • rbmi + Skip to contents + + +
    +
    +
    +

    Validate a stan_data object

    + Source: R/mcmc.R +
    validate.stan_data.Rd
    +
    + +
    +

    Validate a stan_data object

    +
    + +
    +

    Usage

    + 
    # S3 method for class 'stan_data'
+validate(x, ...)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    A stan_data object.

    + + +
    ...
    +

    Not used.

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate_analyse_pars.html b/v1.3.1/reference/validate_analyse_pars.html new file mode 100644 index 000000000..5a9112696 --- /dev/null +++ b/v1.3.1/reference/validate_analyse_pars.html @@ -0,0 +1,87 @@ + +Validate analysis results — validate_analyse_pars • rbmi + Skip to contents + + +
    +
    +
    +

    Validate analysis results

    + Source: R/analyse.R +
    validate_analyse_pars.Rd
    +
    + +
    +

    Validates analysis results generated by analyse().

    +
    + +
    +

    Usage

    + 
    validate_analyse_pars(results, pars)
    +
    + +
    +

    Arguments

    + + +
    results
    +

    A list of results generated by the analysis fun +used in analyse().

    + + +
    pars
    +

    A list of expected parameters in each of the analysis. +lists i.e. c("est", "se", "df").

    + +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate_datalong.html b/v1.3.1/reference/validate_datalong.html new file mode 100644 index 000000000..822e7adc5 --- /dev/null +++ b/v1.3.1/reference/validate_datalong.html @@ -0,0 +1,121 @@ + +Validate a longdata object — validate_datalong • rbmi + Skip to contents + + +
    +
    +
    +

    Validate a longdata object

    + Source: R/validate_datalong.R +
    validate_datalong.Rd
    +
    + +
    +

    Validate a longdata object

    +
    + +
    +

    Usage

    + 
    validate_datalong(data, vars)
+
+validate_datalong_varExists(data, vars)
+
+validate_datalong_types(data, vars)
+
+validate_datalong_notMissing(data, vars)
+
+validate_datalong_complete(data, vars)
+
+validate_datalong_unifromStrata(data, vars)
+
+validate_dataice(data, data_ice, vars, update = FALSE)
    +
    + +
    +

    Arguments

    + + +
    data
    +

    a data.frame containing the longitudinal outcome data + covariates +for multiple subjects

    + + +
    vars
    +

    a vars object as created by set_vars()

    + + +
    data_ice
    +

    a data.frame containing the subjects ICE data. See draws() for details.

    + + +
    update
    +

    logical, indicates if the ICE data is being set for the first time or if an update +is being applied

    + +
    +
    +

    Details

    +

    These functions are used to validate various different parts of the longdata object +to be used in draws(), impute(), analyse() and pool(). In particular:

    • validate_datalong_varExists - Checks that each variable listed in vars actually exists +in the data

      • +

    • validate_datalong_types - Checks that the types of each key variable is as expected +i.e. that visit is a factor variable

      • +

    • validate_datalong_notMissing - Checks that none of the key variables (except the outcome variable) +contain any missing values

      • +

    • validate_datalong_complete - Checks that data is complete i.e. there is 1 row for each subject * +visit combination. e.g. that nrow(data) == length(unique(subjects)) * length(unique(visits))

      • +

    • validate_datalong_unifromStrata - Checks to make sure that any variables listed as stratification +variables do not vary over time. e.g. that subjects don't switch between stratification groups.

      • +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/reference/validate_strategies.html b/v1.3.1/reference/validate_strategies.html new file mode 100644 index 000000000..13e7063a1 --- /dev/null +++ b/v1.3.1/reference/validate_strategies.html @@ -0,0 +1,95 @@ + +Validate user specified strategies — validate_strategies • rbmi + Skip to contents + + +
    +
    +
    +

    Validate user specified strategies

    + Source: R/impute.R +
    validate_strategies.Rd
    +
    + +
    +

    Compares the user provided strategies to those that are +required (the reference). Will throw an error if not all values +of reference have been defined.

    +
    + +
    +

    Usage

    + 
    validate_strategies(strategies, reference)
    +
    + +
    +

    Arguments

    + + +
    strategies
    +

    named list of strategies.

    + + +
    reference
    +

    list or character vector of strategies that need to be defined.

    + +
    +
    +

    Value

    +

    Will throw an error if there is an issue otherwise will return TRUE.

    +
    + +
    + + +
    +

    Developed by Craig Gower-Page, Alessandro Noci, Isaac Gravestock, F. Hoffmann-La Roche AG.

    +
    + +
    +

    Site built with pkgdown 2.1.1.

    +
    + +
    + + + + + + + diff --git a/v1.3.1/search.json b/v1.3.1/search.json new file mode 100644 index 000000000..89412435c --- /dev/null +++ b/v1.3.1/search.json @@ -0,0 +1 @@ +[{"path":"/CONTRIBUTING.html","id":null,"dir":"","previous_headings":"","what":"Contributing to rbmi","title":"Contributing to rbmi","text":"file outlines propose make changes rbmi well providing details obscure aspects package’s development process.","code":""},{"path":"/CONTRIBUTING.html","id":"setup","dir":"","previous_headings":"","what":"Setup","title":"Contributing to rbmi","text":"order develop contribute rbmi need access C/C++ compiler. Windows install rtools macOS install Xcode. Likewise, also need install package’s development dependencies. can done launching R within project root executing:","code":"devtools::install_dev_deps()"},{"path":"/CONTRIBUTING.html","id":"code-changes","dir":"","previous_headings":"","what":"Code changes","title":"Contributing to rbmi","text":"want make code contribution, ’s good idea first file issue make sure someone team agrees ’s needed. ’ve found bug, please file issue illustrates bug minimal reprex (also help write unit test, needed).","code":""},{"path":"/CONTRIBUTING.html","id":"pull-request-process","dir":"","previous_headings":"Code changes","what":"Pull request process","title":"Contributing to rbmi","text":"project uses simple GitHub flow model development. , code changes done feature branch based main branch merged back main branch complete. Pull Requests accepted unless CI/CD checks passed. (See CI/CD section information). Pull Requests relating package’s core R code must accompanied corresponding unit test. pull requests containing changes core R code contain unit test demonstrate working intended accepted. (See Unit Testing section information). Pull Requests add lines changed NEWS.md file.","code":""},{"path":"/CONTRIBUTING.html","id":"coding-considerations","dir":"","previous_headings":"Code changes","what":"Coding Considerations","title":"Contributing to rbmi","text":"use roxygen2, Markdown syntax, documentation. Please ensure code conforms lintr. can check running lintr::lint(\"FILE NAME\") files modified ensuring findings kept possible. hard requirements following lintr’s conventions encourage developers follow guidance closely possible. project uses 4 space indents, contributions following accepted. project makes use S3 R6 OOP. Usage S4 OOP systems avoided unless absolutely necessary ensure consistency. said recommended stick S3 unless modification place R6 specific features required. current desire package keep dependency tree small possible. end discouraged adding additional packages “Depends” / “Imports” section unless absolutely essential. importing package just use single function consider just copying source code function instead, though please check licence include proper attribution/notices. expectations “Suggests” free use package vignettes / unit tests, though please mindful unnecessarily excessive .","code":""},{"path":"/CONTRIBUTING.html","id":"unit-testing--cicd","dir":"","previous_headings":"","what":"Unit Testing & CI/CD","title":"Contributing to rbmi","text":"project uses testthat perform unit testing combination GitHub Actions CI/CD.","code":""},{"path":"/CONTRIBUTING.html","id":"scheduled-testing","dir":"","previous_headings":"Unit Testing & CI/CD","what":"Scheduled Testing","title":"Contributing to rbmi","text":"Due stochastic nature package unit tests take considerable amount time execute. avoid issues usability, unit tests take couple seconds run deferred scheduled testing. tests run occasionally periodic basis (currently twice month) every pull request / push event. defer test scheduled build simply include skip_if_not(is_full_test()) top test_that() block .e. scheduled tests can also manually activated going “https://github.com/insightsengineering/rbmi” -> “Actions” -> “Bi-Weekly” -> “Run Workflow”. advisable releasing CRAN.","code":"test_that(\"some unit test\", { skip_if_not(is_full_test()) expect_equal(1,1) })"},{"path":"/CONTRIBUTING.html","id":"docker-images","dir":"","previous_headings":"Unit Testing & CI/CD","what":"Docker Images","title":"Contributing to rbmi","text":"support CI/CD, terms reducing setup time, Docker images created contains packages system dependencies required project. image can found : ghcr.io/insightsengineering/rbmi:latest image automatically re-built month contain latest version R packages. code create images can found misc/docker. build image locally run following project root directory:","code":"docker build -f misc/docker/Dockerfile -t rbmi:latest ."},{"path":"/CONTRIBUTING.html","id":"reproducibility-print-tests--snaps","dir":"","previous_headings":"Unit Testing & CI/CD","what":"Reproducibility, Print Tests & Snaps","title":"Contributing to rbmi","text":"particular issue testing package reproducibility. part handled well via set.seed() however stan/rstan guarantee reproducibility even seed run different hardware. issue surfaces testing print messages pool object displays treatment estimates thus identical run different machines. address issue pre-made pool objects generated stored R/sysdata.rda (generated data-raw/create_print_test_data.R). generated print messages compared expected values stored tests/testthat/_snaps/ (automatically created testthat::expect_snapshot())","code":""},{"path":"/CONTRIBUTING.html","id":"fitting-mmrms","dir":"","previous_headings":"","what":"Fitting MMRM’s","title":"Contributing to rbmi","text":"package currently uses mmrm package fit MMRM models. package still fairly new far proven stable, fast reliable. spot issues MMRM package please raise corresponding GitHub Repository - link mmrm package uses TMB uncommon see warnings either inconsistent versions TMB Matrix package compiled . order resolve may wish re-compile packages source using: Note need rtools installed Windows machine Xcode running macOS (somehow else access C/C++ compiler).","code":"install.packages(c(\"TMB\", \"mmrm\"), type = \"source\")"},{"path":"/CONTRIBUTING.html","id":"rstan","dir":"","previous_headings":"","what":"rstan","title":"Contributing to rbmi","text":"Bayesian models fitted package implemented via stan/rstan. code can found inst/stan/MMRM.stan. Note package automatically take care compiling code install run devtools::load_all(). Please note package won’t recompile code unless changed source code delete src directory.","code":""},{"path":"/CONTRIBUTING.html","id":"vignettes","dir":"","previous_headings":"","what":"Vignettes","title":"Contributing to rbmi","text":"CRAN imposes 10-minute run limit building, compiling testing package. keep limit vignettes pre-built; say simply changing source code automatically update vignettes, need manually re-build . need run: re-built need commit updated *.html files git repository. reference static vignette process works using “asis” vignette engine provided R.rsp. works getting R recognise vignettes files ending *.html.asis; builds simply copying corresponding files ending *.html relevent docs/ folder built package.","code":"Rscript vignettes/build.R"},{"path":"/CONTRIBUTING.html","id":"misc--local-folders","dir":"","previous_headings":"","what":"Misc & Local Folders","title":"Contributing to rbmi","text":"misc/ folder project used hold useful scripts, analyses, simulations & infrastructure code wish keep isn’t essential build deployment package. Feel free store additional stuff feel worth keeping. Likewise, local/ added .gitignore file meaning anything stored folder won’t committed repository. example, may find useful storing personal scripts testing generally exploring package development.","code":""},{"path":"/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"Apache License","title":"Apache License","text":"Version 2.0, January 2004 ","code":""},{"path":[]},{"path":"/LICENSE.html","id":"id_1-definitions","dir":"","previous_headings":"Terms and Conditions for use, reproduction, and distribution","what":"1. 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However, accepting obligations, may act behalf sole responsibility, behalf Contributor, agree indemnify, defend, hold Contributor harmless liability incurred , claims asserted , Contributor reason accepting warranty additional liability. END TERMS CONDITIONS","code":""},{"path":"/LICENSE.html","id":"appendix-how-to-apply-the-apache-license-to-your-work","dir":"","previous_headings":"","what":"APPENDIX: How to apply the Apache License to your work","title":"Apache License","text":"apply Apache License work, attach following boilerplate notice, fields enclosed brackets [] replaced identifying information. (Don’t include brackets!) text enclosed appropriate comment syntax file format. also recommend file class name description purpose included “printed page” copyright notice easier identification within third-party archives.","code":"Copyright [yyyy] [name of copyright owner] Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License."},{"path":"/articles/CondMean_Inference.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"rbmi: Inference with Conditional Mean Imputation","text":"described section 3.10.2 statistical specifications package (vignette(topic = \"stat_specs\", package = \"rbmi\")), two different types variance estimators proposed reference-based imputation methods statistical literature (Bartlett (2023)). first frequentist variance describes actual repeated sampling variability estimator results inference correct frequentist sense, .e. hypothesis tests accurate type error control confidence intervals correct coverage probabilities repeated sampling reference-based assumption correctly specified (Bartlett (2023), Wolbers et al. (2022)). Reference-based missing data assumption strong borrow information control arm imputation active arm. consequence, size frequentist standard errors treatment effects may decrease increasing amounts missing data. second -called “information-anchored” variance originally proposed context sensitivity analyses (Cro, Carpenter, Kenward (2019)). variance estimator based disentangling point estimation variance estimation altogether. resulting information-anchored variance typically similar variance missing--random (MAR) imputation increases increasing amounts missing data approximately rate MAR imputation. However, information-anchored variance reflect actual variability reference-based estimator resulting frequentist inference highly conservative resulting substantial power loss. Reference-based conditional mean imputation combined resampling method jackknife bootstrap first introduced Wolbers et al. (2022). approach naturally targets frequentist variance. information-anchored variance typically estimated using Rubin’s rules Bayesian multiple imputation applicable within conditional mean imputation framework. However, alternative information-anchored variance proposed Lu (2021) can easily obtained show . basic idea Lu (2021) obtain information-anchored variance via MAR imputation combined delta-adjustment delta selected data-driven way match reference-based estimator. conditional mean imputation, proposal Lu (2021) can implemented choosing delta-adjustment difference conditional mean imputation chosen reference-based assumption MAR original dataset. variance can obtained via jackknife bootstrap keeping delta-adjustment fixed. resulting variance estimate similar Rubin’s variance. Moreover, shown Cro, Carpenter, Kenward (2019), variance MAR-imputation combined delta-adjustment achieves even better information-anchoring properties Rubin’s variance reference-based imputation. Reference-based missing data assumptions strong borrow information control arm imputation active arm. vignette demonstrates first obtain frequentist inference using reference-based conditional mean imputation using rbmi, shows information-anchored inference can also easily implemented using package.","code":""},{"path":"/articles/CondMean_Inference.html","id":"data-and-model-specification","dir":"Articles","previous_headings":"","what":"Data and model specification","title":"rbmi: Inference with Conditional Mean Imputation","text":"use publicly available example dataset antidepressant clinical trial active drug versus placebo. relevant endpoint Hamilton 17-item depression rating scale (HAMD17) assessed baseline weeks 1, 2, 4, 6. Study drug discontinuation occurred 24% subjects active drug 26% subjects placebo. data study drug discontinuation missing single additional intermittent missing observation. consider imputation model mean change baseline HAMD17 score outcome (variable CHANGE dataset). following covariates included imputation model: treatment group (THERAPY), (categorical) visit (VISIT), treatment--visit interactions, baseline HAMD17 score (BASVAL), baseline HAMD17 score--visit interactions. common unstructured covariance matrix structure assumed groups. analysis model ANCOVA model treatment group primary factor adjustment baseline HAMD17 score. example, assume imputation strategy ICE “study-drug discontinuation” Jump Reference (JR) subjects imputation based conditional mean imputation combined jackknife resampling (bootstrap also selected).","code":""},{"path":"/articles/CondMean_Inference.html","id":"reference-based-conditional-mean-imputation---frequentist-inference","dir":"Articles","previous_headings":"","what":"Reference-based conditional mean imputation - frequentist inference","title":"rbmi: Inference with Conditional Mean Imputation","text":"Conditional mean imputation combined resampling method jackknife bootstrap naturally targets frequentist estimation standard error treatment effect, thus providing valid frequentist inference. provide code obtain frequentist inference reference-based conditional mean imputation using rbmi. code used section almost identical code quickstart vignette (vignette(topic = \"quickstart\", package = \"rbmi\")) except use conditional mean imputation combined jackknife (method_condmean(type = \"jackknife\")) rather Bayesian multiple imputation (method_bayes()). therefore refer vignette help files individual functions explanations details.","code":""},{"path":"/articles/CondMean_Inference.html","id":"draws","dir":"Articles","previous_headings":"3 Reference-based conditional mean imputation - frequentist inference","what":"Draws","title":"rbmi: Inference with Conditional Mean Imputation","text":"make use rbmi::expand_locf() expand dataset order one row per subject per visit missing outcomes denoted NA. construct data_ice, vars method input arguments first core rbmi function, draws(). Finally, call function draws() derive parameter estimates base imputation model full dataset leave-one-subject-samples.","code":"library(rbmi) library(dplyr) #> #> Attaching package: 'dplyr' #> The following objects are masked from 'package:stats': #> #> filter, lag #> The following objects are masked from 'package:base': #> #> intersect, setdiff, setequal, union dat <- antidepressant_data # Use expand_locf to add rows corresponding to visits with missing outcomes to # the dataset dat <- expand_locf( dat, PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT VISIT = levels(dat$VISIT), vars = c(\"BASVAL\", \"THERAPY\"), # fill with LOCF BASVAL and THERAPY group = c(\"PATIENT\"), order = c(\"PATIENT\", \"VISIT\") ) # create data_ice and set the imputation strategy to JR for # each patient with at least one missing observation dat_ice <- dat %>% arrange(PATIENT, VISIT) %>% filter(is.na(CHANGE)) %>% group_by(PATIENT) %>% slice(1) %>% ungroup() %>% select(PATIENT, VISIT) %>% mutate(strategy = \"JR\") # In this dataset, subject 3618 has an intermittent missing values which # does not correspond to a study drug discontinuation. We therefore remove # this subject from `dat_ice`. (In the later imputation step, it will # automatically be imputed under the default MAR assumption.) dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),] # Define the names of key variables in our dataset and # the covariates included in the imputation model using `set_vars()` vars <- set_vars( outcome = \"CHANGE\", visit = \"VISIT\", subjid = \"PATIENT\", group = \"THERAPY\", covariates = c(\"BASVAL*VISIT\", \"THERAPY*VISIT\") ) # Define which imputation method to use (here: conditional mean imputation # with jackknife as resampling) method <- method_condmean(type = \"jackknife\") # Create samples for the imputation parameters by running the draws() function drawObj <- draws( data = dat, data_ice = dat_ice, vars = vars, method = method, quiet = TRUE ) drawObj #> #> Draws Object #> ------------ #> Number of Samples: 1 + 172 #> Number of Failed Samples: 0 #> Model Formula: CHANGE ~ 1 + THERAPY + VISIT + BASVAL * VISIT + THERAPY * VISIT #> Imputation Type: condmean #> Method: #> name: Conditional Mean #> covariance: us #> threshold: 0.01 #> same_cov: TRUE #> REML: TRUE #> type: jackknife"},{"path":"/articles/CondMean_Inference.html","id":"impute","dir":"Articles","previous_headings":"3 Reference-based conditional mean imputation - frequentist inference","what":"Impute","title":"rbmi: Inference with Conditional Mean Imputation","text":"can use now function impute() perform imputation original dataset leave-one-samples using results obtained previous step.","code":"references <- c(\"DRUG\" = \"PLACEBO\", \"PLACEBO\" = \"PLACEBO\") imputeObj <- impute(drawObj, references) imputeObj #> #> Imputation Object #> ----------------- #> Number of Imputed Datasets: 1 + 172 #> Fraction of Missing Data (Original Dataset): #> 4: 0% #> 5: 8% #> 6: 13% #> 7: 25% #> References: #> DRUG -> PLACEBO #> PLACEBO -> PLACEBO"},{"path":"/articles/CondMean_Inference.html","id":"analyse","dir":"Articles","previous_headings":"3 Reference-based conditional mean imputation - frequentist inference","what":"Analyse","title":"rbmi: Inference with Conditional Mean Imputation","text":"datasets imputed, can call analyse() function apply complete-data analysis model (ANCOVA) imputed dataset.","code":"# Set analysis variables using `rbmi` function \"set_vars\" vars_an <- set_vars( group = vars$group, visit = vars$visit, outcome = vars$outcome, covariates = \"BASVAL\" ) # Analyse MAR imputation with derived delta adjustment anaObj <- analyse( imputeObj, rbmi::ancova, vars = vars_an ) anaObj #> #> Analysis Object #> --------------- #> Number of Results: 1 + 172 #> Analysis Function: rbmi::ancova #> Delta Applied: FALSE #> Analysis Estimates: #> trt_4 #> lsm_ref_4 #> lsm_alt_4 #> trt_5 #> lsm_ref_5 #> lsm_alt_5 #> trt_6 #> lsm_ref_6 #> lsm_alt_6 #> trt_7 #> lsm_ref_7 #> lsm_alt_7"},{"path":"/articles/CondMean_Inference.html","id":"pool","dir":"Articles","previous_headings":"3 Reference-based conditional mean imputation - frequentist inference","what":"Pool","title":"rbmi: Inference with Conditional Mean Imputation","text":"Finally, can extract treatment effect estimates perform inference using jackknife variance estimator. done calling pool() function. gives estimated treatment effect 2.13 (95% CI 0.44 3.81) last visit associated p-value 0.013.","code":"poolObj <- pool(anaObj) poolObj #> #> Pool Object #> ----------- #> Number of Results Combined: 1 + 172 #> Method: jackknife #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================== #> parameter est se lci uci pval #> -------------------------------------------------- #> trt_4 -0.092 0.695 -1.453 1.27 0.895 #> lsm_ref_4 -1.616 0.588 -2.767 -0.464 0.006 #> lsm_alt_4 -1.708 0.396 -2.484 -0.931 <0.001 #> trt_5 1.305 0.878 -0.416 3.027 0.137 #> lsm_ref_5 -4.133 0.688 -5.481 -2.785 <0.001 #> lsm_alt_5 -2.828 0.604 -4.011 -1.645 <0.001 #> trt_6 1.929 0.862 0.239 3.619 0.025 #> lsm_ref_6 -6.088 0.671 -7.402 -4.773 <0.001 #> lsm_alt_6 -4.159 0.686 -5.503 -2.815 <0.001 #> trt_7 2.126 0.858 0.444 3.807 0.013 #> lsm_ref_7 -6.965 0.685 -8.307 -5.622 <0.001 #> lsm_alt_7 -4.839 0.762 -6.333 -3.346 <0.001 #> --------------------------------------------------"},{"path":"/articles/CondMean_Inference.html","id":"reference-based-conditional-mean-imputation---information-anchored-inference","dir":"Articles","previous_headings":"","what":"Reference-based conditional mean imputation - information-anchored inference","title":"rbmi: Inference with Conditional Mean Imputation","text":"section, present estimation process based conditional mean imputation combined jackknife can adapted obtain information-anchored variance following proposal Lu (2021).","code":""},{"path":"/articles/CondMean_Inference.html","id":"draws-1","dir":"Articles","previous_headings":"4 Reference-based conditional mean imputation - information-anchored inference","what":"Draws","title":"rbmi: Inference with Conditional Mean Imputation","text":"code pre-processing dataset “draws” step equivalent code provided frequentist inference. Please refer section details step.","code":"library(rbmi) library(dplyr) dat <- antidepressant_data # Use expand_locf to add rows corresponding to visits with missing outcomes to # the dataset dat <- expand_locf( dat, PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT VISIT = levels(dat$VISIT), vars = c(\"BASVAL\", \"THERAPY\"), # fill with LOCF BASVAL and THERAPY group = c(\"PATIENT\"), order = c(\"PATIENT\", \"VISIT\") ) # create data_ice and set the imputation strategy to JR for # each patient with at least one missing observation dat_ice <- dat %>% arrange(PATIENT, VISIT) %>% filter(is.na(CHANGE)) %>% group_by(PATIENT) %>% slice(1) %>% ungroup() %>% select(PATIENT, VISIT) %>% mutate(strategy = \"JR\") # In this dataset, subject 3618 has an intermittent missing values which # does not correspond to a study drug discontinuation. We therefore remove # this subject from `dat_ice`. (In the later imputation step, it will # automatically be imputed under the default MAR assumption.) dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),] # Define the names of key variables in our dataset and # the covariates included in the imputation model using `set_vars()` vars <- set_vars( outcome = \"CHANGE\", visit = \"VISIT\", subjid = \"PATIENT\", group = \"THERAPY\", covariates = c(\"BASVAL*VISIT\", \"THERAPY*VISIT\") ) # Define which imputation method to use (here: conditional mean imputation # with jackknife as resampling) method <- method_condmean(type = \"jackknife\") # Create samples for the imputation parameters by running the draws() function drawObj <- draws( data = dat, data_ice = dat_ice, vars = vars, method = method, quiet = TRUE ) drawObj"},{"path":"/articles/CondMean_Inference.html","id":"imputation-step-including-calculation-of-delta-adjustment","dir":"Articles","previous_headings":"4 Reference-based conditional mean imputation - information-anchored inference","what":"Imputation step including calculation of delta-adjustment","title":"rbmi: Inference with Conditional Mean Imputation","text":"proposal Lu (2021) replace reference-based imputation MAR imputation combined delta-adjustment delta selected data-driven way match reference-based estimator. rbmi, implemented first performing imputation defined reference-based imputation strategy (JR) well MAR separately. Second, delta-adjustment defined difference conditional mean imputation reference-based MAR imputation, respectively, original dataset. simplify implementation, written function get_delta_match_refBased performs step. function takes input arguments draws object, data_ice (.e. data.frame containing information intercurrent events imputation strategies), references, named vector identifies references used reference-based imputation methods. function returns list containing imputation objects reference-based MAR imputation, plus data.frame contains delta-adjustment.","code":"#' Get delta adjustment that matches reference-based imputation #' #' @param draws: A `draws` object created by `draws()`. #' @param data_ice: `data.frame` containing the information about the intercurrent #' events and the imputation strategies. Must represent the desired imputation #' strategy and not the MAR-variant. #' @param references: A named vector. Identifies the references to be used #' for reference-based imputation methods. #' #' @return #' The function returns a list containing the imputation objects under both #' reference-based and MAR imputation, plus a `data.frame` which contains the #' delta-adjustment. #' #' @seealso `draws()`, `impute()`. get_delta_match_refBased <- function(draws, data_ice, references) { # Impute according to `data_ice` imputeObj <- impute( draws = drawObj, update_strategy = data_ice, references = references ) vars <- imputeObj$data$vars # Access imputed dataset (index=1 for method_condmean(type = \"jackknife\")) cmi <- extract_imputed_dfs(imputeObj, index = 1, idmap = TRUE)[[1]] idmap <- attributes(cmi)$idmap cmi <- cmi[, c(vars$subjid, vars$visit, vars$outcome)] colnames(cmi)[colnames(cmi) == vars$outcome] <- \"y_imp\" # Map back original patients id since `rbmi` re-code ids to ensure id uniqueness cmi[[vars$subjid]] <- idmap[match(cmi[[vars$subjid]], names(idmap))] # Derive conditional mean imputations under MAR dat_ice_MAR <- data_ice dat_ice_MAR[[vars$strategy]] <- \"MAR\" # Impute under MAR # Note that in this specific context, it is desirable that an update # from a reference-based strategy to MAR uses the exact same data for # fitting the imputation models, i.e. that available post-ICE data are # omitted from the imputation model for both. This is the case when # using argument update_strategy in function impute(). # However, for other settings (i.e. if one is interested in switching to # a standard MAR imputation strategy altogether), this behavior is # undesirable and, consequently, the function throws a warning which # we suppress here. suppressWarnings( imputeObj_MAR <- impute( draws, update_strategy = dat_ice_MAR ) ) # Access imputed dataset (index=1 for method_condmean(type = \"jackknife\")) cmi_MAR <- extract_imputed_dfs(imputeObj_MAR, index = 1, idmap = TRUE)[[1]] idmap <- attributes(cmi_MAR)$idmap cmi_MAR <- cmi_MAR[, c(vars$subjid, vars$visit, vars$outcome)] colnames(cmi_MAR)[colnames(cmi_MAR) == vars$outcome] <- \"y_MAR\" # Map back original patients id since `rbmi` re-code ids to ensure id uniqueness cmi_MAR[[vars$subjid]] <- idmap[match(cmi_MAR[[vars$subjid]], names(idmap))] # Derive delta adjustment \"aligned with ref-based imputation\", # i.e. difference between ref-based imputation and MAR imputation delta_adjust <- merge(cmi, cmi_MAR, by = c(vars$subjid, vars$visit), all = TRUE) delta_adjust$delta <- delta_adjust$y_imp - delta_adjust$y_MAR ret_obj <- list( imputeObj = imputeObj, imputeObj_MAR = imputeObj_MAR, delta_adjust = delta_adjust ) return(ret_obj) } references <- c(\"DRUG\" = \"PLACEBO\", \"PLACEBO\" = \"PLACEBO\") res_delta_adjust <- get_delta_match_refBased(drawObj, dat_ice, references)"},{"path":"/articles/CondMean_Inference.html","id":"analyse-1","dir":"Articles","previous_headings":"4 Reference-based conditional mean imputation - information-anchored inference","what":"Analyse","title":"rbmi: Inference with Conditional Mean Imputation","text":"use function analyse() add delta-adjustment perform analysis imputed datasets MAR. analyse() take input argument imputations = res_delta_adjust$imputeObj_MAR, .e. imputation object corresponding MAR imputation (JR imputation). argument delta can used add delta-adjustment prior analysis set delta-adjustment obtained previous step: delta = res_delta_adjust$delta_adjust.","code":"# Set analysis variables using `rbmi` function \"set_vars\" vars_an <- set_vars( group = vars$group, visit = vars$visit, outcome = vars$outcome, covariates = \"BASVAL\" ) # Analyse MAR imputation with derived delta adjustment anaObj_MAR_delta <- analyse( res_delta_adjust$imputeObj_MAR, rbmi::ancova, delta = res_delta_adjust$delta_adjust, vars = vars_an )"},{"path":"/articles/CondMean_Inference.html","id":"pool-1","dir":"Articles","previous_headings":"4 Reference-based conditional mean imputation - information-anchored inference","what":"Pool","title":"rbmi: Inference with Conditional Mean Imputation","text":"can finally use pool() function extract treatment effect estimate (well estimated marginal means) visit apply jackknife variance estimator analysis estimates imputed leave-one-samples. gives estimated treatment effect 2.13 (95% CI -0.08 4.33) last visit associated p-value 0.058. Per construction delta-adjustment, point estimate identical frequentist analysis. However, standard error much larger (1.12 vs. 0.86). Indeed, information-anchored standard error (resulting inference) similar results Baysesian multiple imputation using Rubin’s rules standard error 1.13 reported quickstart vignette (vignette(topic = \"quickstart\", package = \"rbmi\"). note, shown e.g. Wolbers et al. (2022), hypothesis testing based information-anchored inference conservative, .e. actual type error much lower nominal value. Hence, confidence intervals \\(p\\)-values based information-anchored inference interpreted caution.","code":"poolObj_MAR_delta <- pool(anaObj_MAR_delta) poolObj_MAR_delta #> #> Pool Object #> ----------- #> Number of Results Combined: 1 + 172 #> Method: jackknife #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================== #> parameter est se lci uci pval #> -------------------------------------------------- #> trt_4 -0.092 0.695 -1.453 1.27 0.895 #> lsm_ref_4 -1.616 0.588 -2.767 -0.464 0.006 #> lsm_alt_4 -1.708 0.396 -2.484 -0.931 <0.001 #> trt_5 1.305 0.944 -0.545 3.156 0.167 #> lsm_ref_5 -4.133 0.738 -5.579 -2.687 <0.001 #> lsm_alt_5 -2.828 0.603 -4.01 -1.646 <0.001 #> trt_6 1.929 0.993 -0.018 3.876 0.052 #> lsm_ref_6 -6.088 0.758 -7.574 -4.602 <0.001 #> lsm_alt_6 -4.159 0.686 -5.504 -2.813 <0.001 #> trt_7 2.126 1.123 -0.076 4.327 0.058 #> lsm_ref_7 -6.965 0.85 -8.63 -5.299 <0.001 #> lsm_alt_7 -4.839 0.763 -6.335 -3.343 <0.001 #> --------------------------------------------------"},{"path":[]},{"path":"/articles/FAQ.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"rbmi: Frequently Asked Questions","text":"document provides answers common questions rbmi package. intended read rbmi: Quickstart vignette.","code":""},{"path":"/articles/FAQ.html","id":"is-rbmi-validated","dir":"Articles","previous_headings":"1 Introduction","what":"Is rbmi validated?","title":"rbmi: Frequently Asked Questions","text":"regards software pharmaceutical industry, validation act ensuring software meets needs requirements users given conditions actual use. FDA provides general principles guidance validation leaves individual sponsors define specific validation processes. Therefore, individual R package can claim ‘validated’ independently, validation depends entire software stack specific processes company. said, core components validation process design specification (software supposed ) well testing / test results demonstrate design specification met. rbmi, design specification documented extensively, macro level vignettes literature publications, micro level detailed function manuals. supported extensive suite unit integration tests, ensure software consistently produces correct output across wide range input scenarios. documentation test coverage enable rbmi easily installed integrated R system, alignment system’s broader validation process.","code":""},{"path":"/articles/FAQ.html","id":"how-do-the-methods-in-rbmi-compare-to-the-mixed-model-for-repeated-measures-mmrm-implemented-in-the-mmrm-package","dir":"Articles","previous_headings":"1 Introduction","what":"How do the methods in rbmi compare to the mixed model for repeated measures (MMRM) implemented in the mmrm package?","title":"rbmi: Frequently Asked Questions","text":"rbmi designed complement , occasionally, replace standard MMRM analyses clinical trials longitudinal endpoints. Strengths rbmi compared standard MMRM model : rbmi designed allow analyses fully aligned estimand definition. facilitate , implements methods range different missing data assumptions including standard missing--random (MAR), extended MAR (via inclusion time-varying covariates), reference-based missingness, missing--random random (NMAR; via \\(\\delta\\)-adjustments). contrast, standard MMRM model valid standard MAR assumption always plausible. example, standard MAR assumption rather implausible implementing treatment policy strategy intercurrent event “treatment discontinuation” substantial proportion subjects lost--follow-discontinuation. \\(\\delta\\)-adjustment methods implemented rbmi can used sensitivity analyses primary MMRM- rbmi-type analysis. Weaknesses rbmi compared standard MMRM model : MMRM models de-facto standard analysis method decade. rbmi currently less established. rbmi computationally intensive using requires careful planning.","code":""},{"path":"/articles/FAQ.html","id":"how-does-rbmi-compare-to-general-purpose-software-for-multiple-imputation-mi-such-as-mice","dir":"Articles","previous_headings":"1 Introduction","what":"How does rbmi compare to general-purpose software for multiple imputation (MI) such as mice?","title":"rbmi: Frequently Asked Questions","text":"rbmi covers “MMRM-type” settings, .e. settings single longitudinal continuous outcome may missing visits hence require imputation. settings, several advantages general-purpose MI software: rbmi supports imputation range different missing data assumptions whereas general-purpose MI software mostly focused MAR-based imputation. particular, unclear implement jump reference (JR) copy increments reference (CIR) methods software. rbmi interface fully streamlined setting arguably makes implementation straightforward general-purpose MI software. MICE algorithm stochastic inference always based Rubin’s rules. contrast, method “conditional mean imputation plus jackknifing” (method=\"method_condmean(type = \"jackknife\")\") rbmi require tuning parameters, fully deterministic, provides frequentist-consistent inference also reference-based imputations (Rubin’s rule conservative leading actual type error rates can far nominal values). However, rbmi much limited functionality general-purpose MI software.","code":""},{"path":"/articles/FAQ.html","id":"how-to-handle-missing-data-in-baseline-covariates-in-rbmi","dir":"Articles","previous_headings":"1 Introduction","what":"How to handle missing data in baseline covariates in rbmi?","title":"rbmi: Frequently Asked Questions","text":"rbmi support imputation missing baseline covariates. Therefore, missing baseline covariates need handled outside rbmi. best approach handling missing baseline covariates needs made case--case basis context randomized trials, relatively simple approach often sufficient (White Thompson (2005)).","code":""},{"path":"/articles/FAQ.html","id":"why-does-rbmi-by-default-use-an-ancova-analysis-model-and-not-an-mmrm-analysis-model","dir":"Articles","previous_headings":"1 Introduction","what":"Why does rbmi by default use an ANCOVA analysis model and not an MMRM analysis model?","title":"rbmi: Frequently Asked Questions","text":"theoretical justification conditional mean imputation method requires analysis model leads point estimator linear function outcome vector (Wolbers et al. (2022)). case ANCOVA general MMRM models. imputation methods, ANCOVA MMRM valid analysis methods. MMRM analysis model implemented providing custom analysis function analyse() function. expalanations, also cite end section 2.4 conditional mean imputation paper (Wolbers et al. (2022)): proof relies fact ANCOVA estimator linear function outcome vector. complete data, ANCOVA estimator leads identical parameter estimates MMRM model longitudinal outcomes arbitrary common covariance structure across treatment groups treatment--visit interactions well covariate--visit-interactions included analysis model covariates,17 (p. 197). Hence, proof also applies MMRM models. expect conditional mean imputation also valid general MMRM model used analysis involved argument required formally justify .","code":""},{"path":"/articles/FAQ.html","id":"how-can-i-analyse-the-change-from-baseline-in-the-analysis-model-when-imputation-was-done-on-the-original-outcomes","dir":"Articles","previous_headings":"1 Introduction","what":"How can I analyse the change-from-baseline in the analysis model when imputation was done on the original outcomes?","title":"rbmi: Frequently Asked Questions","text":"can achieved using custom analysis functions outlined Section 7 Advanced Vignette. e.g.","code":"ancova_modified <- function(data, ...) { data2 <- data %>% mutate(ENDPOINT = ENDPOINT - BASELINE) rbmi::ancova(data2, ...) } anaObj <- rbmi::analyse( imputeObj, ancova_modified, vars = vars )"},{"path":"/articles/advanced.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"rbmi: Advanced Functionality","text":"purpose vignette provide overview advanced features rbmi package. sections vignette relatively self-contained, .e. readers able jump directly section covers functionality interested .","code":""},{"path":"/articles/advanced.html","id":"sec:dataSimul","dir":"Articles","previous_headings":"","what":"Data simulation using function simulate_data()","title":"rbmi: Advanced Functionality","text":"order demonstrate advanced functions first create simulated dataset rbmi function simulate_data(). simulate_data() function generates data randomized clinical trial longitudinal continuous outcomes two different types intercurrent events (ICEs). One intercurrent event (ICE1) may thought discontinuation study treatment due study drug condition related (SDCR) reasons. event (ICE2) may thought discontinuation study treatment due study drug condition related (NSDCR) reasons. purpose vignette, simulate data similarly simulation study reported Wolbers et al. (2022) (though change simulation parameters) include one ICE type (ICE1). Specifically, simulate 1:1 randomized trial active drug (intervention) versus placebo (control) 100 subjects per group 6 post-baseline assessments (bi-monthly visits 12 months) following assumptions: mean outcome trajectory placebo group increases linearly 50 baseline (visit 0) 60 visit 6, .e. slope 10 points/year. mean outcome trajectory intervention group identical placebo group visit 2. visit 2 onward, slope decreases 50% 5 points/year. covariance structure baseline follow-values groups implied random intercept slope model standard deviation 5 intercept slope, correlation 0.25. addition, independent residual error standard deviation 2.5 added assessment. probability study drug discontinuation visit calculated according logistic model depends observed outcome visit. Specifically, visit-wise discontinuation probability 2% 3% control intervention group, respectively, specified case observed outcome equal 50 (mean value baseline). odds discontinuation simulated increase +10% +1 point increase observed outcome. Study drug discontinuation simulated effect mean trajectory placebo group. intervention group, subjects discontinue follow slope mean trajectory placebo group time point onward. compatible copy increments reference (CIR) assumption. Study drop-study drug discontinuation visit occurs probability 50% leading missing outcome data time point onward. function simulate_data() requires 3 arguments (see function documentation help(simulate_data) details): pars_c: simulation parameters control group pars_t: simulation parameters intervention group post_ice1_traj: Specifies observed outcomes ICE1 simulated , report data according specifications can simulated function simulate_data():","code":"library(rbmi) library(dplyr) library(ggplot2) library(purrr) set.seed(122) n <- 100 time <- c(0, 2, 4, 6, 8, 10, 12) # Mean trajectory control muC <- c(50.0, 51.66667, 53.33333, 55.0, 56.66667, 58.33333, 60.0) # Mean trajectory intervention muT <- c(50.0, 51.66667, 53.33333, 54.16667, 55.0, 55.83333, 56.66667) # Create Sigma sd_error <- 2.5 covRE <- rbind( c(25.0, 6.25), c(6.25, 25.0) ) Sigma <- cbind(1, time / 12) %*% covRE %*% rbind(1, time / 12) + diag(sd_error^2, nrow = length(time)) # Set probability of discontinuation probDisc_C <- 0.02 probDisc_T <- 0.03 or_outcome <- 1.10 # +1 point increase => +10% odds of discontinuation # Set drop-out rate following discontinuation prob_dropout <- 0.5 # Set simulation parameters of the control group parsC <- set_simul_pars( mu = muC, sigma = Sigma, n = n, prob_ice1 = probDisc_C, or_outcome_ice1 = or_outcome, prob_post_ice1_dropout = prob_dropout ) # Set simulation parameters of the intervention group parsT <- parsC parsT$mu <- muT parsT$prob_ice1 <- probDisc_T # Set assumption about post-ice trajectory post_ice_traj <- \"CIR\" # Simulate data data <- simulate_data( pars_c = parsC, pars_t = parsT, post_ice1_traj = post_ice_traj ) head(data) #> id visit group outcome_bl outcome_noICE ind_ice1 ind_ice2 dropout_ice1 #> 1 id_1 0 Control 57.32704 57.32704 0 0 0 #> 2 id_1 1 Control 57.32704 54.69751 1 0 1 #> 3 id_1 2 Control 57.32704 58.60702 1 0 1 #> 4 id_1 3 Control 57.32704 61.50119 1 0 1 #> 5 id_1 4 Control 57.32704 56.68363 1 0 1 #> 6 id_1 5 Control 57.32704 66.14799 1 0 1 #> outcome #> 1 57.32704 #> 2 NA #> 3 NA #> 4 NA #> 5 NA #> 6 NA # As a simple descriptive of the simulated data, summarize the number of subjects with ICEs and missing data data %>% group_by(id) %>% summarise( group = group[1], any_ICE = (any(ind_ice1 == 1)), any_NA = any(is.na(outcome))) %>% group_by(group) %>% summarise( subjects_with_ICE = sum(any_ICE), subjects_with_missings = sum(any_NA) ) #> # A tibble: 2 × 3 #> group subjects_with_ICE subjects_with_missings #> #> 1 Control 18 8 #> 2 Intervention 25 14"},{"path":"/articles/advanced.html","id":"sec:postICEobs","dir":"Articles","previous_headings":"","what":"Handling of observed post-ICE data in rbmi under reference-based imputation","title":"rbmi: Advanced Functionality","text":"rbmi always uses non-missing outcome data input data set, .e. data never overwritten imputation step removed analysis step. implies data considered irrelevant treatment effect estimation (e.g. data ICE estimand specified hypothetical strategy), data need removed input data set user prior calling rbmi functions. imputation missing random (MAR) strategy, observed outcome data also included fitting base imputation model. However, ICEs handled using reference-based imputation methods (CIR, CR, JR), rbmi excludes observed post-ICE data base imputation model. data excluded, base imputation model mistakenly estimate mean trajectories based mixture observed pre- post-ICE data relevant reference-based imputations. However, observed post-ICE data added back data set fitting base imputation model included subsequent imputation analysis steps. Post-ICE data control reference group also excluded base imputation model user specifies reference-based imputation strategy ICEs. ensures ICE impact data included base imputation model regardless whether ICE occurred control intervention group. hand, imputation reference group based MAR assumption even reference-based imputation methods may preferable settings include post-ICE data control group base imputation model. can implemented specifying MAR strategy ICE control group reference-based strategy ICE intervention group. use latter approach example . simulated trial data section 2 assumed outcomes intervention group observed ICE “treatment discontinuation” follow increments observed control group. Thus imputation missing data intervention group treatment discontinuation might performed reference-based copy increments reference (CIR) assumption. Specifically, implement estimator following assumptions: endpoint interest change outcome baseline visit. imputation model includes treatment group, (categorical) visit, treatment--visit interactions, baseline outcome, baseline outcome--visit interactions covariates. imputation model assumes common unstructured covariance matrix treatment groups control group, missing data imputed MAR whereas intervention group, missing post-ICE data imputed CIR assumption analysis model endpoint imputed datasets separate ANCOVA model visit treatment group primary covariate adjustment baseline outcome value. illustration purposes, chose MI based approximate Bayesian posterior draws 20 random imputations demanding computational perspective. practical applications, number random imputations may need increased. Moreover, imputations also supported rbmi. guidance regarding choice imputation approach, refer user comparison implemented approaches Section 3.9 “Statistical Specifications” vignette (vignette(\"stat_specs\", package = \"rbmi\")). first report code set variables imputation analysis models. yet familiar syntax, recommend first check “quickstart” vignette (vignette(\"quickstart\", package = \"rbmi\")). chosen imputation method can set function method_approxbayes() follows: can now sequentially call 4 key functions rbmi perform multiple imputation. Please note management observed post-ICE data performed without additional complexity user. draws() automatically excludes post-ICE data handled reference-based method (keeps post-ICE data handled using MAR) using information provided argument data_ice. impute() impute truly missing data data[[vars$outcome]]. last output gives estimated difference -4.537 (95% CI -6.420 -2.655) two groups last visit associated p-value lower 0.001.","code":"# Create data_ice including the subject's first visit affected by the ICE and the imputation strategy # Imputation strategy for post-ICE data is CIR in the intervention group and MAR for the control group # (note that ICEs which are handled using MAR are optional and do not impact the analysis # because imputation of missing data under MAR is the default) data_ice_CIR <- data %>% group_by(id) %>% filter(ind_ice1 == 1) %>% # select visits with ICEs mutate(strategy = ifelse(group == \"Intervention\", \"CIR\", \"MAR\")) %>% summarise( visit = visit[1], # Select first visit affected by the ICE strategy = strategy[1] ) # Compute endpoint of interest: change from baseline and # remove rows corresponding to baseline visits data <- data %>% filter(visit != 0) %>% mutate( change = outcome - outcome_bl, visit = factor(visit, levels = unique(visit)) ) # Define key variables for the imputation and analysis models vars <- set_vars( subjid = \"id\", visit = \"visit\", outcome = \"change\", group = \"group\", covariates = c(\"visit*outcome_bl\", \"visit*group\"), strategy = \"strategy\" ) vars_an <- vars vars_an$covariates <- \"outcome_bl\" method <- method_approxbayes(n_sample = 20) draw_obj <- draws( data = data, data_ice = data_ice_CIR, vars = vars, method = method, quiet = TRUE, ncores = 2 ) impute_obj_CIR <- impute( draw_obj, references = c(\"Control\" = \"Control\", \"Intervention\" = \"Control\") ) ana_obj_CIR <- analyse( impute_obj_CIR, vars = vars_an ) pool_obj_CIR <- pool(ana_obj_CIR) pool_obj_CIR #> #> Pool Object #> ----------- #> Number of Results Combined: 20 #> Method: rubin #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================== #> parameter est se lci uci pval #> -------------------------------------------------- #> trt_1 -0.486 0.512 -1.496 0.524 0.343 #> lsm_ref_1 2.62 0.362 1.907 3.333 <0.001 #> lsm_alt_1 2.133 0.362 1.42 2.847 <0.001 #> trt_2 -0.066 0.542 -1.135 1.004 0.904 #> lsm_ref_2 3.707 0.384 2.95 4.464 <0.001 #> lsm_alt_2 3.641 0.383 2.885 4.397 <0.001 #> trt_3 -1.782 0.607 -2.979 -0.585 0.004 #> lsm_ref_3 5.841 0.428 4.997 6.685 <0.001 #> lsm_alt_3 4.059 0.428 3.214 4.904 <0.001 #> trt_4 -2.518 0.692 -3.884 -1.152 <0.001 #> lsm_ref_4 7.656 0.492 6.685 8.627 <0.001 #> lsm_alt_4 5.138 0.488 4.176 6.1 <0.001 #> trt_5 -3.658 0.856 -5.346 -1.97 <0.001 #> lsm_ref_5 9.558 0.598 8.379 10.737 <0.001 #> lsm_alt_5 5.9 0.608 4.699 7.101 <0.001 #> trt_6 -4.537 0.954 -6.42 -2.655 <0.001 #> lsm_ref_6 11.048 0.666 9.735 12.362 <0.001 #> lsm_alt_6 6.511 0.674 5.181 7.841 <0.001 #> --------------------------------------------------"},{"path":"/articles/advanced.html","id":"efficiently-changing-reference-based-imputation-strategies","dir":"Articles","previous_headings":"","what":"Efficiently changing reference-based imputation strategies","title":"rbmi: Advanced Functionality","text":"draws() function far computationally intensive function rbmi. settings, may important explore impact change reference-based imputation strategy results. change affect imputation model affect subsequent imputation step. order allow changes imputation strategy without re-run draws() function, function impute() additional argument update_strategies. However, please note functionality comes important limitations: described beginning Section 3, post-ICE outcomes included input dataset base imputation model imputation method MAR excluded reference-based imputation methods (CIR, CR, JR). Therefore, updata_strategies applied imputation strategy changed MAR non-MAR strategy presence observed post-ICE outcomes. Similarly, change non-MAR strategy MAR triggers warning presence observed post-ICE outcomes base imputation model fitted relevant data MAR. Finally, update_strategies applied timing ICEs changed (argument data_ice) addition imputation strategy. example, described analysis copy increments reference (CIR) assumption previous section. Let’s assume want change strategy jump reference imputation strategy sensitivity analysis. can efficiently implemented using update_strategies follows: imputations jump reference assumption, get estimated difference -4.360 (95% CI -6.238 -2.482) two groups last visit associated p-value <0.001.","code":"# Change ICE strategy from CIR to JR data_ice_JR <- data_ice_CIR %>% mutate(strategy = ifelse(strategy == \"CIR\", \"JR\", strategy)) impute_obj_JR <- impute( draw_obj, references = c(\"Control\" = \"Control\", \"Intervention\" = \"Control\"), update_strategy = data_ice_JR ) ana_obj_JR <- analyse( impute_obj_JR, vars = vars_an ) pool_obj_JR <- pool(ana_obj_JR) pool_obj_JR #> #> Pool Object #> ----------- #> Number of Results Combined: 20 #> Method: rubin #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================== #> parameter est se lci uci pval #> -------------------------------------------------- #> trt_1 -0.485 0.513 -1.496 0.526 0.346 #> lsm_ref_1 2.609 0.363 1.892 3.325 <0.001 #> lsm_alt_1 2.124 0.361 1.412 2.836 <0.001 #> trt_2 -0.06 0.535 -1.115 0.995 0.911 #> lsm_ref_2 3.694 0.378 2.948 4.441 <0.001 #> lsm_alt_2 3.634 0.381 2.882 4.387 <0.001 #> trt_3 -1.767 0.598 -2.948 -0.587 0.004 #> lsm_ref_3 5.845 0.422 5.012 6.677 <0.001 #> lsm_alt_3 4.077 0.432 3.225 4.93 <0.001 #> trt_4 -2.529 0.686 -3.883 -1.175 <0.001 #> lsm_ref_4 7.637 0.495 6.659 8.614 <0.001 #> lsm_alt_4 5.108 0.492 4.138 6.078 <0.001 #> trt_5 -3.523 0.856 -5.212 -1.833 <0.001 #> lsm_ref_5 9.554 0.61 8.351 10.758 <0.001 #> lsm_alt_5 6.032 0.611 4.827 7.237 <0.001 #> trt_6 -4.36 0.952 -6.238 -2.482 <0.001 #> lsm_ref_6 11.003 0.676 9.669 12.337 <0.001 #> lsm_alt_6 6.643 0.687 5.287 8 <0.001 #> --------------------------------------------------"},{"path":"/articles/advanced.html","id":"imputation-under-mar-with-time-varying-covariates","dir":"Articles","previous_headings":"","what":"Imputation under MAR with time-varying covariates","title":"rbmi: Advanced Functionality","text":"rbmi package supports inclusion time-varying covariates imputation model. particularly useful implementing -called retrieved dropout models. vignette “Implementation retrieved-dropout models using rbmi” (vignette(topic = \"retrieved_dropout\", package = \"rbmi\")) contains examples models.","code":""},{"path":"/articles/advanced.html","id":"custom-imputation-strategies","dir":"Articles","previous_headings":"","what":"Custom imputation strategies","title":"rbmi: Advanced Functionality","text":"following imputation strategies implemented rbmi: Missing Random (MAR) Jump Reference (JR) Copy Reference (CR) Copy Increments Reference (CIR) Last Mean Carried Forward (LMCF) addition, rbmi allows user implement imputation strategy. , user needs three things: Define function implementing new imputation strategy. Specify patients use strategy data_ice dataset provided draws(). Provide imputation strategy function impute(). imputation strategy function must take 3 arguments (pars_group, pars_ref, index_mar) calculates mean covariance matrix subject’s marginal imputation distribution applied subjects strategy applies. , pars_group contains predicted mean trajectory (pars_group$mu, numeric vector) covariance matrix (pars_group$sigma) subject conditional assigned treatment group covariates. pars_ref contains corresponding mean trajectory covariance matrix conditional reference group subject’s covariates. index_mar logical vector specifies visit whether visit unaffected ICE handled using non-MAR method . example, user can check CIR strategy implemented looking function strategy_CIR(). illustrate simple example, assume new strategy implemented follows: - marginal mean imputation distribution equal marginal mean trajectory subject according assigned group covariates ICE. - ICE marginal mean imputation distribution equal average visit-wise marginal means based subjects covariates assigned group reference group, respectively. - covariance matrix marginal imputation distribution, covariance matrix assigned group taken. , first need define imputation function example coded follows: example showing use: incorporate rbmi, data_ice needs updated strategy AVG specified visits affected ICE. Additionally, function needs provided impute() via getStrategies() function shown : , analysis proceed calling analyse() pool() .","code":"strategy_CIR #> function (pars_group, pars_ref, index_mar) #> { #> if (all(index_mar)) { #> return(pars_group) #> } #> else if (all(!index_mar)) { #> return(pars_ref) #> } #> mu <- pars_group$mu #> last_mar <- which(!index_mar)[1] - 1 #> increments_from_last_mar_ref <- pars_ref$mu[!index_mar] - #> pars_ref$mu[last_mar] #> mu[!index_mar] <- mu[last_mar] + increments_from_last_mar_ref #> sigma <- compute_sigma(sigma_group = pars_group$sigma, sigma_ref = pars_ref$sigma, #> index_mar = index_mar) #> pars <- list(mu = mu, sigma = sigma) #> return(pars) #> } #> #> strategy_AVG <- function(pars_group, pars_ref, index_mar) { mu_mean <- (pars_group$mu + pars_ref$mu) / 2 x <- pars_group x$mu[!index_mar] <- mu_mean[!index_mar] return(x) } pars_group <- list( mu = c(1, 2, 3), sigma = as_vcov(c(1, 3, 2), c(0.4, 0.5, 0.45)) ) pars_ref <- list( mu = c(5, 6, 7), sigma = as_vcov(c(2, 1, 1), c(0.7, 0.8, 0.5)) ) index_mar <- c(TRUE, TRUE, FALSE) strategy_AVG(pars_group, pars_ref, index_mar) #> $mu #> [1] 1 2 5 #> #> $sigma #> [,1] [,2] [,3] #> [1,] 1.0 1.2 1.0 #> [2,] 1.2 9.0 2.7 #> [3,] 1.0 2.7 4.0 data_ice_AVG <- data_ice_CIR %>% mutate(strategy = ifelse(strategy == \"CIR\", \"AVG\", strategy)) draw_obj <- draws( data = data, data_ice = data_ice_AVG, vars = vars, method = method, quiet = TRUE ) impute_obj <- impute( draw_obj, references = c(\"Control\" = \"Control\", \"Intervention\" = \"Control\"), strategies = getStrategies(AVG = strategy_AVG) )"},{"path":"/articles/advanced.html","id":"custom-analysis-functions","dir":"Articles","previous_headings":"","what":"Custom analysis functions","title":"rbmi: Advanced Functionality","text":"default rbmi analyse data using ancova() function. analysis function fits ANCOVA model outcomes visit separately, returns “treatment effect” estimate well corresponding least square means group. user wants perform different analysis, return different statistics analysis, can done using custom analysis function. Beware validity conditional mean imputation method formally established analysis functions corresponding linear models (ANCOVA) caution required applying alternative analysis functions method. custom analysis function must take data.frame first argument return named list element list containing minimum point estimate, called est. method method_bayes() method_approxbayes(), list must additionally contain standard error (element se) , available, degrees freedom complete-data analysis model (element df). simple example, replicate ANCOVA analysis last visit CIR-based imputations user-defined analysis function : second example, assume supplementary analysis user wants compare proportion subjects change baseline >10 points last visit treatment groups baseline outcome additional covariate. lead following basic analysis function: Note user wants rbmi use normal approximation pooled test statistics, degrees freedom need set df = NA (per example). degrees freedom complete data test statistics known degrees freedom set df = Inf, rbmi pools degrees freedom across imputed datasets according rule Barnard Rubin (see “Statistical Specifications” vignette (vignette(\"stat_specs\", package = \"rbmi\") details). According rule, infinite degrees freedom complete data analysis imply pooled degrees freedom also infinite. Rather, case pooled degrees freedom (M-1)/lambda^2, M number imputations lambda fraction missing information (see Barnard Rubin (1999) details).","code":"compare_change_lastvisit <- function(data, ...) { fit <- lm(change ~ group + outcome_bl, data = data, subset = (visit == 6) ) res <- list( trt = list( est = coef(fit)[\"groupIntervention\"], se = sqrt(vcov(fit)[\"groupIntervention\", \"groupIntervention\"]), df = df.residual(fit) ) ) return(res) } ana_obj_CIR6 <- analyse( impute_obj_CIR, fun = compare_change_lastvisit, vars = vars_an ) pool(ana_obj_CIR6) #> #> Pool Object #> ----------- #> Number of Results Combined: 20 #> Method: rubin #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================= #> parameter est se lci uci pval #> ------------------------------------------------- #> trt -4.537 0.954 -6.42 -2.655 <0.001 #> ------------------------------------------------- compare_prop_lastvisit <- function(data, ...) { fit <- glm( I(change > 10) ~ group + outcome_bl, family = binomial(), data = data, subset = (visit == 6) ) res <- list( trt = list( est = coef(fit)[\"groupIntervention\"], se = sqrt(vcov(fit)[\"groupIntervention\", \"groupIntervention\"]), df = NA ) ) return(res) } ana_obj_prop <- analyse( impute_obj_CIR, fun = compare_prop_lastvisit, vars = vars_an ) pool_obj_prop <- pool(ana_obj_prop) pool_obj_prop #> #> Pool Object #> ----------- #> Number of Results Combined: 20 #> Method: rubin #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================= #> parameter est se lci uci pval #> ------------------------------------------------- #> trt -1.052 0.314 -1.667 -0.438 0.001 #> ------------------------------------------------- tmp <- as.data.frame(pool_obj_prop) %>% mutate( OR = exp(est), OR.lci = exp(lci), OR.uci = exp(uci) ) %>% select(parameter, OR, OR.lci, OR.uci) tmp #> parameter OR OR.lci OR.uci #> 1 trt 0.3491078 0.188807 0.6455073"},{"path":"/articles/advanced.html","id":"sensitivity-analyses-delta-adjustments-and-tipping-point-analyses","dir":"Articles","previous_headings":"","what":"Sensitivity analyses: Delta adjustments and tipping point analyses","title":"rbmi: Advanced Functionality","text":"Delta-adjustments used impute missing data missing random (NMAR) assumption. reflects belief unobserved outcomes systematically “worse” (“better”) “comparable” observed outcomes. extensive discussion delta-adjustment methods, refer Cro et al. (2020). rbmi, marginal delta-adjustment approach implemented. means delta-adjustment applied dataset data imputation MAR reference-based missing data assumptions prior analysis imputed data. Sensitivity analysis using delta-adjustments can therefore performed without re-fit imputation model. rbmi, implemented via delta argument analyse() function.","code":""},{"path":"/articles/advanced.html","id":"simple-delta-adjustments-and-tipping-point-analyses","dir":"Articles","previous_headings":"8 Sensitivity analyses: Delta adjustments and tipping point analyses","what":"Simple delta adjustments and tipping point analyses","title":"rbmi: Advanced Functionality","text":"delta argument analyse() allows users modify outcome variable prior analysis. , user needs provide data.frame contains columns subject visit (identify observation adjusted) plus additional column called delta specifies value added outcomes prior analysis. delta_template() function supports user creating data.frame: creates skeleton data.frame containing one row per subject visit value delta set 0 observations: Note output delta_template() contains additional information can used properly re-set variable delta. example, assume user wants implement delta-adjustment imputed values CIR described section 3. Specifically, assume fixed “worsening adjustment” +5 points applied imputed values regardless treatment group. programmed follows: approach can used implement tipping point analysis. , apply different delta-adjustments imputed data control intervention group, respectively. Assume delta-adjustments less -5 points +15 points considered implausible clinical perspective. Therefore, vary delta-values group -5 +15 points investigate delta combinations lead “tipping” primary analysis result, defined analysis p-value \\(\\geq 0.05\\). According analysis, significant test result primary analysis CIR tipped non-significant result rather extreme delta-adjustments. Please note real analysis recommended use smaller step size grid used .","code":"dat_delta <- delta_template(imputations = impute_obj_CIR) head(dat_delta) #> id visit group is_mar is_missing is_post_ice strategy delta #> 1 id_1 1 Control TRUE TRUE TRUE MAR 0 #> 2 id_1 2 Control TRUE TRUE TRUE MAR 0 #> 3 id_1 3 Control TRUE TRUE TRUE MAR 0 #> 4 id_1 4 Control TRUE TRUE TRUE MAR 0 #> 5 id_1 5 Control TRUE TRUE TRUE MAR 0 #> 6 id_1 6 Control TRUE TRUE TRUE MAR 0 # Set delta-value to 5 for all imputed (previously missing) outcomes and 0 for all other outcomes dat_delta <- delta_template(imputations = impute_obj_CIR) %>% mutate(delta = is_missing * 5) # Repeat the analyses with the delta-adjusted values and pool results ana_delta <- analyse( impute_obj_CIR, delta = dat_delta, vars = vars_an ) pool(ana_delta) #> #> Pool Object #> ----------- #> Number of Results Combined: 20 #> Method: rubin #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================== #> parameter est se lci uci pval #> -------------------------------------------------- #> trt_1 -0.482 0.524 -1.516 0.552 0.359 #> lsm_ref_1 2.718 0.37 1.987 3.448 <0.001 #> lsm_alt_1 2.235 0.37 1.505 2.966 <0.001 #> trt_2 -0.016 0.56 -1.12 1.089 0.978 #> lsm_ref_2 3.907 0.396 3.125 4.688 <0.001 #> lsm_alt_2 3.891 0.395 3.111 4.671 <0.001 #> trt_3 -1.684 0.641 -2.948 -0.42 0.009 #> lsm_ref_3 6.092 0.452 5.201 6.983 <0.001 #> lsm_alt_3 4.408 0.452 3.515 5.3 <0.001 #> trt_4 -2.359 0.741 -3.821 -0.897 0.002 #> lsm_ref_4 7.951 0.526 6.913 8.99 <0.001 #> lsm_alt_4 5.593 0.522 4.563 6.623 <0.001 #> trt_5 -3.34 0.919 -5.153 -1.526 <0.001 #> lsm_ref_5 9.899 0.643 8.631 11.168 <0.001 #> lsm_alt_5 6.559 0.653 5.271 7.848 <0.001 #> trt_6 -4.21 1.026 -6.236 -2.184 <0.001 #> lsm_ref_6 11.435 0.718 10.019 12.851 <0.001 #> lsm_alt_6 7.225 0.725 5.793 8.656 <0.001 #> -------------------------------------------------- perform_tipp_analysis <- function(delta_control, delta_intervention, cl) { # Derive delta offset based on control and intervention specific deltas delta_df <- delta_df_init %>% mutate( delta_ctl = (group == \"Control\") * is_missing * delta_control, delta_int = (group == \"Intervention\") * is_missing * delta_intervention, delta = delta_ctl + delta_int ) ana_delta <- analyse( impute_obj_CIR, fun = compare_change_lastvisit, vars = vars_an, delta = delta_df, ncores = cl ) pool_delta <- as.data.frame(pool(ana_delta)) list( trt_effect_6 = pool_delta[[\"est\"]], pval_6 = pool_delta[[\"pval\"]] ) } # Get initial delta template delta_df_init <- delta_template(impute_obj_CIR) tipp_frame_grid <- expand.grid( delta_control = seq(-5, 15, by = 2), delta_intervention = seq(-5, 15, by = 2) ) %>% as_tibble() # parallelise to speed up computation cl <- make_rbmi_cluster(2) tipp_frame <- tipp_frame_grid %>% mutate( results_list = map2(delta_control, delta_intervention, perform_tipp_analysis, cl = cl), trt_effect_6 = map_dbl(results_list, \"trt_effect_6\"), pval_6 = map_dbl(results_list, \"pval_6\") ) %>% select(-results_list) %>% mutate( pval = cut( pval_6, c(0, 0.001, 0.01, 0.05, 0.2, 1), right = FALSE, labels = c(\"<0.001\", \"0.001 - <0.01\", \"0.01- <0.05\", \"0.05 - <0.20\", \">= 0.20\") ) ) # Close cluster when done with it parallel::stopCluster(cl) # Show delta values which lead to non-significant analysis results tipp_frame %>% filter(pval_6 >= 0.05) #> # A tibble: 3 × 5 #> delta_control delta_intervention trt_effect_6 pval_6 pval #> #> 1 -5 15 -1.99 0.0935 0.05 - <0.20 #> 2 -3 15 -2.15 0.0704 0.05 - <0.20 #> 3 -1 15 -2.31 0.0527 0.05 - <0.20 ggplot(tipp_frame, aes(delta_control, delta_intervention, fill = pval)) + geom_raster() + scale_fill_manual(values = c(\"darkgreen\", \"lightgreen\", \"lightyellow\", \"orange\", \"red\"))"},{"path":"/articles/advanced.html","id":"more-flexible-delta-adjustments-using-the-dlag-and-delta-arguments-of-delta_template","dir":"Articles","previous_headings":"8 Sensitivity analyses: Delta adjustments and tipping point analyses","what":"More flexible delta-adjustments using the dlag and delta arguments of delta_template()","title":"rbmi: Advanced Functionality","text":"far, discussed simple delta arguments add value imputed values. However, user may want apply flexible delta-adjustments missing values intercurrent event (ICE) vary magnitude delta adjustment depending far away visit question ICE visit. facilitate creation flexible delta-adjustments, delta_template() function two optional additional arguments delta dlag. delta argument specifies default amount delta applied post-ICE visit, whilst dlag specifies scaling coefficient applied based upon visits proximity first visit affected ICE. default, delta added unobserved (.e. imputed) post-ICE outcomes can changed setting optional argument missing_only = FALSE. usage delta dlag arguments best illustrated examples: Assume setting 4 visits user specified delta = c(5,6,7,8) dlag=c(1,2,3,4). subject first visit affected ICE visit 2, values delta dlag imply following delta offset: , subject delta offset 0 applied visit v1, 6 visit v2, 20 visit v3 44 visit v4. Assume instead, subject’s first visit affected ICE visit 3. , values delta dlag imply following delta offset: apply constant delta value +5 visits affected ICE regardless proximity first ICE visit, one set delta = c(5,5,5,5) dlag = c(1,0,0,0). Alternatively, may straightforward setting call delta_template() function without delta dlag arguments overwrite delta column resulting data.frame described previous section (additionally relying is_post_ice variable). Another way using arguments set delta difference time visits dlag amount delta per unit time. example, let’s say visits occur weeks 1, 5, 6 9 want delta 3 applied week ICE. simplicity, assume ICE occurs immediately subject’s last visit affected ICE. achieved setting delta = c(1,4,1,3) (difference weeks visit) dlag = c(3, 3, 3, 3). Assume subject’s first visit affected ICE visit v2, values delta dlag imply following delta offsets: wrap , show action simulated dataset section 2 imputed datasets based CIR assumption section 3. simulation setting specified follow-visits months 2, 4, 6, 8, 10, 12. Assume want apply delta-adjustment 1 every month ICE unobserved post-ICE visits intervention group . (E.g. ICE occurred immediately month 4 visit, total delta applied missing value month 10 visit 6.) program , first use delta dlag arguments delta_template() set corresponding template data.frame: Next, can use additional metadata variables provided delta_template() manually reset delta values control group back 0: Finally, can use delta data.frame apply desired delta offset analysis:","code":"v1 v2 v3 v4 -------------- 5 6 7 8 # delta assigned to each visit 0 1 2 3 # scaling starting from the first visit after the subjects ICE -------------- 0 6 14 24 # delta * scaling -------------- 0 6 20 44 # cumulative sum (i.e. delta) to be applied to each visit v1 v2 v3 v4 -------------- 5 6 7 8 # delta assigned to each visit 0 0 1 2 # scaling starting from the first visit after the subjects ICE -------------- 0 0 7 16 # delta * scaling -------------- 0 0 7 23 # cumulative sum (i.e. delta) to be applied to each visit v1 v2 v3 v4 -------------- 1 4 1 3 # delta assigned to each visit 0 3 3 3 # scaling starting from the first visit after the subjects ICE -------------- 0 12 3 9 # delta * scaling -------------- 0 12 15 24 # cumulative sum (i.e. delta) to be applied to each visit delta_df <- delta_template( impute_obj_CIR, delta = c(2, 2, 2, 2, 2, 2), dlag = c(1, 1, 1, 1, 1, 1) ) head(delta_df) #> id visit group is_mar is_missing is_post_ice strategy delta #> 1 id_1 1 Control TRUE TRUE TRUE MAR 2 #> 2 id_1 2 Control TRUE TRUE TRUE MAR 4 #> 3 id_1 3 Control TRUE TRUE TRUE MAR 6 #> 4 id_1 4 Control TRUE TRUE TRUE MAR 8 #> 5 id_1 5 Control TRUE TRUE TRUE MAR 10 #> 6 id_1 6 Control TRUE TRUE TRUE MAR 12 delta_df2 <- delta_df %>% mutate(delta = if_else(group == \"Control\", 0, delta)) head(delta_df2) #> id visit group is_mar is_missing is_post_ice strategy delta #> 1 id_1 1 Control TRUE TRUE TRUE MAR 0 #> 2 id_1 2 Control TRUE TRUE TRUE MAR 0 #> 3 id_1 3 Control TRUE TRUE TRUE MAR 0 #> 4 id_1 4 Control TRUE TRUE TRUE MAR 0 #> 5 id_1 5 Control TRUE TRUE TRUE MAR 0 #> 6 id_1 6 Control TRUE TRUE TRUE MAR 0 ana_delta <- analyse(impute_obj_CIR, delta = delta_df2, vars = vars_an) pool(ana_delta) #> #> Pool Object #> ----------- #> Number of Results Combined: 20 #> Method: rubin #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================== #> parameter est se lci uci pval #> -------------------------------------------------- #> trt_1 -0.446 0.514 -1.459 0.567 0.386 #> lsm_ref_1 2.62 0.363 1.904 3.335 <0.001 #> lsm_alt_1 2.173 0.363 1.458 2.889 <0.001 #> trt_2 0.072 0.546 -1.006 1.15 0.895 #> lsm_ref_2 3.708 0.387 2.945 4.471 <0.001 #> lsm_alt_2 3.78 0.386 3.018 4.542 <0.001 #> trt_3 -1.507 0.626 -2.743 -0.272 0.017 #> lsm_ref_3 5.844 0.441 4.973 6.714 <0.001 #> lsm_alt_3 4.336 0.442 3.464 5.209 <0.001 #> trt_4 -2.062 0.731 -3.504 -0.621 0.005 #> lsm_ref_4 7.658 0.519 6.634 8.682 <0.001 #> lsm_alt_4 5.596 0.515 4.58 6.612 <0.001 #> trt_5 -2.938 0.916 -4.746 -1.13 0.002 #> lsm_ref_5 9.558 0.641 8.293 10.823 <0.001 #> lsm_alt_5 6.62 0.651 5.335 7.905 <0.001 #> trt_6 -3.53 1.045 -5.591 -1.469 0.001 #> lsm_ref_6 11.045 0.73 9.604 12.486 <0.001 #> lsm_alt_6 7.515 0.738 6.058 8.971 <0.001 #> --------------------------------------------------"},{"path":[]},{"path":"/articles/quickstart.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"rbmi: Quickstart","text":"purpose vignette provide 15 minute quickstart guide core functions rbmi package. rbmi package consists 4 core functions (plus several helper functions) typically called sequence: draws() - fits imputation models stores parameters impute() - creates multiple imputed datasets analyse() - analyses multiple imputed datasets pool() - combines analysis results across imputed datasets single statistic example vignette makes use Bayesian multiuple imputation; functionality requires installation suggested package rstan.","code":"install.packages(\"rstan\")"},{"path":"/articles/quickstart.html","id":"the-data","dir":"Articles","previous_headings":"","what":"The Data","title":"rbmi: Quickstart","text":"use publicly available example dataset antidepressant clinical trial active drug versus placebo. relevant endpoint Hamilton 17-item depression rating scale (HAMD17) assessed baseline weeks 1, 2, 4, 6. Study drug discontinuation occurred 24% subjects active drug 26% subjects placebo. data study drug discontinuation missing single additional intermittent missing observation. consider imputation model mean change baseline HAMD17 score outcome (variable CHANGE dataset). following covariates included imputation model: treatment group (THERAPY), (categorical) visit (VISIT), treatment--visit interactions, baseline HAMD17 score (BASVAL), baseline HAMD17 score--visit interactions. common unstructured covariance matrix structure assumed groups. analysis model ANCOVA model treatment group primary factor adjustment baseline HAMD17 score. rbmi expects input dataset complete; , must one row per subject visit. Missing outcome values coded NA, missing covariate values allowed. dataset incomplete, expand_locf() helper function can used add missing rows, using LOCF imputation carry forward observed baseline covariate values visits missing outcomes. Rows corresponding missing outcomes present antidepressant trial dataset. address therefore use expand_locf() function follows:","code":"library(rbmi) library(dplyr) #> #> Attaching package: 'dplyr' #> The following objects are masked from 'package:stats': #> #> filter, lag #> The following objects are masked from 'package:base': #> #> intersect, setdiff, setequal, union data(\"antidepressant_data\") dat <- antidepressant_data # Use expand_locf to add rows corresponding to visits with missing outcomes to the dataset dat <- expand_locf( dat, PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT VISIT = levels(dat$VISIT), vars = c(\"BASVAL\", \"THERAPY\"), # fill with LOCF BASVAL and THERAPY group = c(\"PATIENT\"), order = c(\"PATIENT\", \"VISIT\") )"},{"path":"/articles/quickstart.html","id":"draws","dir":"Articles","previous_headings":"","what":"Draws","title":"rbmi: Quickstart","text":"draws() function fits imputation models stores corresponding parameter estimates Bayesian posterior parameter draws. three main inputs draws() function : data - primary longitudinal data.frame containing outcome variable covariates. data_ice - data.frame specifies first visit affected intercurrent event (ICE) imputation strategy handling missing outcome data ICE. one ICE imputed non-MAR strategy allowed per subject. method - statistical method used fit imputation models create imputed datasets. antidepressant trial data, dataset data_ice provided. However, can derived , dataset, subject’s first visit affected ICE “study drug discontinuation” corresponds first terminal missing observation. first derive dateset data_ice create 150 Bayesian posterior draws imputation model parameters. example, assume imputation strategy ICE Jump Reference (JR) subjects 150 multiple imputed datasets using Bayesian posterior draws imputation model created. Note use set_vars() specifies names key variables within dataset imputation model. Additionally, note whilst vars$group vars$visit added terms imputation model default, interaction , thus inclusion group * visit list covariates. Available imputation methods include: Bayesian multiple imputation - method_bayes() Approximate Bayesian multiple imputation - method_approxbayes() Conditional mean imputation (bootstrap) - method_condmean(type = \"bootstrap\") Conditional mean imputation (jackknife) - method_condmean(type = \"jackknife\") Bootstrapped multiple imputation - method = method_bmlmi() comparison methods, refer stat_specs vignette (Section 3.10). “statistical specifications” vignette (Section 3.10): vignette(\"stat_specs\",package=\"rbmi\"). Available imputation strategies include: Missing Random - \"MAR\" Jump Reference - \"JR\" Copy Reference - \"CR\" Copy Increments Reference - \"CIR\" Last Mean Carried Forward - \"LMCF\"","code":"# create data_ice and set the imputation strategy to JR for # each patient with at least one missing observation dat_ice <- dat %>% arrange(PATIENT, VISIT) %>% filter(is.na(CHANGE)) %>% group_by(PATIENT) %>% slice(1) %>% ungroup() %>% select(PATIENT, VISIT) %>% mutate(strategy = \"JR\") # In this dataset, subject 3618 has an intermittent missing values which does not correspond # to a study drug discontinuation. We therefore remove this subject from `dat_ice`. # (In the later imputation step, it will automatically be imputed under the default MAR assumption.) dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),] dat_ice #> # A tibble: 43 × 3 #> PATIENT VISIT strategy #> #> 1 1513 5 JR #> 2 1514 5 JR #> 3 1517 5 JR #> 4 1804 7 JR #> 5 2104 7 JR #> 6 2118 5 JR #> 7 2218 6 JR #> 8 2230 6 JR #> 9 2721 5 JR #> 10 2729 5 JR #> # ℹ 33 more rows # Define the names of key variables in our dataset and # the covariates included in the imputation model using `set_vars()` # Note that the covariates argument can also include interaction terms vars <- set_vars( outcome = \"CHANGE\", visit = \"VISIT\", subjid = \"PATIENT\", group = \"THERAPY\", covariates = c(\"BASVAL*VISIT\", \"THERAPY*VISIT\") ) # Define which imputation method to use (here: Bayesian multiple imputation with 150 imputed datsets) method <- method_bayes( burn_in = 200, burn_between = 5, n_samples = 150 ) # Create samples for the imputation parameters by running the draws() function set.seed(987) drawObj <- draws( data = dat, data_ice = dat_ice, vars = vars, method = method, quiet = TRUE ) drawObj #> #> Draws Object #> ------------ #> Number of Samples: 150 #> Number of Failed Samples: 0 #> Model Formula: CHANGE ~ 1 + THERAPY + VISIT + BASVAL * VISIT + THERAPY * VISIT #> Imputation Type: random #> Method: #> name: Bayes #> burn_in: 200 #> burn_between: 5 #> same_cov: TRUE #> n_samples: 150"},{"path":"/articles/quickstart.html","id":"impute","dir":"Articles","previous_headings":"","what":"Impute","title":"rbmi: Quickstart","text":"next step use parameters imputation model generate imputed datasets. done via impute() function. function two key inputs: imputation model output draws() reference groups relevant reference-based imputation methods. ’s usage thus: instance, specifying PLACEBO group reference group well DRUG group (standard imputation using reference-based methods). Generally speaking, need see directly interact imputed datasets. However, wish inspect , can extracted imputation object using extract_imputed_dfs() helper function, .e.: Note case method_bayes() method_approxbayes(), imputed datasets correspond random imputations original dataset. method_condmean(), first imputed dataset always correspond completed original dataset containing subjects. method_condmean(type=\"jackknife\"), remaining datasets correspond conditional mean imputations leave-one-subject-datasets, whereas method_condmean(type=\"bootstrap\"), subsequent dataset corresponds conditional mean imputation bootstrapped datasets. method_bmlmi(), imputed datasets correspond sets random imputations bootstrapped datasets.","code":"imputeObj <- impute( drawObj, references = c(\"DRUG\" = \"PLACEBO\", \"PLACEBO\" = \"PLACEBO\") ) imputeObj #> #> Imputation Object #> ----------------- #> Number of Imputed Datasets: 150 #> Fraction of Missing Data (Original Dataset): #> 4: 0% #> 5: 8% #> 6: 13% #> 7: 25% #> References: #> DRUG -> PLACEBO #> PLACEBO -> PLACEBO imputed_dfs <- extract_imputed_dfs(imputeObj) head(imputed_dfs[[10]], 12) # first 12 rows of 10th imputed dataset #> PATIENT HAMATOTL PGIIMP RELDAYS VISIT THERAPY GENDER POOLINV BASVAL #> 1 new_pt_1 21 2 7 4 DRUG F 006 32 #> 2 new_pt_1 19 2 14 5 DRUG F 006 32 #> 3 new_pt_1 21 3 28 6 DRUG F 006 32 #> 4 new_pt_1 17 4 42 7 DRUG F 006 32 #> 5 new_pt_2 18 3 7 4 PLACEBO F 006 14 #> 6 new_pt_2 18 2 15 5 PLACEBO F 006 14 #> 7 new_pt_2 14 3 29 6 PLACEBO F 006 14 #> 8 new_pt_2 8 2 42 7 PLACEBO F 006 14 #> 9 new_pt_3 18 3 7 4 DRUG F 006 21 #> 10 new_pt_3 17 3 14 5 DRUG F 006 21 #> 11 new_pt_3 12 3 28 6 DRUG F 006 21 #> 12 new_pt_3 9 3 44 7 DRUG F 006 21 #> HAMDTL17 CHANGE #> 1 21 -11 #> 2 20 -12 #> 3 19 -13 #> 4 17 -15 #> 5 11 -3 #> 6 14 0 #> 7 9 -5 #> 8 5 -9 #> 9 20 -1 #> 10 18 -3 #> 11 16 -5 #> 12 13 -8"},{"path":"/articles/quickstart.html","id":"analyse","dir":"Articles","previous_headings":"","what":"Analyse","title":"rbmi: Quickstart","text":"next step run analysis model imputed dataset. done defining analysis function calling analyse() apply function imputed dataset. vignette use ancova() function provided rbmi package fits separate ANCOVA model outcomes visit returns treatment effect estimate corresponding least square means group per visit. Note , similar draws(), ancova() function uses set_vars() function determines names key variables within data covariates (addition treatment group) analysis model adjusted. Please also note names analysis estimates contain “ref” “alt” refer two treatment arms. particular “ref” refers first factor level vars$group necessarily coincide control arm. example, since levels(dat[[vars$group]]) = c(\"DRUG\", PLACEBO), results associated “ref” correspond intervention arm, associated “alt” correspond control arm. Additionally, can use delta argument analyse() perform delta adjustments imputed datasets prior analysis. brief, implemented specifying data.frame contains amount adjustment added longitudinal outcome subject visit, .e.  data.frame must contain columns subjid, visit, delta. appreciated carrying procedure potentially tedious, therefore delta_template() helper function provided simplify . particular, delta_template() returns shell data.frame delta-adjustment set 0 patients. Additionally delta_template() adds several meta-variables onto shell data.frame can used manual derivation manipulation delta-adjustment. example lets say want add delta-value 5 imputed values (.e. values missing original dataset) drug arm. implemented follows:","code":"anaObj <- analyse( imputeObj, ancova, vars = set_vars( subjid = \"PATIENT\", outcome = \"CHANGE\", visit = \"VISIT\", group = \"THERAPY\", covariates = c(\"BASVAL\") ) ) anaObj #> #> Analysis Object #> --------------- #> Number of Results: 150 #> Analysis Function: ancova #> Delta Applied: FALSE #> Analysis Estimates: #> trt_4 #> lsm_ref_4 #> lsm_alt_4 #> trt_5 #> lsm_ref_5 #> lsm_alt_5 #> trt_6 #> lsm_ref_6 #> lsm_alt_6 #> trt_7 #> lsm_ref_7 #> lsm_alt_7 # For reference show the additional meta variables provided delta_template(imputeObj) %>% as_tibble() #> # A tibble: 688 × 8 #> PATIENT VISIT THERAPY is_mar is_missing is_post_ice strategy delta #> #> 1 1503 4 DRUG TRUE FALSE FALSE NA 0 #> 2 1503 5 DRUG TRUE FALSE FALSE NA 0 #> 3 1503 6 DRUG TRUE FALSE FALSE NA 0 #> 4 1503 7 DRUG TRUE FALSE FALSE NA 0 #> 5 1507 4 PLACEBO TRUE FALSE FALSE NA 0 #> 6 1507 5 PLACEBO TRUE FALSE FALSE NA 0 #> 7 1507 6 PLACEBO TRUE FALSE FALSE NA 0 #> 8 1507 7 PLACEBO TRUE FALSE FALSE NA 0 #> 9 1509 4 DRUG TRUE FALSE FALSE NA 0 #> 10 1509 5 DRUG TRUE FALSE FALSE NA 0 #> # ℹ 678 more rows delta_df <- delta_template(imputeObj) %>% as_tibble() %>% mutate(delta = if_else(THERAPY == \"DRUG\" & is_missing , 5, 0)) %>% select(PATIENT, VISIT, delta) delta_df #> # A tibble: 688 × 3 #> PATIENT VISIT delta #> #> 1 1503 4 0 #> 2 1503 5 0 #> 3 1503 6 0 #> 4 1503 7 0 #> 5 1507 4 0 #> 6 1507 5 0 #> 7 1507 6 0 #> 8 1507 7 0 #> 9 1509 4 0 #> 10 1509 5 0 #> # ℹ 678 more rows anaObj_delta <- analyse( imputeObj, ancova, delta = delta_df, vars = set_vars( subjid = \"PATIENT\", outcome = \"CHANGE\", visit = \"VISIT\", group = \"THERAPY\", covariates = c(\"BASVAL\") ) )"},{"path":"/articles/quickstart.html","id":"pool","dir":"Articles","previous_headings":"","what":"Pool","title":"rbmi: Quickstart","text":"Finally, pool() function can used summarise analysis results across multiple imputed datasets provide overall statistic standard error, confidence intervals p-value hypothesis test null hypothesis effect equal 0. Note pooling method automatically derived based method specified original call draws(): method_bayes() method_approxbayes() pooling inference based Rubin’s rules. method_condmean(type = \"bootstrap\") inference either based normal approximation using bootstrap standard error (pool(..., type = \"normal\")) bootstrap percentiles (pool(..., type = \"percentile\")). method_condmean(type = \"jackknife\") inference based normal approximation using jackknife estimate standard error. method = method_bmlmi() inference according methods described von Hippel Bartlett (see stat_specs vignette details) Since used Bayesian multiple imputation vignette, pool() function automatically use Rubin’s rules. table values shown print message poolObj can also extracted using .data.frame() function: outputs gives estimated difference 2.180 (95% CI -0.080 4.439) two groups last visit associated p-value 0.059.","code":"poolObj <- pool( anaObj, conf.level = 0.95, alternative = \"two.sided\" ) poolObj #> #> Pool Object #> ----------- #> Number of Results Combined: 150 #> Method: rubin #> Confidence Level: 0.95 #> Alternative: two.sided #> #> Results: #> #> ================================================== #> parameter est se lci uci pval #> -------------------------------------------------- #> trt_4 -0.092 0.683 -1.439 1.256 0.893 #> lsm_ref_4 -1.616 0.486 -2.576 -0.656 0.001 #> lsm_alt_4 -1.708 0.475 -2.645 -0.77 <0.001 #> trt_5 1.332 0.925 -0.495 3.159 0.152 #> lsm_ref_5 -4.157 0.661 -5.462 -2.852 <0.001 #> lsm_alt_5 -2.825 0.646 -4.1 -1.55 <0.001 #> trt_6 1.927 1.005 -0.059 3.913 0.057 #> lsm_ref_6 -6.097 0.721 -7.522 -4.671 <0.001 #> lsm_alt_6 -4.17 0.7 -5.553 -2.786 <0.001 #> trt_7 2.18 1.143 -0.08 4.439 0.059 #> lsm_ref_7 -6.994 0.826 -8.628 -5.36 <0.001 #> lsm_alt_7 -4.815 0.791 -6.379 -3.25 <0.001 #> -------------------------------------------------- as.data.frame(poolObj) #> parameter est se lci uci pval #> 1 trt_4 -0.09180645 0.6826279 -1.43949684 1.2558839 8.931772e-01 #> 2 lsm_ref_4 -1.61581996 0.4862316 -2.57577141 -0.6558685 1.093708e-03 #> 3 lsm_alt_4 -1.70762640 0.4749573 -2.64531931 -0.7699335 4.262148e-04 #> 4 trt_5 1.33217342 0.9248889 -0.49452471 3.1588715 1.517381e-01 #> 5 lsm_ref_5 -4.15685743 0.6607638 -5.46196249 -2.8517524 2.982856e-09 #> 6 lsm_alt_5 -2.82468402 0.6455730 -4.09978956 -1.5495785 2.197441e-05 #> 7 trt_6 1.92723926 1.0050687 -0.05860912 3.9130876 5.706399e-02 #> 8 lsm_ref_6 -6.09679600 0.7213490 -7.52226719 -4.6713248 2.489617e-14 #> 9 lsm_alt_6 -4.16955674 0.7003707 -5.55341225 -2.7857012 1.784937e-08 #> 10 trt_7 2.17964370 1.1426199 -0.07965819 4.4389456 5.852211e-02 #> 11 lsm_ref_7 -6.99418014 0.8260358 -8.62803604 -5.3603242 4.048404e-14 #> 12 lsm_alt_7 -4.81453644 0.7913711 -6.37916058 -3.2499123 1.067031e-08"},{"path":"/articles/quickstart.html","id":"code","dir":"Articles","previous_headings":"","what":"Code","title":"rbmi: Quickstart","text":"report code presented vignette.","code":"library(rbmi) library(dplyr) data(\"antidepressant_data\") dat <- antidepressant_data # Use expand_locf to add rows corresponding to visits with missing outcomes to the dataset dat <- expand_locf( dat, PATIENT = levels(dat$PATIENT), # expand by PATIENT and VISIT VISIT = levels(dat$VISIT), vars = c(\"BASVAL\", \"THERAPY\"), # fill with LOCF BASVAL and THERAPY group = c(\"PATIENT\"), order = c(\"PATIENT\", \"VISIT\") ) # Create data_ice and set the imputation strategy to JR for # each patient with at least one missing observation dat_ice <- dat %>% arrange(PATIENT, VISIT) %>% filter(is.na(CHANGE)) %>% group_by(PATIENT) %>% slice(1) %>% ungroup() %>% select(PATIENT, VISIT) %>% mutate(strategy = \"JR\") # In this dataset, subject 3618 has an intermittent missing values which does not correspond # to a study drug discontinuation. We therefore remove this subject from `dat_ice`. # (In the later imputation step, it will automatically be imputed under the default MAR assumption.) dat_ice <- dat_ice[-which(dat_ice$PATIENT == 3618),] # Define the names of key variables in our dataset using `set_vars()` # and the covariates included in the imputation model # Note that the covariates argument can also include interaction terms vars <- set_vars( outcome = \"CHANGE\", visit = \"VISIT\", subjid = \"PATIENT\", group = \"THERAPY\", covariates = c(\"BASVAL*VISIT\", \"THERAPY*VISIT\") ) # Define which imputation method to use (here: Bayesian multiple imputation with 150 imputed datsets) method <- method_bayes( burn_in = 200, burn_between = 5, n_samples = 150 ) # Create samples for the imputation parameters by running the draws() function set.seed(987) drawObj <- draws( data = dat, data_ice = dat_ice, vars = vars, method = method, quiet = TRUE ) # Impute the data imputeObj <- impute( drawObj, references = c(\"DRUG\" = \"PLACEBO\", \"PLACEBO\" = \"PLACEBO\") ) # Fit the analysis model on each imputed dataset anaObj <- analyse( imputeObj, ancova, vars = set_vars( subjid = \"PATIENT\", outcome = \"CHANGE\", visit = \"VISIT\", group = \"THERAPY\", covariates = c(\"BASVAL\") ) ) # Apply a delta adjustment # Add a delta-value of 5 to all imputed values (i.e. those values # which were missing in the original dataset) in the drug arm. delta_df <- delta_template(imputeObj) %>% as_tibble() %>% mutate(delta = if_else(THERAPY == \"DRUG\" & is_missing , 5, 0)) %>% select(PATIENT, VISIT, delta) # Repeat the analyses with the adjusted values anaObj_delta <- analyse( imputeObj, ancova, delta = delta_df, vars = set_vars( subjid = \"PATIENT\", outcome = \"CHANGE\", visit = \"VISIT\", group = \"THERAPY\", covariates = c(\"BASVAL\") ) ) # Pool the results poolObj <- pool( anaObj, conf.level = 0.95, alternative = \"two.sided\" )"},{"path":"/articles/retrieved_dropout.html","id":"retrieved-dropout-models-in-a-nutshell","dir":"Articles","previous_headings":"","what":"Retrieved dropout models in a nutshell","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"Retrieved dropout models proposed analysis estimands using treatment policy strategy addressing ICE. models, missing outcomes multiply imputed conditional upon whether occur pre- post-ICE. Retrieved dropout models typically rely extended missing--random (MAR) assumption, .e., assume missing outcome data similar observed data subjects treatment group observed outcome history, ICE status. comprehensive description evaluation retrieved dropout models, refer Guizzaro et al. (2021), Polverejan Dragalin (2020), Noci et al. (2023), Drury et al. (2024), Bell et al. (2024). Broadly, publications find retrieved dropout models reduce bias compared alternative analysis approaches based imputation basic MAR assumption reference-based missing data assumption. However, several issues retrieved dropout models also highlighted. Retrieved dropout models require enough post-ICE data collected inform imputation model. Even relatively small amounts missingness, complex retrieved dropout models may face identifiability issues. Another drawback models general loss power relative reference-based imputation methods, becomes meaningful post-ICE observation percentages 50% increases accelerating rate percentage decreases (Bell et al. 2024).","code":""},{"path":"/articles/retrieved_dropout.html","id":"sec:dataSimul","dir":"Articles","previous_headings":"","what":"Data simulation using function simulate_data()","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"purposes vignette first create simulated dataset rbmi function simulate_data(). simulate_data() function generates data randomized clinical trial longitudinal continuous outcomes two different types ICEs. Specifically, simulate 1:1 randomized trial active drug (intervention) versus placebo (control) 100 subjects per group 4 post-baseline assessments (3-monthly visits 12 months): mean outcome trajectory placebo group increases linearly 50 baseline (visit 0) 60 visit 4, .e. slope 10 points/year (2.5 points every 3 months). mean outcome trajectory intervention group identical placebo group month 6. month 6 onward, slope decreases 50% 5 points/year (.e. 1.25 points every 3 months). covariance structure baseline follow-values groups implied random intercept slope model standard deviation 5 intercept slope, correlation 0.25. addition, independent residual error standard deviation 2.5 added assessment. probability intercurrent event study drug discontinuation visit calculated according logistic model depends observed outcome visit. Specifically, visit-wise discontinuation probability 3% 4% control intervention group, respectively, specified case observed outcome equal 50 (mean value baseline). odds discontinuation simulated increase +10% +1 point increase observed outcome. Study drug discontinuation simulated effect mean trajectory placebo group. intervention group, subjects discontinue follow slope mean trajectory placebo group time point onward. compatible copy increments reference (CIR) assumption. Study dropout study drug discontinuation visit occurs probability 50% leading missing outcome data time point onward. function simulate_data() requires 3 arguments (see function documentation help(simulate_data) details): pars_c: simulation parameters control group. pars_t: simulation parameters intervention group. post_ice1_traj: Specifies observed outcomes ICE1 simulated. , report data according specifications can simulated function simulate_data(): frequency ICE proportion data collected ICE impacts variance treatment effect retrieved dropout models. example, large proportion ICE combined small proportion data collected ICE might result substantial variance inflation, especially complex retrieved dropout models. proportion subjects ICE proportion subjects withdrew simulated study summarized : study 23% study participants discontinued study treatment control arm 24% intervention arm. Approximately half participants discontinued treatment dropped-study discontinuation visit leading missing outcomes subsequent visits.","code":"library(rbmi) library(dplyr) ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union set.seed(1392) time <- c(0, 3, 6, 9, 12) # Mean trajectory control muC <- c(50.0, 52.5, 55.0, 57.5, 60.0) # Mean trajectory intervention muT <- c(50.0, 52.5, 55.0, 56.25, 57.50) # Create Sigma sd_error <- 2.5 covRE <- rbind( c(25.0, 6.25), c(6.25, 25.0) ) Sigma <- cbind(1, time / 12) %*% covRE %*% rbind(1, time / 12) + diag(sd_error^2, nrow = length(time)) # Set simulation parameters of the control group parsC <- set_simul_pars( mu = muC, sigma = Sigma, n = 100, # sample size prob_ice1 = 0.03, # prob of discontinuation for outcome equal to 50 or_outcome_ice1 = 1.10, # +1 point increase => +10% odds of discontinuation prob_post_ice1_dropout = 0.5 # dropout rate following discontinuation ) # Set simulation parameters of the intervention group parsT <- parsC parsT$mu <- muT parsT$prob_ice1 <- 0.04 # Simulate data data <- simulate_data( pars_c = parsC, pars_t = parsT, post_ice1_traj = \"CIR\" # Assumption about post-ice trajectory ) %>% select(-c(outcome_noICE, ind_ice2)) # remove unncessary columns head(data) ## id visit group outcome_bl ind_ice1 dropout_ice1 outcome ## 1 id_1 0 Control 53.35397 0 0 53.35397 ## 2 id_1 1 Control 53.35397 0 0 55.15100 ## 3 id_1 2 Control 53.35397 0 0 59.81038 ## 4 id_1 3 Control 53.35397 0 0 61.59709 ## 5 id_1 4 Control 53.35397 0 0 67.08044 ## 6 id_2 0 Control 53.31025 0 0 53.31025 # Compute endpoint of interest: change from baseline data <- data %>% filter(visit != \"0\") %>% mutate( change = outcome - outcome_bl, visit = factor(visit, levels = unique(visit)) ) data %>% group_by(visit) %>% summarise( freq_disc_ctrl = mean(ind_ice1[group == \"Control\"] == 1), freq_dropout_ctrl = mean(dropout_ice1[group == \"Control\"] == 1), freq_disc_interv = mean(ind_ice1[group == \"Intervention\"] == 1), freq_dropout_interv = mean(dropout_ice1[group == \"Intervention\"] == 1) ) ## # A tibble: 4 × 5 ## visit freq_disc_ctrl freq_dropout_ctrl freq_disc_interv freq_dropout_interv ## ## 1 1 0.03 0.01 0.06 0.03 ## 2 2 0.1 0.03 0.1 0.04 ## 3 3 0.19 0.09 0.17 0.06 ## 4 4 0.23 0.12 0.24 0.1"},{"path":"/articles/retrieved_dropout.html","id":"estimators-based-on-retrieved-dropout-models","dir":"Articles","previous_headings":"","what":"Estimators based on retrieved dropout models","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"consider retrieved dropout methods model pre- post-ICE outcomes jointly including time-varying ICE indicators imputation model, .e. allow occurrence ICE impact mean structure covariance matrix. Imputation missing outcomes performed MAR assumption including observed data. analysis completed data, use standard ANCOVA model outcome follow-visit, respectively, treatment assignment main covariate adjustment baseline outcome. Specifically, consider following imputation models: Imputation basic MAR assumption (basic MAR): model ignores whether outcome observed pre- post-ICE, .e. retrieved dropout model. Rather, asymptotically equivalent standard MMRM model analogous “MI1” model Bell et al. (2024). difference “MI1” model rbmi based sequential imputation rather, missing outcomes imputed simultaneously based MMRM-type imputation model. include baseline outcome visit treatment group visit interaction terms imputation model form: change ~ outcome_bl*visit + group*visit. Retrieved dropout model 1 (RD1): model uses following imputation model: change ~ outcome_bl*visit + group*visit + time_since_ice1*group, time_since_ice1 set 0 treatment discontinuation time treatment discontinuation (months) subsequent visits. implies change slope outcome trajectories ICE, modeled separately treatment arm. model similar “TV2-MAR” estimator Noci et al. (2023). Compared basic MAR model, model requires estimation 2 additional parameters. Retrieved dropout model 2 (RD2): model uses following imputation model: change ~ outcome_bl*visit + group*visit + ind_ice1*group*visit. assumes constant shift outcomes ICE, modeled separately treatment arm visit. model analogous “MI2” model Bell et al. (2024). Compared basic MAR model, model requires estimation 2 times “number visits” additional parameters. makes different though rather weaker assumptions RD1 model might also harder fit post-ICE data collection sparse visits.","code":""},{"path":"/articles/retrieved_dropout.html","id":"implementation-of-the-defined-retrieved-dropout-models-in-rbmi","dir":"Articles","previous_headings":"","what":"Implementation of the defined retrieved dropout models in rbmi","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"rbmi supports inclusion time-varying covariates imputation model. requirement time-varying covariate non-missing visits including outcome might missing. Imputation performed (extended) MAR assumption. Therefore, imputation approaches implemented rbmi valid yield comparable estimators standard errors. vignette, used conditional mean imputation approach combined jackknife.","code":""},{"path":"/articles/retrieved_dropout.html","id":"basic-mar-model","dir":"Articles","previous_headings":"4 Implementation of the defined retrieved dropout models in rbmi","what":"Basic MAR model","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"","code":"# Define key variables for the imputation and analysis models vars <- set_vars( subjid = \"id\", visit = \"visit\", outcome = \"change\", group = \"group\", covariates = c(\"outcome_bl*visit\", \"group*visit\") ) vars_an <- vars vars_an$covariates <- \"outcome_bl\" # Define imputation method method <- method_condmean(type = \"jackknife\") draw_obj <- draws( data = data, data_ice = NULL, vars = vars, method = method, quiet = TRUE ) impute_obj <- impute( draw_obj ) ana_obj <- analyse( impute_obj, vars = vars_an ) pool_obj_basicMAR <- pool(ana_obj) pool_obj_basicMAR ## ## Pool Object ## ----------- ## Number of Results Combined: 1 + 200 ## Method: jackknife ## Confidence Level: 0.95 ## Alternative: two.sided ## ## Results: ## ## ================================================== ## parameter est se lci uci pval ## -------------------------------------------------- ## trt_1 -0.991 0.557 -2.083 0.101 0.075 ## lsm_ref_1 3.117 0.401 2.331 3.902 <0.001 ## lsm_alt_1 2.126 0.391 1.36 2.892 <0.001 ## trt_2 -0.937 0.611 -2.134 0.26 0.125 ## lsm_ref_2 5.814 0.447 4.938 6.69 <0.001 ## lsm_alt_2 4.877 0.414 4.066 5.688 <0.001 ## trt_3 -1.491 0.743 -2.948 -0.034 0.045 ## lsm_ref_3 7.725 0.526 6.694 8.757 <0.001 ## lsm_alt_3 6.234 0.522 5.211 7.258 <0.001 ## trt_4 -2.872 0.945 -4.723 -1.02 0.002 ## lsm_ref_4 10.787 0.661 9.491 12.083 <0.001 ## lsm_alt_4 7.915 0.67 6.603 9.228 <0.001 ## --------------------------------------------------"},{"path":"/articles/retrieved_dropout.html","id":"retrieved-dropout-model-1-rd1","dir":"Articles","previous_headings":"4 Implementation of the defined retrieved dropout models in rbmi","what":"Retrieved dropout model 1 (RD1)","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"","code":"# derive variable \"time_since_ice1\" (time since ICE in months) data <- data %>% group_by(id) %>% mutate(time_since_ice1 = cumsum(ind_ice1)*3) vars$covariates <- c(\"outcome_bl*visit\", \"group*visit\", \"time_since_ice1*group\") draw_obj <- draws( data = data, data_ice = NULL, vars = vars, method = method, quiet = TRUE ) impute_obj <- impute( draw_obj ) ana_obj <- analyse( impute_obj, vars = vars_an ) pool_obj_RD1 <- pool(ana_obj) pool_obj_RD1 ## ## Pool Object ## ----------- ## Number of Results Combined: 1 + 200 ## Method: jackknife ## Confidence Level: 0.95 ## Alternative: two.sided ## ## Results: ## ## ================================================== ## parameter est se lci uci pval ## -------------------------------------------------- ## trt_1 -0.931 0.558 -2.025 0.163 0.095 ## lsm_ref_1 3.119 0.4 2.334 3.903 <0.001 ## lsm_alt_1 2.188 0.393 1.419 2.957 <0.001 ## trt_2 -0.805 0.616 -2.013 0.403 0.192 ## lsm_ref_2 5.822 0.445 4.949 6.695 <0.001 ## lsm_alt_2 5.017 0.424 4.186 5.849 <0.001 ## trt_3 -1.263 0.758 -2.748 0.222 0.096 ## lsm_ref_3 7.749 0.52 6.729 8.768 <0.001 ## lsm_alt_3 6.486 0.549 5.41 7.562 <0.001 ## trt_4 -2.506 0.969 -4.406 -0.606 0.01 ## lsm_ref_4 10.837 0.653 9.558 12.116 <0.001 ## lsm_alt_4 8.331 0.718 6.924 9.737 <0.001 ## --------------------------------------------------"},{"path":"/articles/retrieved_dropout.html","id":"retrieved-dropout-model-2-rd2","dir":"Articles","previous_headings":"4 Implementation of the defined retrieved dropout models in rbmi","what":"Retrieved dropout model 2 (RD2)","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"","code":"vars$covariates <- c(\"outcome_bl*visit\", \"group*visit\", \"ind_ice1*group*visit\") draw_obj <- draws( data = data, data_ice = NULL, vars = vars, method = method, quiet = TRUE ) impute_obj <- impute( draw_obj ) ana_obj <- analyse( impute_obj, vars = vars_an ) pool_obj_RD2 <- pool(ana_obj) pool_obj_RD2 ## ## Pool Object ## ----------- ## Number of Results Combined: 1 + 200 ## Method: jackknife ## Confidence Level: 0.95 ## Alternative: two.sided ## ## Results: ## ## ================================================== ## parameter est se lci uci pval ## -------------------------------------------------- ## trt_1 -0.927 0.558 -2.021 0.167 0.097 ## lsm_ref_1 3.125 0.4 2.341 3.908 <0.001 ## lsm_alt_1 2.198 0.395 1.424 2.972 <0.001 ## trt_2 -0.889 0.612 -2.089 0.311 0.146 ## lsm_ref_2 5.837 0.443 4.97 6.705 <0.001 ## lsm_alt_2 4.948 0.421 4.124 5.772 <0.001 ## trt_3 -1.305 0.757 -2.788 0.178 0.085 ## lsm_ref_3 7.648 0.54 6.59 8.707 <0.001 ## lsm_alt_3 6.343 0.528 5.308 7.378 <0.001 ## trt_4 -2.617 0.975 -4.528 -0.706 0.007 ## lsm_ref_4 10.883 0.665 9.58 12.186 <0.001 ## lsm_alt_4 8.267 0.715 6.866 9.667 <0.001 ## --------------------------------------------------"},{"path":"/articles/retrieved_dropout.html","id":"brief-summary-of-results","dir":"Articles","previous_headings":"4 Implementation of the defined retrieved dropout models in rbmi","what":"Brief summary of results","title":"rbmi: Implementation of retrieved-dropout models using rbmi","text":"point estimators treatment effect last visit -2.872, -2.506, -2.617 basic MAR, RD1, RD2 estimators, respectively, .e. slightly smaller retrieved dropout models compared basic MAR model. corresponding standard errors 3 estimators 0.945, 0.969, 0.975, .e. slightly larger retrieved dropout models compared basic MAR model.","code":""},{"path":[]},{"path":"/articles/stat_specs.html","id":"scope-of-this-document","dir":"Articles","previous_headings":"","what":"Scope of this document","title":"rbmi: Statistical Specifications","text":"document describes statistical methods implemented rbmi R package standard reference-based multiple imputation continuous longitudinal outcomes. package implements three classes multiple imputation (MI) approaches: Conventional MI methods based Bayesian (approximate Bayesian) posterior draws model parameters combined Rubin’s rules make inferences described Carpenter, Roger, Kenward (2013) Cro et al. (2020). Conditional mean imputation methods combined re-sampling techniques described Wolbers et al. (2022). Bootstrapped MI methods described von Hippel Bartlett (2021). document structured follows: first provide informal introduction estimands corresponding treatment effect estimation based MI (section 2). core document consists section 3 describes statistical methodology detail also contains comparison implemented approaches (section 3.10). link theory functions included package rbmi described section 4. conclude comparison package alternative software implementations reference-based imputation methods (section 5).","code":""},{"path":[]},{"path":"/articles/stat_specs.html","id":"estimands","dir":"Articles","previous_headings":"2 Introduction to estimands and estimation methods","what":"Estimands","title":"rbmi: Statistical Specifications","text":"ICH E9(R1) addendum estimands sensitivity analyses describes systematic approach ensure alignment among clinical trial objectives, trial execution/conduct, statistical analyses, interpretation results (ICH E9 working group (2019)). per addendum, estimand precise description treatment effect reflecting clinical question posed trial objective summarizes population-level outcomes patients different treatment conditions compared. One important attribute estimand list possible intercurrent events (ICEs), .e. events occurring treatment initiation affect either interpretation existence measurements associated clinical question interest, definition appropriate strategies deal ICEs. three relevant strategies purpose document hypothetical strategy, treatment policy strategy, composite strategy. hypothetical strategy, scenario envisaged ICE occur. scenario, endpoint values ICE directly observable treated using models missing data. treatment policy strategy, treatment effect presence ICEs targeted analyses based observed outcomes regardless whether subject ICE . composite strategy, ICE included component endpoint.","code":""},{"path":"/articles/stat_specs.html","id":"alignment-between-the-estimand-and-the-estimation-method","dir":"Articles","previous_headings":"2 Introduction to estimands and estimation methods","what":"Alignment between the estimand and the estimation method","title":"rbmi: Statistical Specifications","text":"ICH E9(R1) addendum distinguishes ICEs missing data (ICH E9 working group (2019)). Whereas ICEs treatment discontinuations reflect clinical practice, amount missing data can minimized conduct clinical trial. However, many connections missing data ICEs. example, often difficult retain subjects clinical trial treatment discontinuation subject’s dropout trial leads missing data. another example, outcome values ICEs addressed using hypothetical strateg directly observable hypothetical scenario. Consequently, observed outcome values ICEs typically discarded treated missing data. addendum proposes estimation methods address problem presented missing data selected align estimand. recent overview methods align estimator estimand Mallinckrodt et al. (2020). short introduction estimation methods studies longitudinal endpoints can also found Wolbers et al. (2022). One prominent statistical method purpose multiple imputation (MI), target rbmi package.","code":""},{"path":"/articles/stat_specs.html","id":"missing-data-prior-to-ices","dir":"Articles","previous_headings":"2 Introduction to estimands and estimation methods > 2.2 Alignment between the estimand and the estimation method","what":"Missing data prior to ICEs","title":"rbmi: Statistical Specifications","text":"Missing data may occur subjects without ICE prior occurrence ICE. missing outcomes associated ICE, often plausible impute missing--random (MAR) assumption using standard MMRM imputation model longitudinal outcomes. Informally, MAR occurs missing data can fully accounted baseline variables included model observed longitudinal outcomes, model correctly specified.","code":""},{"path":"/articles/stat_specs.html","id":"implementation-of-the-hypothetical-strategy","dir":"Articles","previous_headings":"2 Introduction to estimands and estimation methods > 2.2 Alignment between the estimand and the estimation method","what":"Implementation of the hypothetical strategy","title":"rbmi: Statistical Specifications","text":"MAR imputation model described often also good starting point imputing data ICE handled using hypothetical strategy (Mallinckrodt et al. (2020)). Informally, assumes unobserved values ICE similar observed data subjects ICE remained follow-. However, situations, may reasonable assume missingness “informative” indicates systematically better worse outcome observed subjects. situations, MNAR imputation \\(\\delta\\)-adjustment explored sensitivity analysis. \\(\\delta\\)-adjustments add fixed random quantity imputations order make imputed outcomes systematically worse better observed described Cro et al. (2020). rbmi fixed \\(\\delta\\)-adjustments implemented.","code":""},{"path":"/articles/stat_specs.html","id":"implementation-of-the-treatment-policy-strategy","dir":"Articles","previous_headings":"2 Introduction to estimands and estimation methods > 2.2 Alignment between the estimand and the estimation method","what":"Implementation of the treatment policy strategy","title":"rbmi: Statistical Specifications","text":"Ideally, data collection continues ICE handled treatment policy strategy missing data arises. Indeed, post-ICE data increasingly systematically collected RCTs. However, despite best efforts, missing data ICE study treatment discontinuation may still occur subject drops study discontinuation. difficult give definite recommendations regarding implementation treatment policy strategy presence missing data stage optimal method highly context dependent topic ongoing statistical research. ICEs thought negligible effect efficacy outcomes, standard MAR-based imputation ignores whether outcome observed pre- post-ICE may appropriate. contrast, ICE treatment discontinuation may expected substantial impact efficacy outcomes. settings, MAR assumption may still plausible conditioning subject’s time-varying treatment status (Guizzaro et al. (2021)). case, one option impute missing post-discontinuation data based subjects also discontinued treatment continued followed . Another option may require somewhat less post-discontinuation data include subjects imputation procedure model post-discontinuation data using time-varying treatment status indicators (Guizzaro et al. (2021), Polverejan Dragalin (2020), Noci et al. (2023), Drury et al. (2024), Bell et al. (2024)). approach, post-ICE outcomes included every step analysis, including fitting imputation model. assumes ICEs may impact post-ICE outcomes otherwise missingness non-informative. approach also assumes time-varying covariates contain missing values, deviations outcomes ICE correctly modeled time-varying covariates, sufficient post-ICE data available inform regression coefficients time-varying covariates. resulting imputation models called “retrieved dropout models” statistical literature. models tend less bias alternative analysis approaches based imputation basic MAR assumption reference-based missing data assumption. However, retrieved dropout models associated inflated standard errors associated treatment effect estimators detrimental effect study power. particular, observed post-ICE observation percentages falls 50%, power loss can quite dramatic (Bell et al. 2024). illustrate implementation retrieved dropout models vignette “Implementation retrieved-dropout models using rbmi” (vignette(topic = \"retrieved_dropout\", package = \"rbmi\")). trial settings, subjects discontinue randomized treatment. settings, treatment discontinuation rates higher difficult retain subjects trial treatment discontinuation leading sparse data collection treatment discontinuation. settings, amount available data treatment discontinuation may insufficient inform imputation model explicitly models post-discontinuation data. Depending disease area anticipated mechanism action intervention, may plausible assume subjects intervention group behave similarly subjects control group ICE treatment discontinuation. case, reference-based imputation methods option (Mallinckrodt et al. (2020)). Reference-based imputation methods formalize idea impute missing data intervention group based data control reference group. general description review reference-based imputation methods, refer Carpenter, Roger, Kenward (2013), Cro et al. (2020), . White, Royes, Best (2020) Wolbers et al. (2022). technical description implemented statistical methodology reference-based imputation, refer section 3 (particular section 3.4).","code":""},{"path":"/articles/stat_specs.html","id":"implementation-of-the-composite-strategy","dir":"Articles","previous_headings":"2 Introduction to estimands and estimation methods > 2.2 Alignment between the estimand and the estimation method","what":"Implementation of the composite strategy","title":"rbmi: Statistical Specifications","text":"composite strategy typically applied binary time--event outcomes can also used continuous outcomes ascribing suitably unfavorable value patients experience ICEs composite strategy defined. One possibility implement use MI \\(\\delta\\)-adjustment post-ICE data described Darken et al. (2020).","code":""},{"path":[]},{"path":"/articles/stat_specs.html","id":"sec:methodsOverview","dir":"Articles","previous_headings":"3 Statistical methodology","what":"Overview of the imputation procedure","title":"rbmi: Statistical Specifications","text":"Analyses datasets missing data always rely missing data assumptions. methods described can used produce valid imputations MAR assumption reference-based imputation assumptions. MNAR imputation based fixed \\(\\delta\\)-adjustments typically used sensitivity analyses tipping-point analyses also supported. Three general imputation approaches implemented rbmi: Conventional MI based Bayesian (approximate Bayesian) posterior draws imputation model combined Rubin’s rules inference described Carpenter, Roger, Kenward (2013) Cro et al. (2020). Conditional mean imputation based REML estimate imputation model combined resampling techniques (jackknife bootstrap) inference described Wolbers et al. (2022). Bootstrapped MI methods based REML estimates imputation model described von Hippel Bartlett (2021).","code":""},{"path":"/articles/stat_specs.html","id":"conventional-mi","dir":"Articles","previous_headings":"3 Statistical methodology > 3.1 Overview of the imputation procedure","what":"Conventional MI","title":"rbmi: Statistical Specifications","text":"Conventional MI approaches include following steps: Base imputation model fitting step (Section 3.3) Fit Bayesian multivariate normal mixed model repeated measures (MMRM) observed longitudinal outcomes exclusion data ICEs reference-based missing data imputation desired (Section 3.3.3). Draw \\(M\\) posterior samples estimated parameters (regression coefficients covariance matrices) model. Alternatively, \\(M\\) approximate posterior draws posterior distribution can sampled repeatedly applying conventional restricted maximum-likelihood (REML) parameter estimation MMRM model nonparametric bootstrap samples original dataset (Section 3.3.4). Imputation step (Section 3.4) Take single sample \\(m\\) (\\(m\\1,\\ldots, M)\\) posterior distribution imputation model parameters. subject, use sampled parameters defined imputation strategy determine mean covariance matrix describing subject’s marginal outcome distribution longitudinal outcome assessments (.e. observed missing outcomes). subjects, construct conditional multivariate normal distribution missing outcomes given observed outcomes (including observed outcomes ICEs reference-based assumption desired). subject, draw single sample conditional distribution impute missing outcomes leading complete imputed dataset. sensitivity analyses, pre-defined \\(\\delta\\)-adjustment may applied imputed data prior analysis step. (Section 3.5). Analysis step (Section 3.6) Analyze imputed dataset using analysis model (e.g. ANCOVA) resulting point estimate standard error (corresponding degrees freedom) treatment effect. Pooling step inference (Section 3.7) Repeat steps 2. 3. posterior sample \\(m\\), resulting \\(M\\) complete datasets, \\(M\\) point estimates treatment effect, \\(M\\) standard errors (corresponding degrees freedom). Pool \\(M\\) treatment effect estimates, standard errors, degrees freedom using rules Barnard Rubin obtain final pooled treatment effect estimator, standard error, degrees freedom.","code":""},{"path":"/articles/stat_specs.html","id":"conditional-mean-imputation","dir":"Articles","previous_headings":"3 Statistical methodology > 3.1 Overview of the imputation procedure","what":"Conditional mean imputation","title":"rbmi: Statistical Specifications","text":"conditional mean imputation approach includes following steps: Base imputation model fitting step (Section 3.3) Fit conventional multivariate normal/MMRM model using restricted maximum likelihood (REML) observed longitudinal outcomes exclusion data ICEs reference-based missing data imputation desired (Section 3.3.2). Imputation step (Section 3.4) subject, use fitted parameters step 1. construct conditional distribution missing outcomes given observed outcomes (including observed outcomes ICEs reference-based missing data imputation desired) described . subject, impute missing data deterministically mean conditional distribution leading complete imputed dataset. sensitivity analyses, pre-defined \\(\\delta\\)-adjustment may applied imputed data prior analysis step. (Section 3.5). Analysis step (Section 3.6) Apply analysis model (e.g. ANCOVA) completed dataset resulting point estimate treatment effect. Jackknife bootstrap inference step (Section 3.8) Inference treatment effect estimate 3. based re-sampling techniques. jackknife bootstrap supported. Importantly, methods require repeating steps imputation procedure (.e. imputation, conditional mean imputation, analysis steps) resampled datasets.","code":""},{"path":"/articles/stat_specs.html","id":"bootstrapped-mi","dir":"Articles","previous_headings":"3 Statistical methodology > 3.1 Overview of the imputation procedure","what":"Bootstrapped MI","title":"rbmi: Statistical Specifications","text":"bootstrapped MI approach includes following steps: Base imputation model fitting step (Section 3.3) Apply conventional restricted maximum-likelihood (REML) parameter estimation MMRM model \\(B\\) nonparametric bootstrap samples original dataset using observed longitudinal outcomes exclusion data ICEs reference-based missing data imputation desired. Imputation step (Section 3.4) Take bootstrapped dataset \\(b\\) (\\(b\\1,\\ldots, B)\\) corresponding imputation model parameter estimates. subject (bootstrapped dataset), use parameter estimates defined strategy dealing ICEs determine mean covariance matrix describing subject’s marginal outcome distribution longitudinal outcome assessments (.e. observed missing outcomes). subjects (bootstrapped dataset), construct conditional multivariate normal distribution missing outcomes given observed outcomes (including observed outcomes ICEs reference-based missing data imputation desired). subject (bootstrapped dataset), draw \\(D\\) samples conditional distributions impute missing outcomes leading \\(D\\) complete imputed dataset bootstrap sample \\(b\\). sensitivity analyses, pre-defined \\(\\delta\\)-adjustment may applied imputed data prior analysis step. (Section 3.5). Analysis step (Section 3.6) Analyze \\(B\\times D\\) imputed datasets using analysis model (e.g. ANCOVA) resulting \\(B\\times D\\) point estimates treatment effect. Pooling step inference (Section 3.9) Pool \\(B\\times D\\) treatment effect estimates described von Hippel Bartlett (2021) obtain final pooled treatment effect estimate, standard error, degrees freedom.","code":""},{"path":"/articles/stat_specs.html","id":"setting-notation-and-missing-data-assumptions","dir":"Articles","previous_headings":"3 Statistical methodology","what":"Setting, notation, and missing data assumptions","title":"rbmi: Statistical Specifications","text":"Assume data study \\(n\\) subjects total subject \\(\\) (\\(=1,\\ldots,n\\)) \\(J\\) scheduled follow-visits outcome interest assessed. applications, data randomized trial intervention vs control group treatment effect interest comparison outcomes specific visit randomized groups. However, single-arm trials multi-arm trials principle also supported rbmi implementation. Denote observed outcome vector length \\(J\\) subject \\(\\) \\(Y_i\\) (missing assessments coded NA (available)) non-missing missing components \\(Y_{!}\\) \\(Y_{?}\\), respectively. default, imputation missing outcomes \\(Y_{}\\) performed MAR assumption rbmi. Therefore, missing data following ICE handled using MAR imputation, compatible default assumption. discussed Section 2, MAR assumption often good starting point implementing hypothetical strategy. also note observed outcome data ICE handled using hypothetical strategy compatible strategy. Therefore, assume post-ICE data ICEs handled using hypothetical strategy already set NA \\(Y_i\\) prior calling rbmi functions. However, observed outcomes ICEs handled using treatment policy strategy included \\(Y_i\\) compatible strategy. Subjects may also experience one ICE missing data imputation according reference-based imputation method foreseen. subject \\(\\) ICE, denote first visit affected ICE \\(\\tilde{t}_i \\\\{1,\\ldots,J\\}\\). subjects, set \\(\\tilde{t}_i=\\infty\\). subject’s outcome vector setting observed outcomes visit \\(\\tilde{t}_i\\) onwards missing (.e. NA) denoted \\(Y'_i\\) corresponding data vector removal NA elements \\(Y'_{!}\\). MNAR \\(\\delta\\)-adjustments added imputed datasets formal imputation steps. covered separate section (Section 3.5).","code":""},{"path":[]},{"path":"/articles/stat_specs.html","id":"sec:imputationModelSpecs","dir":"Articles","previous_headings":"3 Statistical methodology > 3.3 The base imputation model","what":"Included data and model specification","title":"rbmi: Statistical Specifications","text":"purpose imputation model estimate (covariate-dependent) mean trajectories covariance matrices group absence ICEs handled using reference-based imputation methods. Conventionally, publications reference-based imputation methods implicitly assumed corresponding post-ICE data missing subjects (Carpenter, Roger, Kenward (2013)). also allow situation post-ICE data available subjects needs imputed using reference-based methods others. However, observed data ICEs reference-based imputation methods specified compatible imputation model described therefore removed considered missing purpose estimating imputation model, purpose . example, patient ICE addressed reference-based method outcomes ICE collected, post-ICE outcomes excluded fitting base imputation model (included following steps). , base imputation model fitted \\(Y'_{!}\\) \\(Y_{!}\\). exclude data, imputation model mistakenly estimate mean trajectories based mixture observed pre- post-ICE data relevant reference-based imputations. Observed post-ICE outcomes control reference group also excluded base imputation model user specifies reference-based imputation strategy ICEs. ensures ICE impact data included imputation model regardless whether ICE occurred control intervention group. hand, imputation reference group based MAR assumption even reference-based imputation methods may preferable settings include post-ICE data control group base imputation model. can implemented specifying MAR strategy ICE control group reference-based strategy ICE intervention group. base imputation model longitudinal outcomes \\(Y'_i\\) assumes mean structure linear function covariates. Full flexibility specification linear predictor model supported. minimum covariates include treatment group, (categorical) visit, treatment--visit interactions. Typically, covariates including baseline outcome also included. External time-varying covariates (e.g. calendar time visit) well internal time-varying (e.g. time-varying indicators treatment discontinuation initiation rescue treatment) may principle also included indicated (Guizzaro et al. (2021)). Missing covariate values allowed. means values time-varying covariates must non-missing every visit regardless whether outcome measured missing. Denote \\(J\\times p\\) design matrix subject \\(\\) corresponding mean structure model \\(X_i\\) matrix removal rows corresponding missing outcomes \\(Y'_{!}\\) \\(X'_{!}\\). \\(p\\) number parameters mean structure model elements \\(Y'_{!}\\). base imputation model observed outcomes defined : \\[ Y'_{!} = X'_{!}\\beta + \\epsilon_{!} \\mbox{ } \\epsilon_{!}\\sim N(0,\\Sigma_{!!})\\] \\(\\beta\\) vector regression coefficients \\(\\Sigma_{!!}\\) covariance matrix obtained complete-data \\(J\\times J\\)-covariance matrix \\(\\Sigma\\) omitting rows columns corresponding missing outcome assessments subject \\(\\). Typically, common unstructured covariance matrix subjects assumed \\(\\Sigma\\) separate covariate matrices per treatment group also supported. Indeed, implementation also supports specification separate covariate matrices according arbitrarily defined categorical variable groups subjects disjoint subset. example, useful different covariance matrices suspected different subject strata. Finally, imputation methods described rely Bayesian model fitting MCMC, flexibility choice covariance structure, .e. unstructured (default), heterogeneous Toeplitz, heterogeneous compound symmetry, AR(1) covariance structures supported.","code":""},{"path":"/articles/stat_specs.html","id":"sec:imputationModelREML","dir":"Articles","previous_headings":"3 Statistical methodology > 3.3 The base imputation model","what":"Restricted maximum likelihood estimation (REML)","title":"rbmi: Statistical Specifications","text":"Frequentist parameter estimation base imputation based REML. use REML improved alternative maximum likelihood (ML) covariance parameter estimation originally proposed Patterson Thompson (1971). Since , become default method parameter estimation linear mixed effects models. rbmi allows choose ML REML methods estimate model parameters, REML default option.","code":""},{"path":"/articles/stat_specs.html","id":"sec:imputationModelBayes","dir":"Articles","previous_headings":"3 Statistical methodology > 3.3 The base imputation model","what":"Bayesian model fitting","title":"rbmi: Statistical Specifications","text":"Bayesian imputation model fitted R package rstan (Stan Development Team (2020)). rstan R interface Stan. Stan powerful flexible statistical software developed dedicated team implements Bayesian inference state---art MCMC sampling procedures. multivariate normal model missing data specified section 3.3.1 can considered generalization models described Stan user’s guide (see Stan Development Team (2020, sec. 3.5)). prior distributions SAS implementation “five macros” used (Roger (2021)), .e. improper flat priors regression coefficients weakly informative inverse Wishart prior covariance matrix (matrices). Specifically, let \\(S \\\\mathbb{R}^{J \\times J}\\) symmetric positive definite matrix \\(\\nu \\(J-1, \\infty)\\). symmetric positive definite matrix \\(x \\\\mathbb{R}^{J \\times J}\\) density: \\[ \\text{InvWish}(x \\vert \\nu, S) = \\frac{1}{2^{\\nu J/2}} \\frac{1}{\\Gamma_J(\\frac{\\nu}{2})} \\vert S \\vert^{\\nu/2} \\vert x \\vert ^{-(\\nu + J + 1)/2} \\text{exp}(-\\frac{1}{2} \\text{tr}(Sx^{-1})). \\] \\(\\nu > J+1\\) mean given : \\[ E[x] = \\frac{S}{\\nu - J - 1}. \\] choose \\(S\\) equal estimated covariance matrix frequentist REML fit \\(\\nu = J+2\\) lowest degrees freedom guarantee finite mean. Setting degrees freedom low \\(\\nu\\) ensures prior little impact posterior. Moreover, choice allows interpret parameter \\(S\\) mean prior distribution. “five macros”, MCMC algorithm initialized parameters frequentist REML fit (see section 3.3.2). described , using weakly informative priors parameters. Therefore, Markov chain essentially starting targeted stationary posterior distribution minimal amount burn-chain required.","code":""},{"path":"/articles/stat_specs.html","id":"sec:imputationModelBoot","dir":"Articles","previous_headings":"3 Statistical methodology > 3.3 The base imputation model","what":"Approximate Bayesian posterior draws via the bootstrap","title":"rbmi: Statistical Specifications","text":"Several authors suggested stabler way get Bayesian posterior draws imputation model bootstrap incomplete data calculate REML estimates bootstrap sample (Little Rubin (2002), Efron (1994), Honaker King (2010), von Hippel Bartlett (2021)). method proper REML estimates bootstrap samples asymptotically equivalent sample posterior distribution may provide additional robustness model misspecification (Little Rubin (2002, sec. 10.2.3, part 6), Honaker King (2010)). order retain balance treatment groups stratification factors across bootstrap samples, user able provide stratification variables bootstrap rbmi implementation.","code":""},{"path":[]},{"path":"/articles/stat_specs.html","id":"sec:imputatioMNAR","dir":"Articles","previous_headings":"3 Statistical methodology > 3.4 Imputation step","what":"Marginal imputation distribution for a subject - MAR case","title":"rbmi: Statistical Specifications","text":"subject \\(\\), marginal distribution complete \\(J\\)-dimensional outcome vector assessment visits according imputation model multivariate normal distribution. mean \\(\\tilde{\\mu}_i\\) given predicted mean imputation model conditional subject’s baseline characteristics, group, , optionally, time-varying covariates. covariance matrix \\(\\tilde{\\Sigma}_i\\) given overall estimated covariance matrix , different covariance matrices assumed different groups, covariance matrix corresponding subject \\(\\)’s group.","code":""},{"path":"/articles/stat_specs.html","id":"sec:imputationRefBased","dir":"Articles","previous_headings":"3 Statistical methodology > 3.4 Imputation step","what":"Marginal imputation distribution for a subject - reference-based imputation methods","title":"rbmi: Statistical Specifications","text":"subject \\(\\), calculate mean covariance matrix complete \\(J\\)-dimensional outcome vector assessment visits MAR case denote \\(\\mu_i\\) \\(\\Sigma_i\\). reference-based imputation methods, corresponding reference group also required group. Typically, reference group intervention group control group. reference mean \\(\\mu_{ref,}\\) defined predicted mean imputation model conditional reference group (rather actual group subject \\(\\) belongs ) subject’s baseline characteristics. reference covariance matrix \\(\\Sigma_{ref,}\\) overall estimated covariance matrix , different covariance matrices assumed different groups, estimated covariance matrix corresponding reference group. principle, time-varying covariates also included reference-based imputation methods. However, sensible external time-varying covariates (e.g. calendar time visit) internal time-varying covariates (e.g. treatment discontinuation) latter likely depend actual treatment group typically sensible assume trajectory time-varying covariate reference group. Based means covariance matrices, subject’s marginal imputation distribution reference-based imputation methods calculated detailed Carpenter, Roger, Kenward (2013, sec. 4.3). Denote mean covariance matrix marginal imputation distribution \\(\\tilde{\\mu}_i\\) \\(\\tilde{\\Sigma}_i\\). Recall subject’s first visit affected ICE denoted \\(\\tilde{t}_i \\\\{1,\\ldots,J\\}\\) (visit \\(\\tilde{t}_i-1\\) last visit unaffected ICE). marginal distribution patient \\(\\) built according specific assumption data post ICE follows: Jump reference (JR): patient’s outcome distribution normally distributed following mean: \\[\\tilde{\\mu}_i = (\\mu_i[1], \\dots, \\mu_i[\\tilde{t}_i-1], \\mu_{ref,}[\\tilde{t}_i], \\dots, \\mu_{ref,}[J])^T.\\] covariance matrix constructed follows. First, partition covariance matrices \\(\\Sigma_i\\) \\(\\Sigma_{ref,}\\) blocks according time ICE \\(\\tilde{t}_i\\): \\[ \\Sigma_{} = \\begin{bmatrix} \\Sigma_{, 11} & \\Sigma_{, 12} \\\\ \\Sigma_{, 21} & \\Sigma_{,22} \\\\ \\end{bmatrix} \\] \\[ \\Sigma_{ref,} = \\begin{bmatrix} \\Sigma_{ref, , 11} & \\Sigma_{ref, , 12} \\\\ \\Sigma_{ref, , 21} & \\Sigma_{ref, ,22} \\\\ \\end{bmatrix}. \\] want covariance matrix \\(\\tilde{\\Sigma}_i\\) match \\(\\Sigma_i\\) pre-deviation measurements, \\(\\Sigma_{ref,}\\) conditional components post-deviation given pre-deviation measurements. solution derived Carpenter, Roger, Kenward (2013, sec. 4.3) given : \\[ \\begin{matrix} \\tilde{\\Sigma}_{,11} = \\Sigma_{, 11} \\\\ \\tilde{\\Sigma}_{, 21} = \\Sigma_{ref,, 21} \\Sigma^{-1}_{ref,, 11} \\Sigma_{, 11} \\\\ \\tilde{\\Sigma}_{, 22} = \\Sigma_{ref, , 22} - \\Sigma_{ref,, 21} \\Sigma^{-1}_{ref,, 11} (\\Sigma_{ref,, 11} - \\Sigma_{,11}) \\Sigma^{-1}_{ref,, 11} \\Sigma_{ref,, 12}. \\end{matrix} \\] Copy increments reference (CIR): patient’s outcome distribution normally distributed following mean: \\[ \\begin{split} \\tilde{\\mu}_i =& (\\mu_i[1], \\dots, \\mu_i[\\tilde{t}_i-1], \\mu_i[\\tilde{t}_i-1] + (\\mu_{ref,}[\\tilde{t}_i] - \\mu_{ref,}[\\tilde{t}_i-1]), \\dots,\\\\ & \\mu_i[\\tilde{t}_i-1]+(\\mu_{ref,}[J] - \\mu_{ref,}[\\tilde{t}_i-1]))^T. \\end{split} \\] covariance matrix derived JR method. Copy reference (CR): patient’s outcome distribution normally distributed mean covariance matrix taken reference group: \\[ \\tilde{\\mu}_i = \\mu_{ref,} \\] \\[ \\tilde{\\Sigma}_i = \\Sigma_{ref,}. \\] Last mean carried forward (LMCF): patient’s outcome distribution normally distributed following mean: \\[ \\tilde{\\mu}_i = (\\mu_i[1], \\dots, \\mu_i[\\tilde{t}_i-1], \\mu_i[\\tilde{t}_i-1], \\dots, \\mu_i[\\tilde{t}_i-1])'\\] covariance matrix: \\[ \\tilde{\\Sigma}_i = \\Sigma_i.\\]","code":""},{"path":"/articles/stat_specs.html","id":"sec:imputationRandomConditionalMean","dir":"Articles","previous_headings":"3 Statistical methodology > 3.4 Imputation step","what":"Imputation of missing outcome data","title":"rbmi: Statistical Specifications","text":"joint marginal multivariate normal imputation distribution subject \\(\\)’s observed missing outcome data mean \\(\\tilde{\\mu}_i\\) covariance matrix \\(\\tilde{\\Sigma}_i\\) defined . actual imputation missing outcome data obtained conditioning marginal distribution subject’s observed outcome data. note, approach valid regardless whether subject intermittent terminal missing data. conditional distribution used imputation multivariate normal distribution explicit formulas conditional mean covariance readily available. completeness, report notation terminology setting. marginal distribution outcome patient \\(\\) \\(Y_i \\sim N(\\tilde{\\mu}_i, \\tilde{\\Sigma}_i)\\) outcome \\(Y_i\\) can decomposed observed (\\(Y_{,!}\\)) unobserved (\\(Y_{,?}\\)) components. Analogously mean \\(\\tilde{\\mu}_i\\) can decomposed \\((\\tilde{\\mu}_{,!},\\tilde{\\mu}_{,?})\\) covariance \\(\\tilde{\\Sigma}_i\\) : \\[ \\tilde{\\Sigma}_i = \\begin{bmatrix} \\tilde{\\Sigma}_{, !!} & \\tilde{\\Sigma}_{,!?} \\\\ \\tilde{\\Sigma}_{, ?!} & \\tilde{\\Sigma}_{, ??} \\end{bmatrix}. \\] conditional distribution \\(Y_{,?}\\) conditional \\(Y_{,!}\\) multivariate normal distribution expectation \\[ E(Y_{,?} \\vert Y_{,!})= \\tilde{\\mu}_{,?} + \\tilde{\\Sigma}_{, ?!} \\tilde{\\Sigma}_{,!!}^{-1} (Y_{,!} - \\tilde{\\mu}_{,!}) \\] covariance matrix \\[ Cov(Y_{,?} \\vert Y_{,!}) = \\tilde{\\Sigma}_{,??} - \\tilde{\\Sigma}_{,?!} \\tilde{\\Sigma}_{,!!}^{-1} \\tilde{\\Sigma}_{,!?}. \\] Conventional random imputation consists sampling conditional multivariate normal distribution. Conditional mean imputation imputes missing values deterministic conditional expectation \\(E(Y_{,?} \\vert Y_{,!})\\).","code":""},{"path":"/articles/stat_specs.html","id":"sec:deltaAdjustment","dir":"Articles","previous_headings":"3 Statistical methodology","what":"\\(\\delta\\)-adjustment","title":"rbmi: Statistical Specifications","text":"marginal \\(\\delta\\)-adjustment approach similar “five macros” SAS implemented (Roger (2021)), .e. fixed non-stochastic values added multivariate normal imputation step prior analysis. relevant sensitivity analyses order make imputed data systematically worse better, respectively, observed data. addition, authors suggested \\(\\delta\\)-type adjustments implement composite strategy continuous outcomes (Darken et al. (2020)). implementation provides full flexibility regarding specific implementation \\(\\delta\\)-adjustment, .e. value added may depend randomized treatment group, timing subject’s ICE, factors. suggestions case studies regarding topic, refer Cro et al. (2020).","code":""},{"path":"/articles/stat_specs.html","id":"sec:analysis","dir":"Articles","previous_headings":"3 Statistical methodology","what":"Analysis step","title":"rbmi: Statistical Specifications","text":"data imputation, standard analysis model can applied completed data resulting treatment effect estimate. imputed data longer contains missing values, analysis model often simple. example, can analysis covariance (ANCOVA) model outcome (change outcome baseline) specific visit j dependent variable, randomized treatment group primary covariate , typically, adjustment baseline covariates imputation model.","code":""},{"path":"/articles/stat_specs.html","id":"sec:pooling","dir":"Articles","previous_headings":"3 Statistical methodology","what":"Pooling step for inference of (approximate) Bayesian MI and Rubin’s rules","title":"rbmi: Statistical Specifications","text":"Assume analysis model applied \\(M\\) multiple imputed random datasets resulted \\(m\\) treatment effect estimates \\(\\hat{\\theta}_m\\) (\\(m=1,\\ldots,M\\)) corresponding standard error \\(SE_m\\) (available) degrees freedom \\(\\nu_{com}\\). degrees freedom available analysis model, set \\(\\nu_{com}=\\infty\\) inference based normal distribution. Rubin’s rules used pooling treatment effect estimates corresponding variances estimates analysis steps across \\(M\\) multiple imputed datasets. According Rubin’s rules, final estimate treatment effect calculated sample mean \\(M\\) treatment effect estimates: \\[ \\hat{\\theta} = \\frac{1}{M} \\sum_{m = 1}^M \\hat{\\theta}_m. \\] pooled variance based two components reflect within variance treatment effects across multiple imputed datasets: \\[ V(\\hat{\\theta}) = V_W(\\hat{\\theta}) + (1 + \\frac{1}{M}) V_B(\\hat{\\theta}) \\] \\(V_W(\\hat{\\theta}) = \\frac{1}{M}\\sum_{m = 1}^M SE^2_m\\) within-variance \\(V_B(\\hat{\\theta}) = \\frac{1}{M-1} \\sum_{m = 1}^M (\\hat{\\theta}_m - \\hat{\\theta})^2\\) -variance. Confidence intervals tests null hypothesis \\(H_0: \\theta=\\theta_0\\) based \\(t\\)-statistics \\(T\\): \\[ T= (\\hat{\\theta}-\\theta_0)/\\sqrt{V(\\hat{\\theta})}. \\] null hypothesis, \\(T\\) approximate \\(t\\)-distribution \\(\\nu\\) degrees freedom. \\(\\nu\\) calculated according Barnard Rubin approximation, see Barnard Rubin (1999) (formula 3) Little Rubin (2002) (formula (5.24), page 87): \\[ \\nu = \\frac{\\nu_{old}* \\nu_{obs}}{\\nu_{old} + \\nu_{obs}} \\] \\[ \\nu_{old} = \\frac{M-1}{\\lambda^2} \\quad\\mbox{}\\quad \\nu_{obs} = \\frac{\\nu_{com} + 1}{\\nu_{com} + 3} \\nu_{com} (1 - \\lambda) \\] \\(\\lambda = \\frac{(1 + \\frac{1}{M})V_B(\\hat{\\theta})}{V(\\hat{\\theta})}\\) fraction missing information.","code":""},{"path":[]},{"path":"/articles/stat_specs.html","id":"point-estimate-of-the-treatment-effect","dir":"Articles","previous_headings":"3 Statistical methodology > 3.8 Bootstrap and jackknife inference for conditional mean imputation","what":"Point estimate of the treatment effect","title":"rbmi: Statistical Specifications","text":"point estimator obtained applying analysis model (Section 3.6) single conditional mean imputation missing data (see Section 3.4.3) based REML estimator parameters imputation model (see Section 3.3.2). denote treatment effect estimator \\(\\hat{\\theta}\\). demonstrated Wolbers et al. (2022) (Section 2.4), treatment effect estimator valid analysis model ANCOVA model , generally, treatment effect estimator linear function imputed outcome vector. Indeed, case, estimator identical pooled treatment effect across multiple random REML imputation infinite number imputations corresponds computationally efficient implementation proposal von Hippel Bartlett (2021). expect conditional mean imputation method also applicable analysis models (e.g. general MMRM analysis models) formally justified.","code":""},{"path":"/articles/stat_specs.html","id":"jackknife-standard-errors-confidence-intervals-ci-and-tests-for-the-treatment-effect","dir":"Articles","previous_headings":"3 Statistical methodology > 3.8 Bootstrap and jackknife inference for conditional mean imputation","what":"Jackknife standard errors, confidence intervals (CI) and tests for the treatment effect","title":"rbmi: Statistical Specifications","text":"dataset containing \\(n\\) subjects, jackknife standard error depends treatment effect estimates \\(\\hat{\\theta}_{(-b)}\\) (\\(b=1,\\ldots,n\\)) samples original dataset leave observation subject \\(b\\). described previously, obtain treatment effect estimates leave-one-subject-datasets, steps imputation procedure (.e. imputation, conditional mean imputation, analysis steps) need repeated new dataset. , jackknife standard error defined \\[\\hat{se}_{jack}=[\\frac{(n-1)}{n}\\cdot\\sum_{b=1}^{n} (\\hat{\\theta}_{(-b)}-\\bar{\\theta}_{(.)})^2]^{1/2}\\] \\(\\bar{\\theta}_{(.)}\\) denotes mean jackknife estimates (Efron Tibshirani (1994), chapter 10). corresponding two-sided normal approximation \\(1-\\alpha\\) CI defined \\(\\hat{\\theta}\\pm z^{1-\\alpha/2}\\cdot \\hat{se}_{jack}\\) \\(\\hat{\\theta}\\) treatment effect estimate original dataset. Tests null hypothesis \\(H_0: \\theta=\\theta_0\\) based \\(Z\\)-score \\(Z=(\\hat{\\theta}-\\theta_0)/\\hat{se}_{jack}\\) using standard normal approximation. simulation study reported Wolbers et al. (2022) demonstrated exact protection type error jackknife-based inference relatively low sample size (n = 100 per group) substantial amount missing data (>25% subjects ICE).","code":""},{"path":"/articles/stat_specs.html","id":"bootstrap-standard-errors-confidence-intervals-ci-and-tests-for-the-treatment-effect","dir":"Articles","previous_headings":"3 Statistical methodology > 3.8 Bootstrap and jackknife inference for conditional mean imputation","what":"Bootstrap standard errors, confidence intervals (CI) and tests for the treatment effect","title":"rbmi: Statistical Specifications","text":"alternative jackknife, bootstrap also implemented rbmi (Efron Tibshirani (1994), Davison Hinkley (1997)). Two different bootstrap methods implemented rbmi: Methods based bootstrap standard error normal approximation percentile bootstrap methods. Denote treatment effect estimates \\(B\\) bootstrap samples \\(\\hat{\\theta}^*_b\\) (\\(b=1,\\ldots,B\\)). bootstrap standard error \\(\\hat{se}_{boot}\\) defined empirical standard deviation bootstrapped treatment effect estimates. Confidence intervals tests based bootstrap standard error can constructed way jackknife. Confidence intervals using percentile bootstrap based empirical quantiles bootstrap distribution corresponding statistical tests implemented rbmi via inversion confidence interval. Explicit formulas bootstrap inference implemented rbmi package considerations regarding required number bootstrap samples included Appendix Wolbers et al. (2022). simulation study reported Wolbers et al. (2022) demonstrated small inflation type error rate inference based bootstrap standard error (\\(5.3\\%\\) nominal type error rate \\(5\\%\\)) sample size n = 100 per group substantial amount missing data (>25% subjects ICE). Based simulations, recommend jackknife bootstrap inference performed better simulation study typically much faster compute bootstrap.","code":""},{"path":"/articles/stat_specs.html","id":"sec:poolbmlmi","dir":"Articles","previous_headings":"3 Statistical methodology","what":"Pooling step for inference of the bootstrapped MI methods","title":"rbmi: Statistical Specifications","text":"Assume analysis model applied \\(B\\times D\\) multiple imputed random datasets resulted \\(B\\times D\\) treatment effect estimates \\(\\hat{\\theta}_{bd}\\) (\\(b=1,\\ldots,B\\); \\(d=1,\\ldots,D\\)). final estimate treatment effect calculated sample mean \\(B*D\\) treatment effect estimates: \\[ \\hat{\\theta} = \\frac{1}{BD} \\sum_{b = 1}^B \\sum_{d = 1}^D \\hat{\\theta}_{bd}. \\] pooled variance based two components reflect variability within imputed bootstrap samples (von Hippel Bartlett (2021), formula 8.4): \\[ V(\\hat{\\theta}) = (1 + \\frac{1}{B})\\frac{MSB - MSW}{D} + \\frac{MSW}{BD} \\] \\(MSB\\) mean square bootstrapped datasets, \\(MSW\\) mean square within bootstrapped datasets imputed datasets: \\[ \\begin{align*} MSB &= \\frac{D}{B-1} \\sum_{b = 1}^B (\\bar{\\theta_{b}} - \\hat{\\theta})^2 \\\\ MSW &= \\frac{1}{B(D-1)} \\sum_{b = 1}^B \\sum_{d = 1}^D (\\theta_{bd} - \\bar{\\theta_b})^2 \\end{align*} \\] \\(\\bar{\\theta_{b}}\\) mean across \\(D\\) estimates obtained random imputation \\(b\\)-th bootstrap sample. degrees freedom estimated following formula (von Hippel Bartlett (2021), formula 8.6): \\[ \\nu = \\frac{(MSB\\cdot (B+1) - MSW\\cdot B)^2}{\\frac{MSB^2\\cdot (B+1)^2}{B-1} + \\frac{MSW^2\\cdot B}{D-1}} \\] Confidence intervals tests null hypothesis \\(H_0: \\theta=\\theta_0\\) based \\(t\\)-statistics \\(T\\): \\[ T= (\\hat{\\theta}-\\theta_0)/\\sqrt{V(\\hat{\\theta})}. \\] null hypothesis, \\(T\\) approximate \\(t\\)-distribution \\(\\nu\\) degrees freedom.","code":""},{"path":[]},{"path":"/articles/stat_specs.html","id":"treatment-effect-estimation","dir":"Articles","previous_headings":"3 Statistical methodology > 3.10 Comparison between the implemented approaches","what":"Treatment effect estimation","title":"rbmi: Statistical Specifications","text":"approaches provide consistent treatment effect estimates standard reference-based imputation methods case analysis model completed datasets general linear model ANCOVA. Methods conditional mean imputation also valid analysis models. validity conditional mean imputation formally demonstrated analyses using general linear model (Wolbers et al. (2022, sec. 2.4)) though may also applicable widely (e.g. general MMRM analysis models). Treatment effects based conditional mean imputation deterministic. methods affected Monte Carlo sampling error precision estimates depends number imputations bootstrap samples, respectively.","code":""},{"path":"/articles/stat_specs.html","id":"standard-errors-of-the-treatment-effect","dir":"Articles","previous_headings":"3 Statistical methodology > 3.10 Comparison between the implemented approaches","what":"Standard errors of the treatment effect","title":"rbmi: Statistical Specifications","text":"approaches imputation MAR assumption provide consistent estimates frequentist standard error. reference-based imputation methods, situation complicated two different types variance estimators proposed statistical literature (Bartlett (2023)). first frequentist variance describes actual repeated sampling variability estimator. reference-based missing data assumption correctly specified, resulting inference based variance correct frequentist sense, .e. hypothesis tests asymptotically correct type error control confidence intervals correct coverage probabilities repeated sampling (Bartlett (2023), Wolbers et al. (2022)). Reference-based missing data assumptions strong borrow information reference arm imputation active arm. consequence, size frequentist standard errors treatment effects may decrease increasing amounts missing data. second proposal -called “information-anchored” variance originally proposed context sensitivity analyses (Cro, Carpenter, Kenward (2019)). variance estimator based disentangling point estimation variance estimation altogether. information-anchoring principle described Cro, Carpenter, Kenward (2019) states relative increase variance treatment effect estimator MAR imputation increasing amounts missing data preserved reference-based imputation methods. resulting information-anchored variance typically similar variance MAR imputation typically increases increasing amounts missing data. However, information-anchored variance reflect actual variability reference-based estimator repeated sampling resulting inference highly conservative resulting substantial power loss (Wolbers et al. (2022)). Moreover, date, Bayesian frequentist framework developed information-anchored variance provides correct inference reference-based missingness assumptions, clear whether framework can even developed. Reference-based conditional mean imputation (method_condmean()) bootstrapped likelihood-based multiple methods (method = method_bmlmi()) obtain standard errors via resampling hence target frequentist variance (Wolbers et al. (2022), von Hippel Bartlett (2021)). finite samples, simulations sample size \\(n=100\\) per group reported Wolbers et al. (2022) demonstrated conditional mean imputation combined jackknife (method_condmean(type = \"jackknife\")) provided exact protection type one error rate whereas bootstrap (method_condmean(type = \"bootstrap\")) associated small type error inflation (5.1% 5.3% nominal level 5%). reference-based conditional mean imputation, alternative information-anchored variance can obtained following proposal Lu (2021). basic idea Lu (2021) obtain information-anchored variance via MAR imputation combined delta-adjustment delta selected data-driven way match reference-based estimator. conditional mean imputation, proposal Lu (2021) can implemented choosing delta-adjustment difference conditional mean imputation chosen reference-based assumption MAR original dataset. illustration different variances can obtained conditional mean imputation rbmi provided vignette “Frequentist information-anchored inference reference-based conditional mean imputation” (vignette(topic = \"CondMean_Inference\", package = \"rbmi\")). Reference-based Bayesian (approximate Bayesian) multiple imputation methods combined Rubin’s rules (method_bayes() method_approxbayes()) target information-anchored variance (Cro, Carpenter, Kenward (2019)). frequentist variance methods principle obtained via bootstrap jackknife re-sampling treatment effect estimates computationally intensive directly supported rbmi. view primary analyses, accurate type error control (can obtained using frequentist variance) important adherence information anchoring principle , us, fully compatible strong reference-based assumptions. case, reference-based imputation used primary analysis, critical chosen reference-based assumption can clinically justified, suitable sensitivity analyses conducted stress-test assumptions. Conditional mean imputation combined jackknife method leads deterministic standard error estimates , consequently, confidence intervals \\(p\\)-values also deterministic. particularly important regulatory setting important ascertain whether calculated \\(p\\)-value close critical boundary 5% truly threshold rather uncertain Monte Carlo error.","code":""},{"path":"/articles/stat_specs.html","id":"computational-complexity","dir":"Articles","previous_headings":"3 Statistical methodology > 3.10 Comparison between the implemented approaches","what":"Computational complexity","title":"rbmi: Statistical Specifications","text":"Bayesian MI methods rely specification prior distributions usage Markov chain Monte Carlo (MCMC) methods. methods based multiple imputation bootstrapping require tuning parameters specification number imputations \\(M\\) bootstrap samples \\(B\\) rely numerical optimization fitting MMRM imputation models via REML. Conditional mean imputation combined jackknife tuning parameters. rbmi implementation, fitting MMRM imputation model via REML computationally expensive. MCMC sampling using rstan (Stan Development Team (2020)) typically relatively fast setting requires small burn-burn-chains. addition, number random imputations reliable inference using Rubin’s rules often smaller number resamples required jackknife bootstrap (see e.g. discussions . R. White, Royston, Wood (2011, sec. 7) Bayesian MI Appendix Wolbers et al. (2022) bootstrap). Thus, many applications, expect conventional MI based Bayesian posterior draws fastest, followed conventional MI using approximate Bayesian posterior draws conditional mean imputation combined jackknife. Conditional mean imputation combined bootstrap bootstrapped MI methods typically computationally demanding. note, implemented methods conceptually straightforward parallelise parallelisation support provided rbmi.","code":""},{"path":"/articles/stat_specs.html","id":"sec:rbmiFunctions","dir":"Articles","previous_headings":"","what":"Mapping of statistical methods to rbmi functions","title":"rbmi: Statistical Specifications","text":"full documentation rbmi package functionality refer help pages functions package vignettes. give brief overview different steps imputation procedure mapped rbmi functions: Bayesian posterior parameter draws imputation model obtained via argument method = method_bayes(). Approximate Bayesian posterior parameter draws imputation model obtained via argument method = method_approxbayes(). ML REML parameter estimates imputation model parameters original dataset leave-one-subject-datasets (required jackknife) obtained via argument method = method_condmean(type = \"jackknife\"). ML REML parameter estimates imputation model parameters original dataset bootstrapped datasets obtained via argument method = method_condmean(type = \"bootstrap\"). Bootstrapped MI methods obtained via argument method = method_bmlmi(B=B, D=D) \\(B\\) refers number bootstrap samples \\(D\\) number random imputations bootstrap sample. imputation step using random imputation deterministic conditional mean imputation, respectively, implemented function impute(). Imputation can performed assuming already implemented imputation strategies presented section 3.4. Additionally, user-defined imputation strategies also supported. analysis step implemented function analyse() applies analysis model imputed datasets. default, analysis model (argument fun) ancova() function alternative analysis functions can also provided user. analyse() function also allows \\(\\delta\\)-adjustments imputed datasets prior analysis via argument delta. inference step implemented function pool() pools results across imputed datasets. Rubin Bernard rule applied case (approximate) Bayesian MI. conditional mean imputation, jackknife bootstrap (normal approximation percentile) inference supported. BMLMI, pooling inference steps performed via pool() case implements method described Section 3.9.","code":""},{"path":"/articles/stat_specs.html","id":"sec:otherSoftware","dir":"Articles","previous_headings":"","what":"Comparison to other software implementations","title":"rbmi: Statistical Specifications","text":"established software implementation reference-based imputation SAS -called “five macros” James Roger (Roger (2021)). alternative R implementation also currently development R package RefBasedMI (McGrath White (2021)). rbmi several features supported implementations: addition Bayesian MI approach implemented also packages, implementation provides three alternative MI approaches: approximate Bayesian MI, conditional mean imputation combined resampling, bootstrapped MI. rbmi allows usage data collected ICE. example, suppose want adopt treatment policy strategy ICE “treatment discontinuation”. possible implementation strategy use observed outcome data subjects remain study ICE use reference-based imputation case subject drops . implementation, implemented excluding observed post ICE data imputation model assumes MAR missingness including analysis model. knowledge, directly supported implementations. RefBasedMI fits imputation model data treatment group separately implies covariate-treatment group interactions covariates pooled data treatment groups. contrast, Roger’s five macros assume joint model including data randomized groups covariate-treatment interactions covariates allowed. also chose implement joint model use flexible model linear predictor may may include interaction term covariate treatment group. addition, imputation model also allows inclusion time-varying covariates. implementation, grouping subjects purpose imputation model (definition reference group) need correspond assigned treatment groups. provides additional flexibility imputation procedure. clear us whether feature supported Roger’s five macros RefBasedMI. believe R-based implementation modular RefBasedMI facilitate package enhancements. contrast, general causal model introduced . White, Royes, Best (2020) available implementations currently supported .","code":""},{"path":[]},{"path":"/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Craig Gower-Page. Author, maintainer. Alessandro Noci. Author. Marcel Wolbers. Contributor. Isaac Gravestock. Author. F. Hoffmann-La Roche AG. Copyright holder, funder.","code":""},{"path":"/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Gower-Page C, Noci , Gravestock (2024). rbmi: Reference Based Multiple Imputation. R package version 1.3.1, https://github.com/insightsengineering/rbmi, https://insightsengineering.github.io/rbmi/. Gower-Page C, Noci , Wolbers M (2022). “rbmi: R package standard reference-based multiple imputation methods.” Journal Open Source Software, 7(74), 4251. doi:10.21105/joss.04251, https://doi.org/10.21105/joss.04251.","code":"@Manual{, title = {rbmi: Reference Based Multiple Imputation}, author = {Craig Gower-Page and Alessandro Noci and Isaac Gravestock}, year = {2024}, note = {R package version 1.3.1, https://github.com/insightsengineering/rbmi}, url = {https://insightsengineering.github.io/rbmi/}, } @Article{, title = {rbmi: A R package for standard and reference-based multiple imputation methods}, author = {Craig Gower-Page and Alessandro Noci and Marcel Wolbers}, year = {2022}, publisher = {The Open Journal}, doi = {10.21105/joss.04251}, url = {https://doi.org/10.21105/joss.04251}, volume = {7}, number = {74}, pages = {4251}, journal = {Journal of Open Source Software}, }"},{"path":[]},{"path":"/index.html","id":"overview","dir":"","previous_headings":"","what":"Overview","title":"Reference Based Multiple Imputation","text":"rbmi package used imputation missing data clinical trials continuous multivariate normal longitudinal outcomes. supports imputation missing random (MAR) assumption, reference-based imputation methods, delta adjustments (required sensitivity analysis tipping point analyses). package implements Bayesian approximate Bayesian multiple imputation combined Rubin’s rules inference, frequentist conditional mean imputation combined (jackknife bootstrap) resampling.","code":""},{"path":"/index.html","id":"installation","dir":"","previous_headings":"","what":"Installation","title":"Reference Based Multiple Imputation","text":"package can installed directly CRAN via: Note usage Bayesian multiple imputation requires installation suggested package rstan.","code":"install.packages(\"rbmi\") install.packages(\"rstan\")"},{"path":"/index.html","id":"usage","dir":"","previous_headings":"","what":"Usage","title":"Reference Based Multiple Imputation","text":"package designed around 4 core functions: draws() - Fits multiple imputation models impute() - Imputes multiple datasets analyse() - Analyses multiple datasets pool() - Pools multiple results single statistic basic usage core functions described quickstart vignette:","code":"vignette(topic = \"quickstart\", package = \"rbmi\")"},{"path":"/index.html","id":"validation","dir":"","previous_headings":"","what":"Validation","title":"Reference Based Multiple Imputation","text":"clarification current validation status rbmi please see FAQ vignette.","code":""},{"path":"/index.html","id":"support","dir":"","previous_headings":"","what":"Support","title":"Reference Based Multiple Imputation","text":"help regards using package find bug please create GitHub issue","code":""},{"path":"/reference/QR_decomp.html","id":null,"dir":"Reference","previous_headings":"","what":"QR decomposition — QR_decomp","title":"QR decomposition — QR_decomp","text":"QR decomposition defined Stan user's guide (section 1.2).","code":""},{"path":"/reference/QR_decomp.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"QR decomposition — QR_decomp","text":"","code":"QR_decomp(mat)"},{"path":"/reference/QR_decomp.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"QR decomposition — QR_decomp","text":"mat matrix perform QR decomposition .","code":""},{"path":"/reference/Stack.html","id":null,"dir":"Reference","previous_headings":"","what":"R6 Class for a FIFO stack — Stack","title":"R6 Class for a FIFO stack — Stack","text":"simple stack object offering add / pop functionality","code":""},{"path":"/reference/Stack.html","id":"public-fields","dir":"Reference","previous_headings":"","what":"Public fields","title":"R6 Class for a FIFO stack — Stack","text":"stack list containing current stack","code":""},{"path":[]},{"path":"/reference/Stack.html","id":"public-methods","dir":"Reference","previous_headings":"","what":"Public methods","title":"R6 Class for a FIFO stack — Stack","text":"Stack$add() Stack$pop() Stack$clone()","code":""},{"path":"/reference/Stack.html","id":"method-add-","dir":"Reference","previous_headings":"","what":"Method add()","title":"R6 Class for a FIFO stack — Stack","text":"Adds content end stack (must list)","code":""},{"path":"/reference/Stack.html","id":"usage","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for a FIFO stack — Stack","text":"","code":"Stack$add(x)"},{"path":"/reference/Stack.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for a FIFO stack — Stack","text":"x content add stack","code":""},{"path":"/reference/Stack.html","id":"method-pop-","dir":"Reference","previous_headings":"","what":"Method pop()","title":"R6 Class for a FIFO stack — Stack","text":"Retrieve content stack","code":""},{"path":"/reference/Stack.html","id":"usage-1","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for a FIFO stack — Stack","text":"","code":"Stack$pop(i)"},{"path":"/reference/Stack.html","id":"arguments-1","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for a FIFO stack — Stack","text":"number items retrieve stack. less items left stack just return everything left.","code":""},{"path":"/reference/Stack.html","id":"method-clone-","dir":"Reference","previous_headings":"","what":"Method clone()","title":"R6 Class for a FIFO stack — Stack","text":"objects class cloneable method.","code":""},{"path":"/reference/Stack.html","id":"usage-2","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for a FIFO stack — Stack","text":"","code":"Stack$clone(deep = FALSE)"},{"path":"/reference/Stack.html","id":"arguments-2","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for a FIFO stack — Stack","text":"deep Whether make deep clone.","code":""},{"path":"/reference/add_class.html","id":null,"dir":"Reference","previous_headings":"","what":"Add a class — add_class","title":"Add a class — add_class","text":"Utility function add class object. Adds new class existing classes.","code":""},{"path":"/reference/add_class.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Add a class — add_class","text":"","code":"add_class(x, cls)"},{"path":"/reference/add_class.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Add a class — add_class","text":"x object add class . cls class added.","code":""},{"path":"/reference/adjust_trajectories.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust trajectories due to the intercurrent event (ICE) — adjust_trajectories","title":"Adjust trajectories due to the intercurrent event (ICE) — adjust_trajectories","text":"Adjust trajectories due intercurrent event (ICE)","code":""},{"path":"/reference/adjust_trajectories.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust trajectories due to the intercurrent event (ICE) — adjust_trajectories","text":"","code":"adjust_trajectories( distr_pars_group, outcome, ids, ind_ice, strategy_fun, distr_pars_ref = NULL )"},{"path":"/reference/adjust_trajectories.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust trajectories due to the intercurrent event (ICE) — adjust_trajectories","text":"distr_pars_group Named list containing simulation parameters multivariate normal distribution assumed given treatment group. contains following elements: mu: Numeric vector indicating mean outcome trajectory. include outcome baseline. sigma Covariance matrix outcome trajectory. outcome Numeric variable specifies longitudinal outcome. ids Factor variable specifies id subject. ind_ice binary variable takes value 1 corresponding outcome affected ICE 0 otherwise. strategy_fun Function implementing trajectories intercurrent event (ICE). Must one getStrategies(). See getStrategies() details. distr_pars_ref Optional. Named list containing simulation parameters reference arm. contains following elements: mu: Numeric vector indicating mean outcome trajectory assuming ICEs. include outcome baseline. sigma Covariance matrix outcome trajectory assuming ICEs.","code":""},{"path":"/reference/adjust_trajectories.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust trajectories due to the intercurrent event (ICE) — adjust_trajectories","text":"numeric vector containing adjusted trajectories.","code":""},{"path":[]},{"path":"/reference/adjust_trajectories_single.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust trajectory of a subject's outcome due to the intercurrent event (ICE) — adjust_trajectories_single","title":"Adjust trajectory of a subject's outcome due to the intercurrent event (ICE) — adjust_trajectories_single","text":"Adjust trajectory subject's outcome due intercurrent event (ICE)","code":""},{"path":"/reference/adjust_trajectories_single.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust trajectory of a subject's outcome due to the intercurrent event (ICE) — adjust_trajectories_single","text":"","code":"adjust_trajectories_single( distr_pars_group, outcome, strategy_fun, distr_pars_ref = NULL )"},{"path":"/reference/adjust_trajectories_single.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust trajectory of a subject's outcome due to the intercurrent event (ICE) — adjust_trajectories_single","text":"distr_pars_group Named list containing simulation parameters multivariate normal distribution assumed given treatment group. contains following elements: mu: Numeric vector indicating mean outcome trajectory. include outcome baseline. sigma Covariance matrix outcome trajectory. outcome Numeric variable specifies longitudinal outcome. strategy_fun Function implementing trajectories intercurrent event (ICE). Must one getStrategies(). See getStrategies() details. distr_pars_ref Optional. Named list containing simulation parameters reference arm. contains following elements: mu: Numeric vector indicating mean outcome trajectory assuming ICEs. include outcome baseline. sigma Covariance matrix outcome trajectory assuming ICEs.","code":""},{"path":"/reference/adjust_trajectories_single.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust trajectory of a subject's outcome due to the intercurrent event (ICE) — adjust_trajectories_single","text":"numeric vector containing adjusted trajectory single subject.","code":""},{"path":"/reference/adjust_trajectories_single.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Adjust trajectory of a subject's outcome due to the intercurrent event (ICE) — adjust_trajectories_single","text":"outcome specified --post-ICE observations (.e. observations adjusted) set NA.","code":""},{"path":"/reference/analyse.html","id":null,"dir":"Reference","previous_headings":"","what":"Analyse Multiple Imputed Datasets — analyse","title":"Analyse Multiple Imputed Datasets — analyse","text":"function takes multiple imputed datasets (generated impute() function) runs analysis function .","code":""},{"path":"/reference/analyse.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Analyse Multiple Imputed Datasets — analyse","text":"","code":"analyse( imputations, fun = ancova, delta = NULL, ..., ncores = 1, .validate = TRUE )"},{"path":"/reference/analyse.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Analyse Multiple Imputed Datasets — analyse","text":"imputations imputations object created impute(). fun analysis function applied imputed dataset. See details. delta data.frame containing delta transformation applied imputed datasets prior running fun. See details. ... Additional arguments passed onto fun. ncores number parallel processes use running function. Can also cluster object created make_rbmi_cluster(). See parallisation section . .validate inputations checked ensure conforms required format (default = TRUE) ? Can gain small performance increase set FALSE analysing large number samples.","code":""},{"path":"/reference/analyse.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Analyse Multiple Imputed Datasets — analyse","text":"function works performing following steps: Extract dataset imputations object. Apply delta adjustments specified delta argument. Run analysis function fun dataset. Repeat steps 1-3 across datasets inside imputations object. Collect return analysis results. analysis function fun must take data.frame first argument. options analyse() passed onto fun via .... fun must return named list element list containing single numeric element called est (additionally se df originally specified method_bayes() method_approxbayes()) .e.: Please note vars$subjid column (defined original call draws()) scrambled data.frames provided fun. say contain original subject values hard coding subject ids strictly avoided. default fun ancova() function. Please note function requires vars object, created set_vars(), provided via vars argument e.g. analyse(imputeObj, vars = set_vars(...)). Please see documentation ancova() full details. Please also note theoretical justification conditional mean imputation method (method = method_condmean() draws()) relies fact ANCOVA linear transformation outcomes. Thus care required applying alternative analysis functions setting. delta argument can used specify offsets applied outcome variable imputed datasets prior analysis. typically used sensitivity tipping point analyses. delta dataset must contain columns vars$subjid, vars$visit (specified original call draws()) delta. Essentially data.frame merged onto imputed dataset vars$subjid vars$visit outcome variable modified : Please note order provide maximum flexibility, delta argument can used modify /outcome values including imputed. Care must taken defining offsets. recommend use helper function delta_template() define delta datasets provides utility variables is_missing can used identify exactly visits imputed.","code":"myfun <- function(dat, ...) { mod_1 <- lm(data = dat, outcome ~ group) mod_2 <- lm(data = dat, outcome ~ group + covar) x <- list( trt_1 = list( est = coef(mod_1)[[group]], se = sqrt(vcov(mod_1)[group, group]), df = df.residual(mod_1) ), trt_2 = list( est = coef(mod_2)[[group]], se = sqrt(vcov(mod_2)[group, group]), df = df.residual(mod_2) ) ) return(x) } imputed_data[[vars$outcome]] <- imputed_data[[vars$outcome]] + imputed_data[[\"delta\"]]"},{"path":"/reference/analyse.html","id":"parallelisation","dir":"Reference","previous_headings":"","what":"Parallelisation","title":"Analyse Multiple Imputed Datasets — analyse","text":"speed evaluation analyse() can use ncores argument enable parallelisation. Simply providing integer get rbmi automatically spawn many background processes parallelise across. using custom analysis function need ensure libraries global objects required function available sub-processes. need use make_rbmi_cluster() function example: Note significant overhead setting sub-processes transferring data back--forth main process sub-processes. parallelisation analyse() function tends worth > 2000 samples generated draws(). Conversely using parallelisation samples smaller may lead longer run times just running sequentially. important note implementation parallel processing within analyse() optimised around assumption parallel processes spawned machine remote cluster. One optimisation required data saved temporary file local disk read sub-process. done avoid overhead transferring data network. assumption stage need parallelising analysis remote cluster likely better parallelising across multiple rbmi runs rather within single rbmi run. Finally, tipping point analysis can get reasonable performance improvement re-using cluster call analyse() e.g.","code":"my_custom_fun <- function(...) cl <- make_rbmi_cluster( 4, objects = list(\"my_custom_fun\" = my_custom_fun), packages = c(\"dplyr\", \"nlme\") ) analyse( imputations = imputeObj, fun = my_custom_fun, ncores = cl ) parallel::stopCluster(cl) cl <- make_rbmi_cluster(4) ana_1 <- analyse( imputations = imputeObj, delta = delta_plan_1, ncores = cl ) ana_2 <- analyse( imputations = imputeObj, delta = delta_plan_2, ncores = cl ) ana_3 <- analyse( imputations = imputeObj, delta = delta_plan_3, ncores = cl ) parallel::clusterStop(cl)"},{"path":[]},{"path":"/reference/analyse.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Analyse Multiple Imputed Datasets — analyse","text":"","code":"if (FALSE) { # \\dontrun{ vars <- set_vars( subjid = \"subjid\", visit = \"visit\", outcome = \"outcome\", group = \"group\", covariates = c(\"sex\", \"age\", \"sex*age\") ) analyse( imputations = imputeObj, vars = vars ) deltadf <- data.frame( subjid = c(\"Pt1\", \"Pt1\", \"Pt2\"), visit = c(\"Visit_1\", \"Visit_2\", \"Visit_2\"), delta = c( 5, 9, -10) ) analyse( imputations = imputeObj, delta = deltadf, vars = vars ) } # }"},{"path":"/reference/ancova.html","id":null,"dir":"Reference","previous_headings":"","what":"Analysis of Covariance — ancova","title":"Analysis of Covariance — ancova","text":"Performs analysis covariance two groups returning estimated \"treatment effect\" (.e. contrast two treatment groups) least square means estimates group.","code":""},{"path":"/reference/ancova.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Analysis of Covariance — ancova","text":"","code":"ancova( data, vars, visits = NULL, weights = c(\"counterfactual\", \"equal\", \"proportional_em\", \"proportional\") )"},{"path":"/reference/ancova.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Analysis of Covariance — ancova","text":"data data.frame containing data used model. vars vars object generated set_vars(). group, visit, outcome covariates elements required. See details. visits optional character vector specifying visits fit ancova model . NULL, separate ancova model fit outcomes visit (determined unique(data[[vars$visit]])). See details. weights Character, either \"counterfactual\" (default), \"equal\", \"proportional_em\" \"proportional\". Specifies weighting strategy used calculating lsmeans. See weighting section details.","code":""},{"path":"/reference/ancova.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Analysis of Covariance — ancova","text":"function works follows: Select first value visits. Subset data observations occurred visit. Fit linear model vars$outcome ~ vars$group + vars$covariates. Extract \"treatment effect\" & least square means treatment group. Repeat points 2-3 values visits. value visits provided set unique(data[[vars$visit]]). order meet formatting standards set analyse() results collapsed single list suffixed visit name, e.g.: Please note \"ref\" refers first factor level vars$group necessarily coincide control arm. Analogously, \"alt\" refers second factor level vars$group. \"trt\" refers model contrast translating mean difference second level first level. want include interaction terms model can done providing covariates argument set_vars() e.g. set_vars(covariates = c(\"sex*age\")).","code":"list( trt_visit_1 = list(est = ...), lsm_ref_visit_1 = list(est = ...), lsm_alt_visit_1 = list(est = ...), trt_visit_2 = list(est = ...), lsm_ref_visit_2 = list(est = ...), lsm_alt_visit_2 = list(est = ...), ... )"},{"path":[]},{"path":"/reference/ancova.html","id":"counterfactual","dir":"Reference","previous_headings":"","what":"Counterfactual","title":"Analysis of Covariance — ancova","text":"weights = \"counterfactual\" (default) lsmeans obtained taking average predicted values patient assigning patients arm turn. approach equivalent standardization g-computation. comparison emmeans approach equivalent : Note ensure backwards compatibility previous versions rbmi weights = \"proportional\" alias weights = \"counterfactual\". get results consistent emmeans's weights = \"proportional\" please use weights = \"proportional_em\".","code":"emmeans::emmeans(model, specs = \"\", counterfactual = \"\")"},{"path":"/reference/ancova.html","id":"equal","dir":"Reference","previous_headings":"","what":"Equal","title":"Analysis of Covariance — ancova","text":"weights = \"equal\" lsmeans obtained taking model fitted value hypothetical patient whose covariates defined follows: Continuous covariates set mean(X) Dummy categorical variables set 1/N N number levels Continuous * continuous interactions set mean(X) * mean(Y) Continuous * categorical interactions set mean(X) * 1/N Dummy categorical * categorical interactions set 1/N * 1/M comparison emmeans approach equivalent :","code":"emmeans::emmeans(model, specs = \"\", weights = \"equal\")"},{"path":"/reference/ancova.html","id":"proportional","dir":"Reference","previous_headings":"","what":"Proportional","title":"Analysis of Covariance — ancova","text":"weights = \"proportional_em\" lsmeans obtained per weights = \"equal\" except instead weighting observation equally weighted proportion given combination categorical values occurred data. comparison emmeans approach equivalent : Note confused weights = \"proportional\" alias weights = \"counterfactual\".","code":"emmeans::emmeans(model, specs = \"\", weights = \"proportional\")"},{"path":[]},{"path":"/reference/ancova_single.html","id":null,"dir":"Reference","previous_headings":"","what":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"Performance analysis covariance. See ancova() full details.","code":""},{"path":"/reference/ancova_single.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"","code":"ancova_single( data, outcome, group, covariates, weights = c(\"counterfactual\", \"equal\", \"proportional_em\", \"proportional\") )"},{"path":"/reference/ancova_single.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"data data.frame containing data used model. outcome Character, name outcome variable data. group Character, name group variable data. covariates Character vector containing name additional covariates included model well interaction terms. weights Character, either \"counterfactual\" (default), \"equal\", \"proportional_em\" \"proportional\". Specifies weighting strategy used calculating lsmeans. See weighting section details.","code":""},{"path":"/reference/ancova_single.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"group must factor variable 2 levels. outcome must continuous numeric variable.","code":""},{"path":[]},{"path":"/reference/ancova_single.html","id":"counterfactual","dir":"Reference","previous_headings":"","what":"Counterfactual","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"weights = \"counterfactual\" (default) lsmeans obtained taking average predicted values patient assigning patients arm turn. approach equivalent standardization g-computation. comparison emmeans approach equivalent : Note ensure backwards compatibility previous versions rbmi weights = \"proportional\" alias weights = \"counterfactual\". get results consistent emmeans's weights = \"proportional\" please use weights = \"proportional_em\".","code":"emmeans::emmeans(model, specs = \"\", counterfactual = \"\")"},{"path":"/reference/ancova_single.html","id":"equal","dir":"Reference","previous_headings":"","what":"Equal","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"weights = \"equal\" lsmeans obtained taking model fitted value hypothetical patient whose covariates defined follows: Continuous covariates set mean(X) Dummy categorical variables set 1/N N number levels Continuous * continuous interactions set mean(X) * mean(Y) Continuous * categorical interactions set mean(X) * 1/N Dummy categorical * categorical interactions set 1/N * 1/M comparison emmeans approach equivalent :","code":"emmeans::emmeans(model, specs = \"\", weights = \"equal\")"},{"path":"/reference/ancova_single.html","id":"proportional","dir":"Reference","previous_headings":"","what":"Proportional","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"weights = \"proportional_em\" lsmeans obtained per weights = \"equal\" except instead weighting observation equally weighted proportion given combination categorical values occurred data. comparison emmeans approach equivalent : Note confused weights = \"proportional\" alias weights = \"counterfactual\".","code":"emmeans::emmeans(model, specs = \"\", weights = \"proportional\")"},{"path":[]},{"path":"/reference/ancova_single.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Implements an Analysis of Covariance (ANCOVA) — ancova_single","text":"","code":"if (FALSE) { # \\dontrun{ iris2 <- iris[ iris$Species %in% c(\"versicolor\", \"virginica\"), ] iris2$Species <- factor(iris2$Species) ancova_single(iris2, \"Sepal.Length\", \"Species\", c(\"Petal.Length * Petal.Width\")) } # }"},{"path":"/reference/antidepressant_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Antidepressant trial data — antidepressant_data","title":"Antidepressant trial data — antidepressant_data","text":"dataset containing data publicly available example data set antidepressant clinical trial. dataset available website Drug Information Association Scientific Working Group Estimands Missing Data. per website, original data antidepressant clinical trial four treatments; two doses experimental medication, positive control, placebo published Goldstein et al (2004). mask real data, week 8 observations removed two arms created: original placebo arm \"drug arm\" created randomly selecting patients three non-placebo arms.","code":""},{"path":"/reference/antidepressant_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Antidepressant trial data — antidepressant_data","text":"","code":"antidepressant_data"},{"path":"/reference/antidepressant_data.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Antidepressant trial data — antidepressant_data","text":"data.frame 608 rows 11 variables: PATIENT: patients IDs. HAMATOTL: total score Hamilton Anxiety Rating Scale. PGIIMP: patient's Global Impression Improvement Rating Scale. RELDAYS: number days visit baseline. VISIT: post-baseline visit. levels 4,5,6,7. THERAPY: treatment group variable. equal PLACEBO observations placebo arm, DRUG observations active arm. GENDER: patient's gender. POOLINV: pooled investigator. BASVAL: baseline outcome value. HAMDTL17: Hamilton 17-item rating scale value. CHANGE: change baseline Hamilton 17-item rating scale.","code":""},{"path":"/reference/antidepressant_data.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Antidepressant trial data — antidepressant_data","text":"relevant endpoint Hamilton 17-item rating scale depression (HAMD17) baseline weeks 1, 2, 4, 6 assessments included. Study drug discontinuation occurred 24% subjects active drug 26% placebo. data study drug discontinuation missing single additional intermittent missing observation.","code":""},{"path":"/reference/antidepressant_data.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Antidepressant trial data — antidepressant_data","text":"Goldstein, Lu, Detke, Wiltse, Mallinckrodt, Demitrack. Duloxetine treatment depression: double-blind placebo-controlled comparison paroxetine. J Clin Psychopharmacol 2004;24: 389-399.","code":""},{"path":"/reference/apply_delta.html","id":null,"dir":"Reference","previous_headings":"","what":"Applies delta adjustment — apply_delta","title":"Applies delta adjustment — apply_delta","text":"Takes delta dataset adjusts outcome variable adding corresponding delta.","code":""},{"path":"/reference/apply_delta.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Applies delta adjustment — apply_delta","text":"","code":"apply_delta(data, delta = NULL, group = NULL, outcome = NULL)"},{"path":"/reference/apply_delta.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Applies delta adjustment — apply_delta","text":"data data.frame outcome column adjusted. delta data.frame (must contain column called delta). group character vector variables data delta used merge 2 data.frames together . outcome character, name outcome variable data.","code":""},{"path":"/reference/as_analysis.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct an analysis object — as_analysis","title":"Construct an analysis object — as_analysis","text":"Creates analysis object ensuring components correctly defined.","code":""},{"path":"/reference/as_analysis.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct an analysis object — as_analysis","text":"","code":"as_analysis(results, method, delta = NULL, fun = NULL, fun_name = NULL)"},{"path":"/reference/as_analysis.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct an analysis object — as_analysis","text":"results list lists contain analysis results imputation See analyse() details object look like. method method object specified draws(). delta delta dataset used. See analyse() details specified. fun analysis function used. fun_name character name analysis function (used printing) purposes.","code":""},{"path":"/reference/as_ascii_table.html","id":null,"dir":"Reference","previous_headings":"","what":"as_ascii_table — as_ascii_table","title":"as_ascii_table — as_ascii_table","text":"function takes data.frame attempts convert simple ascii format suitable printing screen assumed variable values .character() method order cast character.","code":""},{"path":"/reference/as_ascii_table.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"as_ascii_table — as_ascii_table","text":"","code":"as_ascii_table(dat, line_prefix = \" \", pcol = NULL)"},{"path":"/reference/as_ascii_table.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"as_ascii_table — as_ascii_table","text":"dat Input dataset convert ascii table line_prefix Symbols prefix infront every line table pcol name column handled p-value. Sets value <0.001 value 0 rounding","code":""},{"path":"/reference/as_class.html","id":null,"dir":"Reference","previous_headings":"","what":"Set Class — as_class","title":"Set Class — as_class","text":"Utility function set objects class.","code":""},{"path":"/reference/as_class.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set Class — as_class","text":"","code":"as_class(x, cls)"},{"path":"/reference/as_class.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set Class — as_class","text":"x object set class . cls class set.","code":""},{"path":"/reference/as_cropped_char.html","id":null,"dir":"Reference","previous_headings":"","what":"as_cropped_char — as_cropped_char","title":"as_cropped_char — as_cropped_char","text":"Makes character string x chars Reduce x char string ...","code":""},{"path":"/reference/as_cropped_char.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"as_cropped_char — as_cropped_char","text":"","code":"as_cropped_char(inval, crop_at = 30, ndp = 3)"},{"path":"/reference/as_cropped_char.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"as_cropped_char — as_cropped_char","text":"inval single element value crop_at character limit ndp Number decimal places display","code":""},{"path":"/reference/as_dataframe.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert object to dataframe — as_dataframe","title":"Convert object to dataframe — as_dataframe","text":"Convert object dataframe","code":""},{"path":"/reference/as_dataframe.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert object to dataframe — as_dataframe","text":"","code":"as_dataframe(x)"},{"path":"/reference/as_dataframe.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert object to dataframe — as_dataframe","text":"x data.frame like object Utility function convert \"data.frame-like\" object actual data.frame avoid issues inconsistency methods ( [() dplyr's grouped dataframes)","code":""},{"path":"/reference/as_draws.html","id":null,"dir":"Reference","previous_headings":"","what":"Creates a draws object — as_draws","title":"Creates a draws object — as_draws","text":"Creates draws object final output call draws().","code":""},{"path":"/reference/as_draws.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Creates a draws object — as_draws","text":"","code":"as_draws(method, samples, data, formula, n_failures = NULL, fit = NULL)"},{"path":"/reference/as_draws.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Creates a draws object — as_draws","text":"method method object generated either method_bayes(), method_approxbayes(), method_condmean() method_bmlmi(). samples list sample_single objects. See sample_single(). data R6 longdata object containing relevant input data information. formula Fixed effects formula object used model specification. n_failures Absolute number failures model fit. fit method_bayes() chosen, returns MCMC Stan fit object. Otherwise NULL.","code":""},{"path":"/reference/as_draws.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Creates a draws object — as_draws","text":"draws object named list containing following: data: R6 longdata object containing relevant input data information. method: method object generated either method_bayes(), method_approxbayes() method_condmean(). samples: list containing estimated parameters interest. element samples named list containing following: ids: vector characters containing ids subjects included original dataset. beta: numeric vector estimated regression coefficients. sigma: list estimated covariance matrices (one level vars$group). theta: numeric vector transformed covariances. failed: Logical. TRUE model fit failed. ids_samp: vector characters containing ids subjects included given sample. fit: method_bayes() chosen, returns MCMC Stan fit object. Otherwise NULL. n_failures: absolute number failures model fit. Relevant method_condmean(type = \"bootstrap\"), method_approxbayes() method_bmlmi(). formula: fixed effects formula object used model specification.","code":""},{"path":"/reference/as_imputation.html","id":null,"dir":"Reference","previous_headings":"","what":"Create an imputation object — as_imputation","title":"Create an imputation object — as_imputation","text":"function creates object returned impute(). Essentially glorified wrapper around list() ensuring required elements set class added expected.","code":""},{"path":"/reference/as_imputation.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create an imputation object — as_imputation","text":"","code":"as_imputation(imputations, data, method, references)"},{"path":"/reference/as_imputation.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create an imputation object — as_imputation","text":"imputations list imputations_list's created imputation_df() data longdata object created longDataConstructor() method method object created method_condmean(), method_bayes() method_approxbayes() references named vector. Identifies references used generating imputed values. form c(\"Group\" = \"Reference\", \"Group\" = \"Reference\").","code":""},{"path":"/reference/as_indices.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert indicator to index — as_indices","title":"Convert indicator to index — as_indices","text":"Converts string 0's 1's index positions 1's padding results 0's length","code":""},{"path":"/reference/as_indices.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert indicator to index — as_indices","text":"","code":"as_indices(x)"},{"path":"/reference/as_indices.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert indicator to index — as_indices","text":"x character vector whose values either \"0\" \"1\". elements vector must length","code":""},{"path":"/reference/as_indices.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Convert indicator to index — as_indices","text":".e.","code":"patmap(c(\"1101\", \"0001\")) -> list(c(1,2,4,999), c(4,999, 999, 999))"},{"path":"/reference/as_mmrm_df.html","id":null,"dir":"Reference","previous_headings":"","what":"Creates a ","title":"Creates a ","text":"Converts design matrix + key variables common format particular function following: Renames covariates V1, V2, etc avoid issues special characters variable names Ensures key variables right type Inserts outcome, visit subjid variables data.frame naming outcome, visit subjid provided also insert group variable data.frame named group","code":""},{"path":"/reference/as_mmrm_df.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Creates a ","text":"","code":"as_mmrm_df(designmat, outcome, visit, subjid, group = NULL)"},{"path":"/reference/as_mmrm_df.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Creates a ","text":"designmat data.frame matrix containing covariates use MMRM model. Dummy variables must already expanded , .e. via stats::model.matrix(). contain missing values outcome numeric vector. outcome value regressed MMRM model. visit character / factor vector. Indicates visit outcome value occurred . subjid character / factor vector. subject identifier used link separate visits belong subject. group character / factor vector. Indicates treatment group patient belongs .","code":""},{"path":"/reference/as_mmrm_formula.html","id":null,"dir":"Reference","previous_headings":"","what":"Create MMRM formula — as_mmrm_formula","title":"Create MMRM formula — as_mmrm_formula","text":"Derives MMRM model formula structure mmrm_df. returns formula object form:","code":""},{"path":"/reference/as_mmrm_formula.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create MMRM formula — as_mmrm_formula","text":"","code":"as_mmrm_formula(mmrm_df, cov_struct)"},{"path":"/reference/as_mmrm_formula.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create MMRM formula — as_mmrm_formula","text":"mmrm_df mmrm data.frame created as_mmrm_df() cov_struct Character - covariance structure used, must one \"us\" (default), \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\")","code":""},{"path":"/reference/as_mmrm_formula.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create MMRM formula — as_mmrm_formula","text":"","code":"outcome ~ 0 + V1 + V2 + V4 + ... + us(visit | group / subjid)"},{"path":"/reference/as_model_df.html","id":null,"dir":"Reference","previous_headings":"","what":"Expand data.frame into a design matrix — as_model_df","title":"Expand data.frame into a design matrix — as_model_df","text":"Expands data.frame using formula create design matrix. Key details always place outcome variable first column return object.","code":""},{"path":"/reference/as_model_df.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Expand data.frame into a design matrix — as_model_df","text":"","code":"as_model_df(dat, frm)"},{"path":"/reference/as_model_df.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Expand data.frame into a design matrix — as_model_df","text":"dat data.frame frm formula","code":""},{"path":"/reference/as_model_df.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Expand data.frame into a design matrix — as_model_df","text":"outcome column may contain NA's none variables listed formula contain missing values","code":""},{"path":"/reference/as_simple_formula.html","id":null,"dir":"Reference","previous_headings":"","what":"Creates a simple formula object from a string — as_simple_formula","title":"Creates a simple formula object from a string — as_simple_formula","text":"Converts string list variables formula object","code":""},{"path":"/reference/as_simple_formula.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Creates a simple formula object from a string — as_simple_formula","text":"","code":"as_simple_formula(outcome, covars)"},{"path":"/reference/as_simple_formula.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Creates a simple formula object from a string — as_simple_formula","text":"outcome character (length 1 vector). Name outcome variable covars character (vector). Name covariates","code":""},{"path":"/reference/as_simple_formula.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Creates a simple formula object from a string — as_simple_formula","text":"formula","code":""},{"path":"/reference/as_stan_array.html","id":null,"dir":"Reference","previous_headings":"","what":"As array — as_stan_array","title":"As array — as_stan_array","text":"Converts numeric value length 1 1 dimension array. avoid type errors thrown stan length 1 numeric vectors provided R stan::vector inputs","code":""},{"path":"/reference/as_stan_array.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"As array — as_stan_array","text":"","code":"as_stan_array(x)"},{"path":"/reference/as_stan_array.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"As array — as_stan_array","text":"x numeric vector","code":""},{"path":"/reference/as_strata.html","id":null,"dir":"Reference","previous_headings":"","what":"Create vector of Stratas — as_strata","title":"Create vector of Stratas — as_strata","text":"Collapse multiple categorical variables distinct unique categories. e.g. return","code":"as_strata(c(1,1,2,2,2,1), c(5,6,5,5,6,5)) c(1,2,3,3,4,1)"},{"path":"/reference/as_strata.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create vector of Stratas — as_strata","text":"","code":"as_strata(...)"},{"path":"/reference/as_strata.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create vector of Stratas — as_strata","text":"... numeric/character/factor vectors length","code":""},{"path":"/reference/as_strata.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create vector of Stratas — as_strata","text":"","code":"if (FALSE) { # \\dontrun{ as_strata(c(1,1,2,2,2,1), c(5,6,5,5,6,5)) } # }"},{"path":"/reference/assert_variables_exist.html","id":null,"dir":"Reference","previous_headings":"","what":"Assert that all variables exist within a dataset — assert_variables_exist","title":"Assert that all variables exist within a dataset — assert_variables_exist","text":"Performs assertion check ensure vector variable exists within data.frame expected.","code":""},{"path":"/reference/assert_variables_exist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Assert that all variables exist within a dataset — assert_variables_exist","text":"","code":"assert_variables_exist(data, vars)"},{"path":"/reference/assert_variables_exist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Assert that all variables exist within a dataset — assert_variables_exist","text":"data data.frame vars character vector variable names","code":""},{"path":"/reference/char2fct.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert character variables to factor — char2fct","title":"Convert character variables to factor — char2fct","text":"Provided vector variable names function converts character variables factors. affect numeric existing factor variables","code":""},{"path":"/reference/char2fct.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert character variables to factor — char2fct","text":"","code":"char2fct(data, vars = NULL)"},{"path":"/reference/char2fct.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert character variables to factor — char2fct","text":"data data.frame vars character vector variables data","code":""},{"path":"/reference/check_ESS.html","id":null,"dir":"Reference","previous_headings":"","what":"Diagnostics of the MCMC based on ESS — check_ESS","title":"Diagnostics of the MCMC based on ESS — check_ESS","text":"Check quality MCMC draws posterior distribution checking whether relative ESS sufficiently large.","code":""},{"path":"/reference/check_ESS.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Diagnostics of the MCMC based on ESS — check_ESS","text":"","code":"check_ESS(stan_fit, n_draws, threshold_lowESS = 0.4)"},{"path":"/reference/check_ESS.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Diagnostics of the MCMC based on ESS — check_ESS","text":"stan_fit stanfit object. n_draws Number MCMC draws. threshold_lowESS number [0,1] indicating minimum acceptable value relative ESS. See details.","code":""},{"path":"/reference/check_ESS.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Diagnostics of the MCMC based on ESS — check_ESS","text":"warning message case detected problems.","code":""},{"path":"/reference/check_ESS.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Diagnostics of the MCMC based on ESS — check_ESS","text":"check_ESS() works follows: Extract ESS stan_fit parameter model. Compute relative ESS (.e. ESS divided number draws). Check whether parameter ESS lower threshold. least one parameter relative ESS threshold, warning thrown.","code":""},{"path":"/reference/check_hmc_diagn.html","id":null,"dir":"Reference","previous_headings":"","what":"Diagnostics of the MCMC based on HMC-related measures. — check_hmc_diagn","title":"Diagnostics of the MCMC based on HMC-related measures. — check_hmc_diagn","text":"Check : divergent iterations. Bayesian Fraction Missing Information (BFMI) sufficiently low. number iterations saturated max treedepth zero. Please see rstan::check_hmc_diagnostics() details.","code":""},{"path":"/reference/check_hmc_diagn.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Diagnostics of the MCMC based on HMC-related measures. — check_hmc_diagn","text":"","code":"check_hmc_diagn(stan_fit)"},{"path":"/reference/check_hmc_diagn.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Diagnostics of the MCMC based on HMC-related measures. — check_hmc_diagn","text":"stan_fit stanfit object.","code":""},{"path":"/reference/check_hmc_diagn.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Diagnostics of the MCMC based on HMC-related measures. — check_hmc_diagn","text":"warning message case detected problems.","code":""},{"path":"/reference/check_mcmc.html","id":null,"dir":"Reference","previous_headings":"","what":"Diagnostics of the MCMC — check_mcmc","title":"Diagnostics of the MCMC — check_mcmc","text":"Diagnostics MCMC","code":""},{"path":"/reference/check_mcmc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Diagnostics of the MCMC — check_mcmc","text":"","code":"check_mcmc(stan_fit, n_draws, threshold_lowESS = 0.4)"},{"path":"/reference/check_mcmc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Diagnostics of the MCMC — check_mcmc","text":"stan_fit stanfit object. n_draws Number MCMC draws. threshold_lowESS number [0,1] indicating minimum acceptable value relative ESS. See details.","code":""},{"path":"/reference/check_mcmc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Diagnostics of the MCMC — check_mcmc","text":"warning message case detected problems.","code":""},{"path":"/reference/check_mcmc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Diagnostics of the MCMC — check_mcmc","text":"Performs checks quality MCMC. See check_ESS() check_hmc_diagn() details.","code":""},{"path":"/reference/compute_sigma.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute covariance matrix for some reference-based methods (JR, CIR) — compute_sigma","title":"Compute covariance matrix for some reference-based methods (JR, CIR) — compute_sigma","text":"Adapt covariance matrix reference-based methods. Used Copy Increments Reference (CIR) Jump Reference (JTR) methods, adapt covariance matrix different pre-deviation post deviation covariance structures. See Carpenter et al. (2013)","code":""},{"path":"/reference/compute_sigma.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute covariance matrix for some reference-based methods (JR, CIR) — compute_sigma","text":"","code":"compute_sigma(sigma_group, sigma_ref, index_mar)"},{"path":"/reference/compute_sigma.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute covariance matrix for some reference-based methods (JR, CIR) — compute_sigma","text":"sigma_group covariance matrix dimensions equal index_mar subjects original group sigma_ref covariance matrix dimensions equal index_mar subjects reference group index_mar logical vector indicating visits meet MAR assumption subject. .e. identifies observations non-MAR intercurrent event (ICE).","code":""},{"path":"/reference/compute_sigma.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute covariance matrix for some reference-based methods (JR, CIR) — compute_sigma","text":"Carpenter, James R., James H. Roger, Michael G. Kenward. \"Analysis longitudinal trials protocol deviation: framework relevant, accessible assumptions, inference via multiple imputation.\" Journal Biopharmaceutical statistics 23.6 (2013): 1352-1371.","code":""},{"path":"/reference/convert_to_imputation_list_df.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert list of imputation_list_single() objects to an imputation_list_df() object (i.e. a list of imputation_df() objects's) — convert_to_imputation_list_df","title":"Convert list of imputation_list_single() objects to an imputation_list_df() object (i.e. a list of imputation_df() objects's) — convert_to_imputation_list_df","text":"Convert list imputation_list_single() objects imputation_list_df() object (.e. list imputation_df() objects's)","code":""},{"path":"/reference/convert_to_imputation_list_df.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert list of imputation_list_single() objects to an imputation_list_df() object (i.e. a list of imputation_df() objects's) — convert_to_imputation_list_df","text":"","code":"convert_to_imputation_list_df(imputes, sample_ids)"},{"path":"/reference/convert_to_imputation_list_df.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert list of imputation_list_single() objects to an imputation_list_df() object (i.e. a list of imputation_df() objects's) — convert_to_imputation_list_df","text":"imputes list imputation_list_single() objects sample_ids list 1 element per required imputation_df. element must contain vector \"ID\"'s correspond imputation_single() ID's required dataset. total number ID's must equal total number rows within imputes$imputations accommodate method_bmlmi() impute_data_individual() function returns list imputation_list_single() objects 1 object per subject. imputation_list_single() stores subjects imputations matrix columns matrix correspond D method_bmlmi(). Note methods (.e. methods_*()) special case D = 1. number rows matrix varies subject equal number times patient selected imputation (non-conditional mean methods 1 per subject per imputed dataset). function best illustrated example: convert_to_imputation_df(imputes, sample_ids) result : Note different repetitions (.e. value set D) grouped together sequentially.","code":"imputes = list( imputation_list_single( id = \"Tom\", imputations = matrix( imputation_single_t_1_1, imputation_single_t_1_2, imputation_single_t_2_1, imputation_single_t_2_2, imputation_single_t_3_1, imputation_single_t_3_2 ) ), imputation_list_single( id = \"Tom\", imputations = matrix( imputation_single_h_1_1, imputation_single_h_1_2, ) ) ) sample_ids <- list( c(\"Tom\", \"Harry\", \"Tom\"), c(\"Tom\") ) imputation_list_df( imputation_df( imputation_single_t_1_1, imputation_single_h_1_1, imputation_single_t_2_1 ), imputation_df( imputation_single_t_1_2, imputation_single_h_1_2, imputation_single_t_2_2 ), imputation_df( imputation_single_t_3_1 ), imputation_df( imputation_single_t_3_2 ) )"},{"path":"/reference/d_lagscale.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate delta from a lagged scale coefficient — d_lagscale","title":"Calculate delta from a lagged scale coefficient — d_lagscale","text":"Calculates delta value based upon baseline delta value post ICE scaling coefficient.","code":""},{"path":"/reference/d_lagscale.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate delta from a lagged scale coefficient — d_lagscale","text":"","code":"d_lagscale(delta, dlag, is_post_ice)"},{"path":"/reference/d_lagscale.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate delta from a lagged scale coefficient — d_lagscale","text":"delta numeric vector. Determines baseline amount delta applied visit. dlag numeric vector. Determines scaling applied delta based upon visit ICE occurred . Must length delta. is_post_ice logical vector. Indicates whether visit \"post-ICE\" .","code":""},{"path":"/reference/d_lagscale.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate delta from a lagged scale coefficient — d_lagscale","text":"See delta_template() full details calculation performed.","code":""},{"path":"/reference/delta_template.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a delta data.frame template — delta_template","title":"Create a delta data.frame template — delta_template","text":"Creates data.frame format required analyse() use applying delta adjustment.","code":""},{"path":"/reference/delta_template.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a delta data.frame template — delta_template","text":"","code":"delta_template(imputations, delta = NULL, dlag = NULL, missing_only = TRUE)"},{"path":"/reference/delta_template.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a delta data.frame template — delta_template","text":"imputations imputation object created impute(). delta NULL numeric vector. Determines baseline amount delta applied visit. See details. numeric vector must length number unique visits original dataset. dlag NULL numeric vector. Determines scaling applied delta based upon visit ICE occurred . See details. numeric vector must length number unique visits original dataset. missing_only Logical, TRUE non-missing post-ICE data delta value 0 assigned. Note calculation (described details section) performed first overwritten 0's end (.e. delta values missing post-ICE visits stay regardless option).","code":""},{"path":"/reference/delta_template.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create a delta data.frame template — delta_template","text":"apply delta adjustment analyse() function expects delta data.frame 3 variables: vars$subjid, vars$visit delta (vars object supplied original call draws() created set_vars() function). function return data.frame aforementioned variables one row per subject per visit. delta argument function NULL delta column returned data.frame 0 observations. delta argument NULL delta calculated separately subject accumulative sum delta multiplied scaling coefficient dlag based upon many visits subject's intercurrent event (ICE) visit question . best illustrated example: Let delta = c(5,6,7,8) dlag=c(1,2,3,4) (.e. assuming 4 visits) lets say subject ICE visit 2. calculation follows: say subject delta offset 0 applied visit-1, 6 visit-2, 20 visit-3 44 visit-4. comparison, lets say subject instead ICE visit 3, calculation follows: terms practical usage, lets say wanted delta 5 used post ICE visits regardless proximity ICE visit. can achieved setting delta = c(5,5,5,5) dlag = c(1,0,0,0). example lets say subject ICE visit-1, calculation follows: Another way using arguments set delta difference time visits dlag amount delta per unit time. example lets say visit weeks 1, 5, 6 & 9 want delta 3 applied week ICE. can achieved setting delta = c(0,4,1,3) (difference weeks visit) dlag = c(3, 3, 3, 3). example lets say subject ICE week-5 (.e. visit-2) calculation : .e. week-6 (1 week ICE) delta 3 week-9 (4 weeks ICE) delta 12. Please note function also returns several utility variables user can create custom logic defining delta set . additional variables include: is_mar - observation missing regarded MAR? variable set FALSE observations occurred non-MAR ICE, otherwise set TRUE. is_missing - outcome variable observation missing. is_post_ice - observation occur patient's ICE defined data_ice dataset supplied draws(). strategy - imputation strategy assigned subject. design implementation function largely based upon functionality implemented called \"five marcos\" James Roger. See Roger (2021).","code":"v1 v2 v3 v4 -------------- 5 6 7 8 # delta assigned to each visit 0 1 2 3 # lagged scaling starting from the first visit after the subjects ICE -------------- 0 6 14 24 # delta * lagged scaling -------------- 0 6 20 44 # accumulative sum of delta to be applied to each visit v1 v2 v3 v4 -------------- 5 6 7 8 # delta assigned to each visit 0 0 1 2 # lagged scaling starting from the first visit after the subjects ICE -------------- 0 0 7 16 # delta * lagged scaling -------------- 0 0 7 23 # accumulative sum of delta to be applied to each visit v1 v2 v3 v4 -------------- 5 5 5 5 # delta assigned to each visit 1 0 0 0 # lagged scaling starting from the first visit after the subjects ICE -------------- 5 0 0 0 # delta * lagged scaling -------------- 5 5 5 5 # accumulative sum of delta to be applied to each visit v1 v2 v3 v4 -------------- 0 4 1 3 # delta assigned to each visit 0 0 3 3 # lagged scaling starting from the first visit after the subjects ICE -------------- 0 0 3 9 # delta * lagged scaling -------------- 0 0 3 12 # accumulative sum of delta to be applied to each visit"},{"path":"/reference/delta_template.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Create a delta data.frame template — delta_template","text":"Roger, James. Reference-based mi via multivariate normal rm (“five macros” miwithd), 2021. URL https://www.lshtm.ac.uk/research/centres-projects-groups/missing-data#dia-missing-data.","code":""},{"path":[]},{"path":"/reference/delta_template.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a delta data.frame template — delta_template","text":"","code":"if (FALSE) { # \\dontrun{ delta_template(imputeObj) delta_template(imputeObj, delta = c(5,6,7,8), dlag = c(1,2,3,4)) } # }"},{"path":"/reference/draws.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit the base imputation model and get parameter estimates — draws","title":"Fit the base imputation model and get parameter estimates — draws","text":"draws fits base imputation model observed outcome data according given multiple imputation methodology. According user's method specification, returns either draws posterior distribution model parameters required Bayesian multiple imputation frequentist parameter estimates original data bootstrapped leave-one-datasets required conditional mean imputation. purpose imputation model estimate model parameters absence intercurrent events (ICEs) handled using reference-based imputation methods. reason, observed outcome data ICEs, reference-based imputation methods specified, removed considered missing purpose estimating imputation model, purpose . imputation model mixed model repeated measures (MMRM) valid missing--random (MAR) assumption. can fit using maximum likelihood (ML) restricted ML (REML) estimation, Bayesian approach, approximate Bayesian approach according user's method specification. ML/REML approaches approximate Bayesian approach support several possible covariance structures, Bayesian approach based MCMC sampling supports unstructured covariance structure. case covariance matrix can assumed different across group.","code":""},{"path":"/reference/draws.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit the base imputation model and get parameter estimates — draws","text":"","code":"draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE) # S3 method for class 'approxbayes' draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE) # S3 method for class 'condmean' draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE) # S3 method for class 'bmlmi' draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE) # S3 method for class 'bayes' draws(data, data_ice = NULL, vars, method, ncores = 1, quiet = FALSE)"},{"path":"/reference/draws.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit the base imputation model and get parameter estimates — draws","text":"data data.frame containing data used model. See details. data_ice data.frame specifies information related ICEs imputation strategies. See details. vars vars object generated set_vars(). See details. method method object generated either method_bayes(), method_approxbayes(), method_condmean() method_bmlmi(). specifies multiple imputation methodology used. See details. ncores single numeric specifying number cores use creating draws object. Note parameter ignored method_bayes() (Default = 1). Can also cluster object generated make_rbmi_cluster() quiet Logical, TRUE suppress printing progress information printed console.","code":""},{"path":"/reference/draws.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit the base imputation model and get parameter estimates — draws","text":"draws object named list containing following: data: R6 longdata object containing relevant input data information. method: method object generated either method_bayes(), method_approxbayes() method_condmean(). samples: list containing estimated parameters interest. element samples named list containing following: ids: vector characters containing ids subjects included original dataset. beta: numeric vector estimated regression coefficients. sigma: list estimated covariance matrices (one level vars$group). theta: numeric vector transformed covariances. failed: Logical. TRUE model fit failed. ids_samp: vector characters containing ids subjects included given sample. fit: method_bayes() chosen, returns MCMC Stan fit object. Otherwise NULL. n_failures: absolute number failures model fit. Relevant method_condmean(type = \"bootstrap\"), method_approxbayes() method_bmlmi(). formula: fixed effects formula object used model specification.","code":""},{"path":"/reference/draws.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit the base imputation model and get parameter estimates — draws","text":"draws performs first step multiple imputation (MI) procedure: fitting base imputation model. goal estimate parameters interest needed imputation phase (.e. regression coefficients covariance matrices MMRM model). function distinguishes following methods: Bayesian MI based MCMC sampling: draws returns draws posterior distribution parameters using Bayesian approach based MCMC sampling. method can specified using method = method_bayes(). Approximate Bayesian MI based bootstrapping: draws returns draws posterior distribution parameters using approximate Bayesian approach, sampling posterior distribution simulated fitting MMRM model bootstrap samples original dataset. method can specified using method = method_approxbayes()]. Conditional mean imputation bootstrap re-sampling: draws returns MMRM parameter estimates original dataset n_samples bootstrap samples. method can specified using method = method_condmean() argument type = \"bootstrap\". Conditional mean imputation jackknife re-sampling: draws returns MMRM parameter estimates original dataset leave-one-subject-sample. method can specified using method = method_condmean() argument type = \"jackknife\". Bootstrapped Maximum Likelihood MI: draws returns MMRM parameter estimates given number bootstrap samples needed perform random imputations bootstrapped samples. method can specified using method = method_bmlmi(). Bayesian MI based MCMC sampling proposed Carpenter, Roger, Kenward (2013) first introduced reference-based imputation methods. Approximate Bayesian MI discussed Little Rubin (2002). Conditional mean imputation methods discussed Wolbers et al (2022). Bootstrapped Maximum Likelihood MI described Von Hippel & Bartlett (2021). argument data contains longitudinal data. must least following variables: subjid: factor vector containing subject ids. visit: factor vector containing visit outcome observed . group: factor vector containing group subject belongs . outcome: numeric vector containing outcome variable. might contain missing values. Additional baseline time-varying covariates must included data. data must one row per visit per subject. means incomplete outcome data must set NA instead related row missing. Missing values covariates allowed. data incomplete expand_locf() helper function can used insert missing rows using Last Observation Carried Forward (LOCF) imputation impute covariates values. Note LOCF generally principled imputation method used appropriate specific covariate. Please note special provisioning baseline outcome values. want baseline observations included model part response variable removed advance outcome variable data. time want include baseline outcome covariate model, included separate column data (covariate). Character covariates explicitly cast factors. use custom analysis function requires specific reference levels character covariates (example computation least square means computation) advised manually cast character covariates factor advance running draws(). argument data_ice contains information occurrence ICEs. data.frame 3 columns: Subject ID: character vector containing ids subjects experienced ICE. column must named specified vars$subjid. Visit: character vector containing first visit occurrence ICE (.e. first visit affected ICE). visits must equal one levels data[[vars$visit]]. multiple ICEs happen subject, first non-MAR visit used. column must named specified vars$visit. Strategy: character vector specifying imputation strategy address ICE subject. column must named specified vars$strategy. Possible imputation strategies : \"MAR\": Missing Random. \"CIR\": Copy Increments Reference. \"CR\": Copy Reference. \"JR\": Jump Reference. \"LMCF\": Last Mean Carried Forward. explanations imputation strategies, see Carpenter, Roger, Kenward (2013), Cro et al (2021), Wolbers et al (2022). Please note user-defined imputation strategies can also set. data_ice argument necessary stage since (explained Wolbers et al (2022)), model fitted removing observations incompatible imputation model, .e. observed data data_ice[[vars$visit]] addressed imputation strategy different MAR excluded model fit. However observations discarded data imputation phase (performed function (impute()). summarize, stage pre-ICE data post-ICE data ICEs MAR imputation specified used. data_ice argument omitted, subject record within data_ice, assumed relevant subject's data pre-ICE missing visits imputed MAR assumption observed data used fit base imputation model. Please note ICE visit updated via update_strategy argument impute(); means subjects record data_ice always missing data imputed MAR assumption even strategy updated. vars argument named list specifies names key variables within data data_ice. list created set_vars() contains following named elements: subjid: name column data data_ice contains subject ids variable. visit: name column data data_ice contains visit variable. group: name column data contains group variable. outcome: name column data contains outcome variable. covariates: vector characters contains covariates included model (including interactions specified \"covariateName1*covariateName2\"). covariates provided default model specification outcome ~ 1 + visit + group used. Please note group*visit interaction included model default. strata: covariates used stratification variables bootstrap sampling. default vars$group set stratification variable. Needed method_condmean(type = \"bootstrap\") method_approxbayes(). strategy: name column data_ice contains subject-specific imputation strategy. experience, Bayesian MI (method = method_bayes()) relatively low number samples (e.g. n_samples 100) frequently triggers STAN warnings R-hat \"largest R-hat X.XX, indicating chains mixed\". many instances, warning might spurious, .e. standard diagnostics analysis MCMC samples indicate issues results look reasonable. Increasing number samples e.g. 150 usually gets rid warning.","code":""},{"path":"/reference/draws.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit the base imputation model and get parameter estimates — draws","text":"James R Carpenter, James H Roger, Michael G Kenward. Analysis longitudinal trials protocol deviation: framework relevant, accessible assumptions, inference via multiple imputation. Journal Biopharmaceutical Statistics, 23(6):1352–1371, 2013. Suzie Cro, Tim P Morris, Michael G Kenward, James R Carpenter. Sensitivity analysis clinical trials missing continuous outcome data using controlled multiple imputation: practical guide. Statistics Medicine, 39(21):2815–2842, 2020. Roderick J. . Little Donald B. Rubin. Statistical Analysis Missing Data, Second Edition. John Wiley & Sons, Hoboken, New Jersey, 2002. [Section 10.2.3] Marcel Wolbers, Alessandro Noci, Paul Delmar, Craig Gower-Page, Sean Yiu, Jonathan W. Bartlett. Standard reference-based conditional mean imputation. https://arxiv.org/abs/2109.11162, 2022. Von Hippel, Paul T Bartlett, Jonathan W. Maximum likelihood multiple imputation: Faster imputations consistent standard errors without posterior draws. 2021.","code":""},{"path":[]},{"path":"/reference/ensure_rstan.html","id":null,"dir":"Reference","previous_headings":"","what":"Ensure rstan exists — ensure_rstan","title":"Ensure rstan exists — ensure_rstan","text":"Checks see rstan exists throws helpful error message","code":""},{"path":"/reference/ensure_rstan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Ensure rstan exists — ensure_rstan","text":"","code":"ensure_rstan()"},{"path":"/reference/eval_mmrm.html","id":null,"dir":"Reference","previous_headings":"","what":"Evaluate a call to mmrm — eval_mmrm","title":"Evaluate a call to mmrm — eval_mmrm","text":"utility function attempts evaluate call mmrm managing warnings errors thrown. particular function attempts catch warnings errors instead surfacing simply add additional element failed value TRUE. allows multiple calls made without program exiting.","code":""},{"path":"/reference/eval_mmrm.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Evaluate a call to mmrm — eval_mmrm","text":"","code":"eval_mmrm(expr)"},{"path":"/reference/eval_mmrm.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Evaluate a call to mmrm — eval_mmrm","text":"expr expression evaluated. call mmrm::mmrm().","code":""},{"path":"/reference/eval_mmrm.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Evaluate a call to mmrm — eval_mmrm","text":"function originally developed use glmmTMB needed hand-holding dropping false-positive warnings. important now kept around encase need catch false-positive warnings future.","code":""},{"path":[]},{"path":"/reference/eval_mmrm.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Evaluate a call to mmrm — eval_mmrm","text":"","code":"if (FALSE) { # \\dontrun{ eval_mmrm({ mmrm::mmrm(formula, data) }) } # }"},{"path":"/reference/expand.html","id":null,"dir":"Reference","previous_headings":"","what":"Expand and fill in missing data.frame rows — expand","title":"Expand and fill in missing data.frame rows — expand","text":"functions essentially wrappers around base::expand.grid() ensure missing combinations data inserted data.frame imputation/fill methods updating covariate values newly created rows.","code":""},{"path":"/reference/expand.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Expand and fill in missing data.frame rows — expand","text":"","code":"expand(data, ...) fill_locf(data, vars, group = NULL, order = NULL) expand_locf(data, ..., vars, group, order)"},{"path":"/reference/expand.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Expand and fill in missing data.frame rows — expand","text":"data dataset expand fill . ... variables levels expanded (note duplicate entries levels result multiple rows level). vars character vector containing names variables need filled . group character vector containing names variables group performing LOCF imputation var. order character vector containing names additional variables sort data.frame performing LOCF.","code":""},{"path":"/reference/expand.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Expand and fill in missing data.frame rows — expand","text":"draws() function makes assumption subjects visits present data.frame covariate values non missing; expand(), fill_locf() expand_locf() utility functions support users ensuring data.frame's conform assumptions. expand() takes vectors expected levels data.frame expands combinations inserting missing rows data.frame. Note \"expanded\" variables cast factors. fill_locf() applies LOCF imputation named covariates fill NAs created insertion new rows expand() (though note distinction made existing NAs newly created NAs). Note data.frame sorted c(group, order) performing LOCF imputation; data.frame returned original sort order however. expand_locf() simple composition function fill_locf() expand() .e. fill_locf(expand(...)).","code":""},{"path":"/reference/expand.html","id":"missing-first-values","dir":"Reference","previous_headings":"","what":"Missing First Values","title":"Expand and fill in missing data.frame rows — expand","text":"fill_locf() function performs last observation carried forward imputation. natural consequence unable impute missing observations observation first value given subject / grouping. values deliberately imputed risks silent errors case time varying covariates. One solution first use expand_locf() just visit variable time varying covariates merge baseline covariates afterwards .e.","code":"library(dplyr) dat_expanded <- expand( data = dat, subject = c(\"pt1\", \"pt2\", \"pt3\", \"pt4\"), visit = c(\"vis1\", \"vis2\", \"vis3\") ) dat_filled <- dat_expanded %>% left_join(baseline_covariates, by = \"subject\")"},{"path":"/reference/expand.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Expand and fill in missing data.frame rows — expand","text":"","code":"if (FALSE) { # \\dontrun{ dat_expanded <- expand( data = dat, subject = c(\"pt1\", \"pt2\", \"pt3\", \"pt4\"), visit = c(\"vis1\", \"vis2\", \"vis3\") ) dat_filled <- fill_loc( data = dat_expanded, vars = c(\"Sex\", \"Age\"), group = \"subject\", order = \"visit\" ) ## Or dat_filled <- expand_locf( data = dat, subject = c(\"pt1\", \"pt2\", \"pt3\", \"pt4\"), visit = c(\"vis1\", \"vis2\", \"vis3\"), vars = c(\"Sex\", \"Age\"), group = \"subject\", order = \"visit\" ) } # }"},{"path":"/reference/extract_covariates.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract Variables from string vector — extract_covariates","title":"Extract Variables from string vector — extract_covariates","text":"Takes string including potentially model terms like * : extracts individual variables","code":""},{"path":"/reference/extract_covariates.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract Variables from string vector — extract_covariates","text":"","code":"extract_covariates(x)"},{"path":"/reference/extract_covariates.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract Variables from string vector — extract_covariates","text":"x string variable names potentially including interaction terms","code":""},{"path":"/reference/extract_covariates.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Extract Variables from string vector — extract_covariates","text":".e. c(\"v1\", \"v2\", \"v2*v3\", \"v1:v2\") becomes c(\"v1\", \"v2\", \"v3\")","code":""},{"path":"/reference/extract_data_nmar_as_na.html","id":null,"dir":"Reference","previous_headings":"","what":"Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy) — extract_data_nmar_as_na","title":"Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy) — extract_data_nmar_as_na","text":"Set NA outcome values MNAR missing (.e. occur ICE handled using reference-based imputation strategy)","code":""},{"path":"/reference/extract_data_nmar_as_na.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy) — extract_data_nmar_as_na","text":"","code":"extract_data_nmar_as_na(longdata)"},{"path":"/reference/extract_data_nmar_as_na.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy) — extract_data_nmar_as_na","text":"longdata R6 longdata object containing relevant input data information.","code":""},{"path":"/reference/extract_data_nmar_as_na.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Set to NA outcome values that would be MNAR if they were missing (i.e. which occur after an ICE handled using a reference-based imputation strategy) — extract_data_nmar_as_na","text":"data.frame containing longdata$get_data(longdata$ids), MNAR outcome values set NA.","code":""},{"path":"/reference/extract_draws.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract draws from a stanfit object — extract_draws","title":"Extract draws from a stanfit object — extract_draws","text":"Extract draws stanfit object convert lists. function rstan::extract() returns draws given parameter array. function calls rstan::extract() extract draws stanfit object convert arrays lists.","code":""},{"path":"/reference/extract_draws.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract draws from a stanfit object — extract_draws","text":"","code":"extract_draws(stan_fit)"},{"path":"/reference/extract_draws.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract draws from a stanfit object — extract_draws","text":"stan_fit stanfit object.","code":""},{"path":"/reference/extract_draws.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extract draws from a stanfit object — extract_draws","text":"named list length 2 containing: beta: list length equal number draws containing draws posterior distribution regression coefficients. sigma: list length equal number draws containing draws posterior distribution covariance matrices. element list list length equal 1 same_cov = TRUE equal number groups same_cov = FALSE.","code":""},{"path":"/reference/extract_imputed_df.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract imputed dataset — extract_imputed_df","title":"Extract imputed dataset — extract_imputed_df","text":"Takes imputation object generated imputation_df() uses extract completed dataset longdata object created longDataConstructor(). Also applies delta transformation data.frame provided delta argument. See analyse() details structure data.frame. Subject IDs returned data.frame scrambled .e. original values.","code":""},{"path":"/reference/extract_imputed_df.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract imputed dataset — extract_imputed_df","text":"","code":"extract_imputed_df(imputation, ld, delta = NULL, idmap = FALSE)"},{"path":"/reference/extract_imputed_df.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract imputed dataset — extract_imputed_df","text":"imputation imputation object generated imputation_df(). ld longdata object generated longDataConstructor(). delta Either NULL data.frame. used offset outcome values imputed dataset. idmap Logical. TRUE attribute called \"idmap\" attached return object contains list maps old subject ids new subject ids.","code":""},{"path":"/reference/extract_imputed_df.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extract imputed dataset — extract_imputed_df","text":"data.frame.","code":""},{"path":"/reference/extract_imputed_dfs.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract imputed datasets — extract_imputed_dfs","title":"Extract imputed datasets — extract_imputed_dfs","text":"Extracts imputed datasets contained within imputations object generated impute().","code":""},{"path":"/reference/extract_imputed_dfs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract imputed datasets — extract_imputed_dfs","text":"","code":"extract_imputed_dfs( imputations, index = seq_along(imputations$imputations), delta = NULL, idmap = FALSE )"},{"path":"/reference/extract_imputed_dfs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract imputed datasets — extract_imputed_dfs","text":"imputations imputations object created impute(). index indexes imputed datasets return. default, datasets within imputations object returned. delta data.frame containing delta transformation applied imputed dataset. See analyse() details format specification data.frame. idmap Logical. subject IDs imputed data.frame's replaced new IDs ensure unique. Setting argument TRUE attaches attribute, called idmap, returned data.frame's provide map new subject IDs old subject IDs.","code":""},{"path":"/reference/extract_imputed_dfs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extract imputed datasets — extract_imputed_dfs","text":"list data.frames equal length index argument.","code":""},{"path":[]},{"path":"/reference/extract_imputed_dfs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Extract imputed datasets — extract_imputed_dfs","text":"","code":"if (FALSE) { # \\dontrun{ extract_imputed_dfs(imputeObj) extract_imputed_dfs(imputeObj, c(1:3)) } # }"},{"path":"/reference/extract_params.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract parameters from a MMRM model — extract_params","title":"Extract parameters from a MMRM model — extract_params","text":"Extracts beta sigma coefficients MMRM model created mmrm::mmrm().","code":""},{"path":"/reference/extract_params.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract parameters from a MMRM model — extract_params","text":"","code":"extract_params(fit)"},{"path":"/reference/extract_params.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract parameters from a MMRM model — extract_params","text":"fit object created mmrm::mmrm()","code":""},{"path":"/reference/fit_mcmc.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit the base imputation model using a Bayesian approach — fit_mcmc","title":"Fit the base imputation model using a Bayesian approach — fit_mcmc","text":"fit_mcmc() fits base imputation model using Bayesian approach. done MCMC method implemented stan run using function rstan::sampling(). function returns draws posterior distribution model parameters stanfit object. Additionally performs multiple diagnostics checks chain returns warnings case detected issues.","code":""},{"path":"/reference/fit_mcmc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit the base imputation model using a Bayesian approach — fit_mcmc","text":"","code":"fit_mcmc(designmat, outcome, group, subjid, visit, method, quiet = FALSE)"},{"path":"/reference/fit_mcmc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit the base imputation model using a Bayesian approach — fit_mcmc","text":"designmat design matrix fixed effects. outcome response variable. Must numeric. group Character vector containing group variable. subjid Character vector containing subjects IDs. visit Character vector containing visit variable. method method object generated method_bayes(). quiet Specify whether stan sampling log printed console.","code":""},{"path":"/reference/fit_mcmc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit the base imputation model using a Bayesian approach — fit_mcmc","text":"named list composed following: samples: named list containing draws parameter. corresponds output extract_draws(). fit: stanfit object.","code":""},{"path":"/reference/fit_mcmc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit the base imputation model using a Bayesian approach — fit_mcmc","text":"Bayesian model assumes multivariate normal likelihood function weakly-informative priors model parameters: particular, uniform priors assumed regression coefficients inverse-Wishart priors covariance matrices. chain initialized using REML parameter estimates MMRM starting values. function performs following steps: Fit MMRM using REML approach. Prepare input data MCMC fit described data{} block Stan file. See prepare_stan_data() details. Run MCMC according input arguments using starting values REML parameter estimates estimated point 1. Performs diagnostics checks MCMC. See check_mcmc() details. Extract draws model fit. chains perform method$n_samples draws keeping one every method$burn_between iterations. Additionally first method$burn_in iterations discarded. total number iterations method$burn_in + method$burn_between*method$n_samples. purpose method$burn_in ensure samples drawn stationary distribution Markov Chain. method$burn_between aims keep draws uncorrelated .","code":""},{"path":"/reference/fit_mmrm.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit a MMRM model — fit_mmrm","title":"Fit a MMRM model — fit_mmrm","text":"Fits MMRM model allowing different covariance structures using mmrm::mmrm(). Returns list key model parameters beta, sigma additional element failed indicating whether fit failed converge. fit fail converge beta sigma present.","code":""},{"path":"/reference/fit_mmrm.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit a MMRM model — fit_mmrm","text":"","code":"fit_mmrm( designmat, outcome, subjid, visit, group, cov_struct = c(\"us\", \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\"), REML = TRUE, same_cov = TRUE )"},{"path":"/reference/fit_mmrm.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit a MMRM model — fit_mmrm","text":"designmat data.frame matrix containing covariates use MMRM model. Dummy variables must already expanded , .e. via stats::model.matrix(). contain missing values outcome numeric vector. outcome value regressed MMRM model. subjid character / factor vector. subject identifier used link separate visits belong subject. visit character / factor vector. Indicates visit outcome value occurred . group character / factor vector. Indicates treatment group patient belongs . cov_struct character value. Specifies covariance structure use. Must one \"us\" (default), \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\") REML logical. Specifies whether restricted maximum likelihood used same_cov logical. Used specify shared individual covariance matrix used per group","code":""},{"path":"/reference/generate_data_single.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate data for a single group — generate_data_single","title":"Generate data for a single group — generate_data_single","text":"Generate data single group","code":""},{"path":"/reference/generate_data_single.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate data for a single group — generate_data_single","text":"","code":"generate_data_single(pars_group, strategy_fun = NULL, distr_pars_ref = NULL)"},{"path":"/reference/generate_data_single.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate data for a single group — generate_data_single","text":"pars_group simul_pars object generated set_simul_pars(). specifies simulation parameters given group. strategy_fun Function implementing trajectories intercurrent event (ICE). Must one getStrategies(). See getStrategies() details. NULL post-ICE outcomes untouched. distr_pars_ref Optional. Named list containing simulation parameters reference arm. contains following elements: mu: Numeric vector indicating mean outcome trajectory assuming ICEs. include outcome baseline. sigma Covariance matrix outcome trajectory assuming ICEs. NULL, parameters inherited pars_group.","code":""},{"path":"/reference/generate_data_single.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate data for a single group — generate_data_single","text":"data.frame containing simulated data. includes following variables: id: Factor variable specifies id subject. visit: Factor variable specifies visit assessment. Visit 0 denotes baseline visit. group: Factor variable specifies treatment group subject belongs . outcome_bl: Numeric variable specifies baseline outcome. outcome_noICE: Numeric variable specifies longitudinal outcome assuming ICEs. ind_ice1: Binary variable takes value 1 corresponding visit affected ICE1 0 otherwise. dropout_ice1: Binary variable takes value 1 corresponding visit affected drop-following ICE1 0 otherwise. ind_ice2: Binary variable takes value 1 corresponding visit affected ICE2. outcome: Numeric variable specifies longitudinal outcome including ICE1, ICE2 intermittent missing values.","code":""},{"path":[]},{"path":"/reference/getStrategies.html","id":null,"dir":"Reference","previous_headings":"","what":"Get imputation strategies — getStrategies","title":"Get imputation strategies — getStrategies","text":"Returns list defining imputation strategies used create multivariate normal distribution parameters merging source group reference group per patient.","code":""},{"path":"/reference/getStrategies.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get imputation strategies — getStrategies","text":"","code":"getStrategies(...)"},{"path":"/reference/getStrategies.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get imputation strategies — getStrategies","text":"... User defined methods added return list. Input must function.","code":""},{"path":"/reference/getStrategies.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Get imputation strategies — getStrategies","text":"default Jump Reference (JR), Copy Reference (CR), Copy Increments Reference (CIR), Last Mean Carried Forward (LMCF) Missing Random (MAR) defined. user can define strategy functions (overwrite pre-defined ones) specifying named input function .e. NEW = function(...) .... exception MAR overwritten. user defined functions must take 3 inputs: pars_group, pars_ref index_mar. pars_group pars_ref lists elements mu sigma representing multivariate normal distribution parameters subject's current group reference group respectively. index_mar logical vector specifying visits subject met MAR assumption . function must return list elements mu sigma. See implementation strategy_JR() example.","code":""},{"path":"/reference/getStrategies.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get imputation strategies — getStrategies","text":"","code":"if (FALSE) { # \\dontrun{ getStrategies() getStrategies( NEW = function(pars_group, pars_ref, index_mar) code , JR = function(pars_group, pars_ref, index_mar) more_code ) } # }"},{"path":"/reference/get_ESS.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract the Effective Sample Size (ESS) from a stanfit object — get_ESS","title":"Extract the Effective Sample Size (ESS) from a stanfit object — get_ESS","text":"Extract Effective Sample Size (ESS) stanfit object","code":""},{"path":"/reference/get_ESS.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract the Effective Sample Size (ESS) from a stanfit object — get_ESS","text":"","code":"get_ESS(stan_fit)"},{"path":"/reference/get_ESS.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract the Effective Sample Size (ESS) from a stanfit object — get_ESS","text":"stan_fit stanfit object.","code":""},{"path":"/reference/get_ESS.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Extract the Effective Sample Size (ESS) from a stanfit object — get_ESS","text":"named vector containing ESS parameter model.","code":""},{"path":"/reference/get_bootstrap_stack.html","id":null,"dir":"Reference","previous_headings":"","what":"Creates a stack object populated with bootstrapped samples — get_bootstrap_stack","title":"Creates a stack object populated with bootstrapped samples — get_bootstrap_stack","text":"Function creates Stack() object populated stack bootstrap samples based upon method$n_samples","code":""},{"path":"/reference/get_bootstrap_stack.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Creates a stack object populated with bootstrapped samples — get_bootstrap_stack","text":"","code":"get_bootstrap_stack(longdata, method, stack = Stack$new())"},{"path":"/reference/get_bootstrap_stack.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Creates a stack object populated with bootstrapped samples — get_bootstrap_stack","text":"longdata longDataConstructor() object method method object stack Stack() object (exposed unit testing purposes)","code":""},{"path":"/reference/get_conditional_parameters.html","id":null,"dir":"Reference","previous_headings":"","what":"Derive conditional multivariate normal parameters — get_conditional_parameters","title":"Derive conditional multivariate normal parameters — get_conditional_parameters","text":"Takes parameters multivariate normal distribution observed values calculate conditional distribution unobserved values.","code":""},{"path":"/reference/get_conditional_parameters.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Derive conditional multivariate normal parameters — get_conditional_parameters","text":"","code":"get_conditional_parameters(pars, values)"},{"path":"/reference/get_conditional_parameters.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Derive conditional multivariate normal parameters — get_conditional_parameters","text":"pars list elements mu sigma defining mean vector covariance matrix respectively. values vector observed values condition , must length pars$mu. Missing values must represented NA.","code":""},{"path":"/reference/get_conditional_parameters.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Derive conditional multivariate normal parameters — get_conditional_parameters","text":"list conditional distribution parameters: mu - conditional mean vector. sigma - conditional covariance matrix.","code":""},{"path":"/reference/get_delta_template.html","id":null,"dir":"Reference","previous_headings":"","what":"Get delta utility variables — get_delta_template","title":"Get delta utility variables — get_delta_template","text":"function creates default delta template (1 row per subject per visit) extracts utility information users need define logic defining delta. See delta_template() full details.","code":""},{"path":"/reference/get_delta_template.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get delta utility variables — get_delta_template","text":"","code":"get_delta_template(imputations)"},{"path":"/reference/get_delta_template.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get delta utility variables — get_delta_template","text":"imputations imputations object created impute().","code":""},{"path":"/reference/get_draws_mle.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit the base imputation model on bootstrap samples — get_draws_mle","title":"Fit the base imputation model on bootstrap samples — get_draws_mle","text":"Fit base imputation model using ML/REML approach given number bootstrap samples specified method$n_samples. Returns parameter estimates model fit.","code":""},{"path":"/reference/get_draws_mle.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit the base imputation model on bootstrap samples — get_draws_mle","text":"","code":"get_draws_mle( longdata, method, sample_stack, n_target_samples, first_sample_orig, use_samp_ids, failure_limit = 0, ncores = 1, quiet = FALSE )"},{"path":"/reference/get_draws_mle.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit the base imputation model on bootstrap samples — get_draws_mle","text":"longdata R6 longdata object containing relevant input data information. method method object generated either method_approxbayes() method_condmean() argument type = \"bootstrap\". sample_stack stack object containing subject ids used mmrm iteration. n_target_samples Number samples needed created first_sample_orig Logical. TRUE function returns method$n_samples + 1 samples first sample contains parameter estimates original dataset method$n_samples samples contain parameter estimates bootstrap samples. FALSE function returns method$n_samples samples containing parameter estimates bootstrap samples. use_samp_ids Logical. TRUE, sampled subject ids returned. Otherwise subject ids original dataset returned. values used tell impute() subjects used derive imputed dataset. failure_limit Number failed samples allowed throwing error ncores Number processes parallelise job quiet Logical, TRUE suppress printing progress information printed console.","code":""},{"path":"/reference/get_draws_mle.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit the base imputation model on bootstrap samples — get_draws_mle","text":"draws object named list containing following: data: R6 longdata object containing relevant input data information. method: method object generated either method_bayes(), method_approxbayes() method_condmean(). samples: list containing estimated parameters interest. element samples named list containing following: ids: vector characters containing ids subjects included original dataset. beta: numeric vector estimated regression coefficients. sigma: list estimated covariance matrices (one level vars$group). theta: numeric vector transformed covariances. failed: Logical. TRUE model fit failed. ids_samp: vector characters containing ids subjects included given sample. fit: method_bayes() chosen, returns MCMC Stan fit object. Otherwise NULL. n_failures: absolute number failures model fit. Relevant method_condmean(type = \"bootstrap\"), method_approxbayes() method_bmlmi(). formula: fixed effects formula object used model specification.","code":""},{"path":"/reference/get_draws_mle.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit the base imputation model on bootstrap samples — get_draws_mle","text":"function takes Stack object contains multiple lists patient ids. function takes Stack pulls set ids constructs dataset just consisting patients (.e. potentially bootstrap jackknife sample). function fits MMRM model dataset create sample object. function repeats process n_target_samples reached. failure_limit samples fail converge function throws error. reaching desired number samples function generates returns draws object.","code":""},{"path":"/reference/get_ests_bmlmi.html","id":null,"dir":"Reference","previous_headings":"","what":"Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi","title":"Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi","text":"Compute pooled point estimates, standard error degrees freedom according Von Hippel Bartlett formula Bootstrapped Maximum Likelihood Multiple Imputation (BMLMI).","code":""},{"path":"/reference/get_ests_bmlmi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi","text":"","code":"get_ests_bmlmi(ests, D)"},{"path":"/reference/get_ests_bmlmi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi","text":"ests numeric vector containing estimates analysis imputed datasets. D numeric representing number imputations bootstrap sample BMLMI method.","code":""},{"path":"/reference/get_ests_bmlmi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi","text":"list containing point estimate, standard error degrees freedom.","code":""},{"path":"/reference/get_ests_bmlmi.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi","text":"ests must provided following order: firsts D elements related analyses random imputation one bootstrap sample. second set D elements (.e. D+1 2*D) related second bootstrap sample .","code":""},{"path":"/reference/get_ests_bmlmi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Von Hippel and Bartlett pooling of BMLMI method — get_ests_bmlmi","text":"Von Hippel, Paul T Bartlett, Jonathan W8. Maximum likelihood multiple imputation: Faster imputations consistent standard errors without posterior draws. 2021","code":""},{"path":"/reference/get_example_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate a realistic example dataset — get_example_data","title":"Simulate a realistic example dataset — get_example_data","text":"Simulate realistic example dataset using simulate_data() hard-coded values input arguments.","code":""},{"path":"/reference/get_example_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate a realistic example dataset — get_example_data","text":"","code":"get_example_data()"},{"path":"/reference/get_example_data.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulate a realistic example dataset — get_example_data","text":"get_example_data() simulates 1:1 randomized trial active drug (intervention) versus placebo (control) 100 subjects per group 6 post-baseline assessments (bi-monthly visits 12 months). One intercurrent event corresponding treatment discontinuation also simulated. Specifically, data simulated following assumptions: mean outcome trajectory placebo group increases linearly 50 baseline (visit 0) 60 visit 6, .e. slope 10 points/year. mean outcome trajectory intervention group identical placebo group visit 2. visit 2 onward, slope decreases 50% 5 points/year. covariance structure baseline follow-values groups implied random intercept slope model standard deviation 5 intercept slope, correlation 0.25. addition, independent residual error standard deviation 2.5 added assessment. probability study drug discontinuation visit calculated according logistic model depends observed outcome visit. Specifically, visit-wise discontinuation probability 2% 3% control intervention group, respectively, specified case observed outcome equal 50 (mean value baseline). odds discontinuation simulated increase +10% +1 point increase observed outcome. Study drug discontinuation simulated effect mean trajectory placebo group. intervention group, subjects discontinue follow slope mean trajectory placebo group time point onward. compatible copy increments reference (CIR) assumption. Study drop-study drug discontinuation visit occurs probability 50% leading missing outcome data time point onward.","code":""},{"path":[]},{"path":"/reference/get_jackknife_stack.html","id":null,"dir":"Reference","previous_headings":"","what":"Creates a stack object populated with jackknife samples — get_jackknife_stack","title":"Creates a stack object populated with jackknife samples — get_jackknife_stack","text":"Function creates Stack() object populated stack jackknife samples based upon","code":""},{"path":"/reference/get_jackknife_stack.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Creates a stack object populated with jackknife samples — get_jackknife_stack","text":"","code":"get_jackknife_stack(longdata, method, stack = Stack$new())"},{"path":"/reference/get_jackknife_stack.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Creates a stack object populated with jackknife samples — get_jackknife_stack","text":"longdata longDataConstructor() object method method object stack Stack() object (exposed unit testing purposes)","code":""},{"path":"/reference/get_mmrm_sample.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit MMRM and returns parameter estimates — get_mmrm_sample","title":"Fit MMRM and returns parameter estimates — get_mmrm_sample","text":"get_mmrm_sample fits base imputation model using ML/REML approach. Returns parameter estimates fit.","code":""},{"path":"/reference/get_mmrm_sample.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit MMRM and returns parameter estimates — get_mmrm_sample","text":"","code":"get_mmrm_sample(ids, longdata, method)"},{"path":"/reference/get_mmrm_sample.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit MMRM and returns parameter estimates — get_mmrm_sample","text":"ids vector characters containing ids subjects. longdata R6 longdata object containing relevant input data information. method method object generated either method_approxbayes() method_condmean().","code":""},{"path":"/reference/get_mmrm_sample.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit MMRM and returns parameter estimates — get_mmrm_sample","text":"named list class sample_single. contains following: ids vector characters containing ids subjects included original dataset. beta numeric vector estimated regression coefficients. sigma list estimated covariance matrices (one level vars$group). theta numeric vector transformed covariances. failed logical. TRUE model fit failed. ids_samp vector characters containing ids subjects included given sample.","code":""},{"path":"/reference/get_pattern_groups.html","id":null,"dir":"Reference","previous_headings":"","what":"Determine patients missingness group — get_pattern_groups","title":"Determine patients missingness group — get_pattern_groups","text":"Takes design matrix multiple rows per subject returns dataset 1 row per subject new column pgroup indicating group patient belongs (based upon missingness pattern treatment group)","code":""},{"path":"/reference/get_pattern_groups.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Determine patients missingness group — get_pattern_groups","text":"","code":"get_pattern_groups(ddat)"},{"path":"/reference/get_pattern_groups.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Determine patients missingness group — get_pattern_groups","text":"ddat data.frame columns subjid, visit, group, is_avail","code":""},{"path":"/reference/get_pattern_groups.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Determine patients missingness group — get_pattern_groups","text":"column is_avail must character numeric 0 1","code":""},{"path":"/reference/get_pattern_groups_unique.html","id":null,"dir":"Reference","previous_headings":"","what":"Get Pattern Summary — get_pattern_groups_unique","title":"Get Pattern Summary — get_pattern_groups_unique","text":"Takes dataset pattern information creates summary dataset just 1 row per pattern","code":""},{"path":"/reference/get_pattern_groups_unique.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get Pattern Summary — get_pattern_groups_unique","text":"","code":"get_pattern_groups_unique(patterns)"},{"path":"/reference/get_pattern_groups_unique.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get Pattern Summary — get_pattern_groups_unique","text":"patterns data.frame columns pgroup, pattern group","code":""},{"path":"/reference/get_pattern_groups_unique.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Get Pattern Summary — get_pattern_groups_unique","text":"column pgroup must numeric vector indicating pattern group patient belongs column pattern must character string 0's 1's. must identical rows within pgroup column group must character / numeric vector indicating covariance group observation belongs . must identical within pgroup","code":""},{"path":"/reference/get_pool_components.html","id":null,"dir":"Reference","previous_headings":"","what":"Expected Pool Components — get_pool_components","title":"Expected Pool Components — get_pool_components","text":"Returns elements expected contained analyse object depending analysis method specified.","code":""},{"path":"/reference/get_pool_components.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Expected Pool Components — get_pool_components","text":"","code":"get_pool_components(x)"},{"path":"/reference/get_pool_components.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Expected Pool Components — get_pool_components","text":"x Character name analysis method, must one either \"rubin\", \"jackknife\", \"bootstrap\" \"bmlmi\".","code":""},{"path":"/reference/get_session_hash.html","id":null,"dir":"Reference","previous_headings":"","what":"Get session hash — get_session_hash","title":"Get session hash — get_session_hash","text":"Gets unique string based current R version relevant packages.","code":""},{"path":"/reference/get_session_hash.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get session hash — get_session_hash","text":"","code":"get_session_hash()"},{"path":"/reference/get_stan_model.html","id":null,"dir":"Reference","previous_headings":"","what":"Get Compiled Stan Object — get_stan_model","title":"Get Compiled Stan Object — get_stan_model","text":"Gets compiled Stan object can used rstan::sampling()","code":""},{"path":"/reference/get_stan_model.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get Compiled Stan Object — get_stan_model","text":"","code":"get_stan_model()"},{"path":"/reference/get_visit_distribution_parameters.html","id":null,"dir":"Reference","previous_headings":"","what":"Derive visit distribution parameters — get_visit_distribution_parameters","title":"Derive visit distribution parameters — get_visit_distribution_parameters","text":"Takes patient level data beta coefficients expands get patient specific estimate visit distribution parameters mu sigma. Returns values specific format expected downstream functions imputation process (namely list(list(mu = ..., sigma = ...), list(mu = ..., sigma = ...))).","code":""},{"path":"/reference/get_visit_distribution_parameters.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Derive visit distribution parameters — get_visit_distribution_parameters","text":"","code":"get_visit_distribution_parameters(dat, beta, sigma)"},{"path":"/reference/get_visit_distribution_parameters.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Derive visit distribution parameters — get_visit_distribution_parameters","text":"dat Patient level dataset, must 1 row per visit. Column order must order beta. number columns must match length beta beta List model beta coefficients. 1 element sample e.g. 3 samples models 4 beta coefficients argument form list( c(1,2,3,4) , c(5,6,7,8), c(9,10,11,12)). elements beta must length must length order dat. sigma List sigma. Must number entries beta.","code":""},{"path":"/reference/has_class.html","id":null,"dir":"Reference","previous_headings":"","what":"Does object have a class ? — has_class","title":"Does object have a class ? — has_class","text":"Utility function see object particular class. Useful know many classes object may .","code":""},{"path":"/reference/has_class.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Does object have a class ? — has_class","text":"","code":"has_class(x, cls)"},{"path":"/reference/has_class.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Does object have a class ? — has_class","text":"x object want check class . cls class want know .","code":""},{"path":"/reference/has_class.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Does object have a class ? — has_class","text":"TRUE object class. FALSE object class.","code":""},{"path":"/reference/ife.html","id":null,"dir":"Reference","previous_headings":"","what":"if else — ife","title":"if else — ife","text":"wrapper around () else() prevent unexpected interactions ifelse() factor variables","code":""},{"path":"/reference/ife.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"if else — ife","text":"","code":"ife(x, a, b)"},{"path":"/reference/ife.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"if else — ife","text":"x True / False value return True b value return False","code":""},{"path":"/reference/ife.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"if else — ife","text":"default ifelse() convert factor variables numeric values often undesirable. connivance function avoids problem","code":""},{"path":"/reference/imputation_df.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a valid imputation_df object — imputation_df","title":"Create a valid imputation_df object — imputation_df","text":"Create valid imputation_df object","code":""},{"path":"/reference/imputation_df.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a valid imputation_df object — imputation_df","text":"","code":"imputation_df(...)"},{"path":"/reference/imputation_df.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a valid imputation_df object — imputation_df","text":"... list imputation_single.","code":""},{"path":"/reference/imputation_list_df.html","id":null,"dir":"Reference","previous_headings":"","what":"List of imputations_df — imputation_list_df","title":"List of imputations_df — imputation_list_df","text":"container multiple imputation_df's","code":""},{"path":"/reference/imputation_list_df.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"List of imputations_df — imputation_list_df","text":"","code":"imputation_list_df(...)"},{"path":"/reference/imputation_list_df.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"List of imputations_df — imputation_list_df","text":"... objects class imputation_df","code":""},{"path":"/reference/imputation_list_single.html","id":null,"dir":"Reference","previous_headings":"","what":"A collection of imputation_singles() grouped by a single subjid ID — imputation_list_single","title":"A collection of imputation_singles() grouped by a single subjid ID — imputation_list_single","text":"collection imputation_singles() grouped single subjid ID","code":""},{"path":"/reference/imputation_list_single.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"A collection of imputation_singles() grouped by a single subjid ID — imputation_list_single","text":"","code":"imputation_list_single(imputations, D = 1)"},{"path":"/reference/imputation_list_single.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"A collection of imputation_singles() grouped by a single subjid ID — imputation_list_single","text":"imputations list imputation_single() objects ordered repetitions grouped sequentially D number repetitions performed determines many columns imputation matrix constructor function create imputation_list_single object contains matrix imputation_single() objects grouped single id. matrix split D columns (.e. non-bmlmi methods always 1) id attribute determined extracting id attribute contributing imputation_single() objects. error throw multiple id detected","code":""},{"path":"/reference/imputation_single.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a valid imputation_single object — imputation_single","title":"Create a valid imputation_single object — imputation_single","text":"Create valid imputation_single object","code":""},{"path":"/reference/imputation_single.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a valid imputation_single object — imputation_single","text":"","code":"imputation_single(id, values)"},{"path":"/reference/imputation_single.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a valid imputation_single object — imputation_single","text":"id character string specifying subject id. values numeric vector indicating imputed values.","code":""},{"path":"/reference/impute.html","id":null,"dir":"Reference","previous_headings":"","what":"Create imputed datasets — impute","title":"Create imputed datasets — impute","text":"impute() creates imputed datasets based upon data options specified call draws(). One imputed dataset created per \"sample\" created draws().","code":""},{"path":"/reference/impute.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create imputed datasets — impute","text":"","code":"impute( draws, references = NULL, update_strategy = NULL, strategies = getStrategies() ) # S3 method for class 'random' impute( draws, references = NULL, update_strategy = NULL, strategies = getStrategies() ) # S3 method for class 'condmean' impute( draws, references = NULL, update_strategy = NULL, strategies = getStrategies() )"},{"path":"/reference/impute.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create imputed datasets — impute","text":"draws draws object created draws(). references named vector. Identifies references used reference-based imputation methods. form c(\"Group1\" = \"Reference1\", \"Group2\" = \"Reference2\"). NULL (default), references assumed form c(\"Group1\" = \"Group1\", \"Group2\" = \"Group2\"). argument NULL imputation strategy (defined data_ice[[vars$strategy]] call draws) MAR set. update_strategy optional data.frame. Updates imputation method originally set via data_ice option draws(). See details section information. strategies named list functions. Defines imputation functions used. names list mirror values specified strategy column data_ice. Default = getStrategies(). See getStrategies() details.","code":""},{"path":"/reference/impute.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create imputed datasets — impute","text":"impute() uses imputation model parameter estimates, generated draws(), first calculate marginal (multivariate normal) distribution subject's longitudinal outcome variable depending covariate values. subjects intercurrent events (ICEs) handled using non-MAR methods, marginal distribution updated depending time first visit affected ICE, chosen imputation strategy chosen reference group described Carpenter, Roger, Kenward (2013) . subject's imputation distribution used imputing missing values defined marginal distribution conditional observed outcome values. One dataset generated per set parameter estimates provided draws(). exact manner missing values imputed conditional imputation distribution depends method object provided draws(), particular: Bayes & Approximate Bayes: imputed dataset contains 1 row per subject & visit original dataset missing values imputed taking single random sample conditional imputation distribution. Conditional Mean: imputed dataset contains 1 row per subject & visit bootstrapped jackknife dataset used generate corresponding parameter estimates draws(). Missing values imputed using mean conditional imputation distribution. Please note first imputed dataset refers conditional mean imputation original dataset whereas subsequent imputed datasets refer conditional mean imputations bootstrap jackknife samples, respectively, original data. Bootstrapped Maximum Likelihood MI (BMLMI): performs D random imputations bootstrapped dataset used generate corresponding parameter estimates draws(). total number B*D imputed datasets provided, B number bootstrapped datasets. Missing values imputed taking random sample conditional imputation distribution. update_strategy argument can used update imputation strategy originally set via data_ice option draws(). avoids re-run draws() function changing imputation strategy certain circumstances (detailed ). data.frame provided update_strategy argument must contain two columns, one subject ID another imputation strategy, whose names defined vars argument specified call draws(). Please note argument allows update imputation strategy arguments time first visit affected ICE. key limitation functionality one can switch MAR non-MAR strategy (vice versa) subjects without observed post-ICE data. reason change affect whether post-ICE data included base imputation model (explained help draws()). example, subject ICE \"Visit 2\" observed/known values \"Visit 3\" function throw error one tries switch strategy MAR non-MAR strategy. contrast, switching non-MAR MAR strategy, whilst valid, raise warning usable data utilised imputation model.","code":""},{"path":"/reference/impute.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Create imputed datasets — impute","text":"James R Carpenter, James H Roger, Michael G Kenward. Analysis longitudinal trials protocol deviation: framework relevant, accessible assumptions, inference via multiple imputation. Journal Biopharmaceutical Statistics, 23(6):1352–1371, 2013. [Section 4.2 4.3]","code":""},{"path":"/reference/impute.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create imputed datasets — impute","text":"","code":"if (FALSE) { # \\dontrun{ impute( draws = drawobj, references = c(\"Trt\" = \"Placebo\", \"Placebo\" = \"Placebo\") ) new_strategy <- data.frame( subjid = c(\"Pt1\", \"Pt2\"), strategy = c(\"MAR\", \"JR\") ) impute( draws = drawobj, references = c(\"Trt\" = \"Placebo\", \"Placebo\" = \"Placebo\"), update_strategy = new_strategy ) } # }"},{"path":"/reference/impute_data_individual.html","id":null,"dir":"Reference","previous_headings":"","what":"Impute data for a single subject — impute_data_individual","title":"Impute data for a single subject — impute_data_individual","text":"function performs imputation single subject time implementing process detailed impute().","code":""},{"path":"/reference/impute_data_individual.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Impute data for a single subject — impute_data_individual","text":"","code":"impute_data_individual( id, index, beta, sigma, data, references, strategies, condmean, n_imputations = 1 )"},{"path":"/reference/impute_data_individual.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Impute data for a single subject — impute_data_individual","text":"id Character string identifying subject. index sample indexes subject belongs e.g c(1,1,1,2,2,4). beta list beta coefficients sample, .e. beta[[1]] set beta coefficients first sample. sigma list sigma coefficients sample split group .e. sigma[[1]][[\"\"]] give sigma coefficients group first sample. data longdata object created longDataConstructor() references named vector. Identifies references used generating imputed values. form c(\"Group\" = \"Reference\", \"Group\" = \"Reference\"). strategies named list functions. Defines imputation functions used. names list mirror values specified method column data_ice. Default = getStrategies(). See getStrategies() details. condmean Logical. TRUE impute using conditional mean values, FALSE impute taking random draw multivariate normal distribution. n_imputations condmean = FALSE numeric representing number random imputations performed sample. Default 1 (one random imputation per sample).","code":""},{"path":"/reference/impute_data_individual.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Impute data for a single subject — impute_data_individual","text":"Note function performs required imputations subject time. .e. subject included samples 1,3,5,9 imputations (using sample-dependent imputation model parameters) performed one step order avoid look subjects's covariates expanding design matrix multiple times (computationally expensive). function also supports subject belonging sample multiple times, .e. 1,1,2,3,5,5, typically occur bootstrapped datasets.","code":""},{"path":"/reference/impute_internal.html","id":null,"dir":"Reference","previous_headings":"","what":"Create imputed datasets — impute_internal","title":"Create imputed datasets — impute_internal","text":"work horse function implements functionality impute. See user level function impute() details.","code":""},{"path":"/reference/impute_internal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create imputed datasets — impute_internal","text":"","code":"impute_internal( draws, references = NULL, update_strategy, strategies, condmean )"},{"path":"/reference/impute_internal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create imputed datasets — impute_internal","text":"draws draws object created draws(). references named vector. Identifies references used reference-based imputation methods. form c(\"Group1\" = \"Reference1\", \"Group2\" = \"Reference2\"). NULL (default), references assumed form c(\"Group1\" = \"Group1\", \"Group2\" = \"Group2\"). argument NULL imputation strategy (defined data_ice[[vars$strategy]] call draws) MAR set. update_strategy optional data.frame. Updates imputation method originally set via data_ice option draws(). See details section information. strategies named list functions. Defines imputation functions used. names list mirror values specified strategy column data_ice. Default = getStrategies(). See getStrategies() details. condmean logical. TRUE impute using conditional mean values, values impute taking random draw multivariate normal distribution.","code":""},{"path":"/reference/impute_outcome.html","id":null,"dir":"Reference","previous_headings":"","what":"Sample outcome value — impute_outcome","title":"Sample outcome value — impute_outcome","text":"Draws random sample multivariate normal distribution.","code":""},{"path":"/reference/impute_outcome.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sample outcome value — impute_outcome","text":"","code":"impute_outcome(conditional_parameters, n_imputations = 1, condmean = FALSE)"},{"path":"/reference/impute_outcome.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sample outcome value — impute_outcome","text":"conditional_parameters list elements mu sigma contain mean vector covariance matrix sample . n_imputations numeric representing number random samples multivariate normal distribution performed. Default 1. condmean conditional mean imputation performed (opposed random sampling)","code":""},{"path":"/reference/invert.html","id":null,"dir":"Reference","previous_headings":"","what":"invert — invert","title":"invert — invert","text":"Utility function used replicated purrr::transpose. Turns list inside .","code":""},{"path":"/reference/invert.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"invert — invert","text":"","code":"invert(x)"},{"path":"/reference/invert.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"invert — invert","text":"x list","code":""},{"path":"/reference/invert_indexes.html","id":null,"dir":"Reference","previous_headings":"","what":"Invert and derive indexes — invert_indexes","title":"Invert and derive indexes — invert_indexes","text":"Takes list elements creates new list containing 1 entry per unique element value containing indexes original elements occurred .","code":""},{"path":"/reference/invert_indexes.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Invert and derive indexes — invert_indexes","text":"","code":"invert_indexes(x)"},{"path":"/reference/invert_indexes.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Invert and derive indexes — invert_indexes","text":"x list elements invert calculate index (see details).","code":""},{"path":"/reference/invert_indexes.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Invert and derive indexes — invert_indexes","text":"functions purpose best illustrated example: input: becomes:","code":"list( c(\"A\", \"B\", \"C\"), c(\"A\", \"A\", \"B\"))} list( \"A\" = c(1,2,2), \"B\" = c(1,2), \"C\" = 1 )"},{"path":"/reference/is_absent.html","id":null,"dir":"Reference","previous_headings":"","what":"Is value absent — is_absent","title":"Is value absent — is_absent","text":"Returns true value either NULL, NA \"\". case vector values must NULL/NA/\"\" x regarded absent.","code":""},{"path":"/reference/is_absent.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Is value absent — is_absent","text":"","code":"is_absent(x, na = TRUE, blank = TRUE)"},{"path":"/reference/is_absent.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Is value absent — is_absent","text":"x value check absent na NAs count absent blank blanks .e. \"\" count absent","code":""},{"path":"/reference/is_char_fact.html","id":null,"dir":"Reference","previous_headings":"","what":"Is character or factor — is_char_fact","title":"Is character or factor — is_char_fact","text":"returns true x character factor vector","code":""},{"path":"/reference/is_char_fact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Is character or factor — is_char_fact","text":"","code":"is_char_fact(x)"},{"path":"/reference/is_char_fact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Is character or factor — is_char_fact","text":"x character factor vector","code":""},{"path":"/reference/is_char_one.html","id":null,"dir":"Reference","previous_headings":"","what":"Is single character — is_char_one","title":"Is single character — is_char_one","text":"returns true x length 1 character vector","code":""},{"path":"/reference/is_char_one.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Is single character — is_char_one","text":"","code":"is_char_one(x)"},{"path":"/reference/is_char_one.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Is single character — is_char_one","text":"x character vector","code":""},{"path":"/reference/is_in_rbmi_development.html","id":null,"dir":"Reference","previous_headings":"","what":"Is package in development mode? — is_in_rbmi_development","title":"Is package in development mode? — is_in_rbmi_development","text":"Returns TRUE package developed .e. local copy source code actively editing Returns FALSE otherwise","code":""},{"path":"/reference/is_in_rbmi_development.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Is package in development mode? — is_in_rbmi_development","text":"","code":"is_in_rbmi_development()"},{"path":"/reference/is_in_rbmi_development.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Is package in development mode? — is_in_rbmi_development","text":"Main use function parallel processing indicate whether sub-processes need load current development version code whether load main installed package system","code":""},{"path":"/reference/is_num_char_fact.html","id":null,"dir":"Reference","previous_headings":"","what":"Is character, factor or numeric — is_num_char_fact","title":"Is character, factor or numeric — is_num_char_fact","text":"returns true x character, numeric factor vector","code":""},{"path":"/reference/is_num_char_fact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Is character, factor or numeric — is_num_char_fact","text":"","code":"is_num_char_fact(x)"},{"path":"/reference/is_num_char_fact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Is character, factor or numeric — is_num_char_fact","text":"x character, numeric factor vector","code":""},{"path":"/reference/locf.html","id":null,"dir":"Reference","previous_headings":"","what":"Last Observation Carried Forward — locf","title":"Last Observation Carried Forward — locf","text":"Returns vector applied last observation carried forward imputation.","code":""},{"path":"/reference/locf.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Last Observation Carried Forward — locf","text":"","code":"locf(x)"},{"path":"/reference/locf.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Last Observation Carried Forward — locf","text":"x vector.","code":""},{"path":"/reference/locf.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Last Observation Carried Forward — locf","text":"","code":"if (FALSE) { # \\dontrun{ locf(c(NA, 1, 2, 3, NA, 4)) # Returns c(NA, 1, 2, 3, 3, 4) } # }"},{"path":"/reference/longDataConstructor.html","id":null,"dir":"Reference","previous_headings":"","what":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"longdata object allows efficient storage recall longitudinal datasets use bootstrap sampling. object works de-constructing data lists based upon subject id thus enabling efficient lookup.","code":""},{"path":"/reference/longDataConstructor.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"object also handles multiple operations specific rbmi defining whether outcome value MAR / Missing well tracking imputation strategy assigned subject. recognised objects functionality fairly overloaded hoped can split area specific objects / functions future. additions functionality object avoided possible.","code":""},{"path":"/reference/longDataConstructor.html","id":"public-fields","dir":"Reference","previous_headings":"","what":"Public fields","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"data original dataset passed constructor (sorted id visit) vars vars object (list key variables) passed constructor visits character vector containing distinct visit levels ids character vector containing unique ids subject self$data formula formula expressing design matrix data constructed strata numeric vector indicating strata corresponding value self$ids belongs . stratification variable defined default 1 subjects (.e. group). field used part self$sample_ids() function enable stratified bootstrap sampling ice_visit_index list indexed subject storing index number first visit affected ICE. ICE set equal number visits plus 1. values list indexed subject storing numeric vector original (unimputed) outcome values group list indexed subject storing single character indicating imputation group subject belongs defined self$data[id, self$ivars$group] used determine reference group used imputing subjects data. is_mar list indexed subject storing logical values indicating subjects outcome values MAR . list defaulted TRUE subjects & outcomes modified calls self$set_strategies(). Note indicate values missing, variable True outcome values either occurred ICE visit post ICE visit imputation strategy MAR strategies list indexed subject storing single character value indicating imputation strategy assigned subject. list defaulted \"MAR\" subjects modified calls either self$set_strategies() self$update_strategies() strategy_lock list indexed subject storing single logical value indicating whether patients imputation strategy locked . strategy locked means change MAR non-MAR. Strategies can changed non-MAR MAR though trigger warning. Strategies locked patient assigned MAR strategy non-missing ICE date. list populated call self$set_strategies(). indexes list indexed subject storing numeric vector indexes specify rows original dataset belong subject .e. recover full data subject \"pt3\" can use self$data[self$indexes[[\"pt3\"]],]. may seem redundant filtering data directly however enables efficient bootstrap sampling data .e. list populated object initialisation. is_missing list indexed subject storing logical vector indicating whether corresponding outcome subject missing. list populated object initialisation. is_post_ice list indexed subject storing logical vector indicating whether corresponding outcome subject post date ICE. ICE data provided defaults False observations. list populated call self$set_strategies().","code":"indexes <- unlist(self$indexes[c(\"pt3\", \"pt3\")]) self$data[indexes,]"},{"path":[]},{"path":"/reference/longDataConstructor.html","id":"public-methods","dir":"Reference","previous_headings":"","what":"Public methods","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"longDataConstructor$get_data() longDataConstructor$add_subject() longDataConstructor$validate_ids() longDataConstructor$sample_ids() longDataConstructor$extract_by_id() longDataConstructor$update_strategies() longDataConstructor$set_strategies() longDataConstructor$check_has_data_at_each_visit() longDataConstructor$set_strata() longDataConstructor$new() longDataConstructor$clone()","code":""},{"path":"/reference/longDataConstructor.html","id":"method-get-data-","dir":"Reference","previous_headings":"","what":"Method get_data()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Returns data.frame based upon required subject IDs. Replaces missing values new ones provided.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$get_data( obj = NULL, nmar.rm = FALSE, na.rm = FALSE, idmap = FALSE )"},{"path":"/reference/longDataConstructor.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"obj Either NULL, character vector subjects IDs imputation list object. See details. nmar.rm Logical value. TRUE remove observations regarded MAR (determined self$is_mar). na.rm Logical value. TRUE remove outcome values missing (determined self$is_missing). idmap Logical value. TRUE add attribute idmap contains mapping new subject ids old subject ids. See details.","code":""},{"path":"/reference/longDataConstructor.html","id":"details-1","dir":"Reference","previous_headings":"","what":"Details","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"obj NULL full original dataset returned. obj character vector new dataset consisting just subjects returned; character vector contains duplicate entries subject returned multiple times. obj imputation_df object (created imputation_df()) subject ids specified object returned missing values filled specified imputation list object. .e. return data.frame consisting observations pt1 twice observations pt3 . first set observations pt1 missing values filled c(1,2,3) second set filled c(4,5,6). length values must equal sum(self$is_missing[[id]]). obj NULL subject IDs scrambled order ensure unique .e. pt2 requested twice process guarantees set observations unique subject ID number. idmap attribute (requested) can used map new ids back old ids.","code":"obj <- imputation_df( imputation_single( id = \"pt1\", values = c(1,2,3)), imputation_single( id = \"pt1\", values = c(4,5,6)), imputation_single( id = \"pt3\", values = c(7,8)) ) longdata$get_data(obj)"},{"path":"/reference/longDataConstructor.html","id":"returns","dir":"Reference","previous_headings":"","what":"Returns","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"data.frame.","code":""},{"path":"/reference/longDataConstructor.html","id":"method-add-subject-","dir":"Reference","previous_headings":"","what":"Method add_subject()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"function decomposes patient data self$data populates corresponding lists .e. self$is_missing, self$values, self$group, etc. function called upon objects initialization.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-1","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$add_subject(id)"},{"path":"/reference/longDataConstructor.html","id":"arguments-1","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"id Character subject id exists within self$data.","code":""},{"path":"/reference/longDataConstructor.html","id":"method-validate-ids-","dir":"Reference","previous_headings":"","what":"Method validate_ids()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Throws error element ids within source data self$data.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-2","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$validate_ids(ids)"},{"path":"/reference/longDataConstructor.html","id":"arguments-2","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"ids character vector ids.","code":""},{"path":"/reference/longDataConstructor.html","id":"returns-1","dir":"Reference","previous_headings":"","what":"Returns","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"TRUE","code":""},{"path":"/reference/longDataConstructor.html","id":"method-sample-ids-","dir":"Reference","previous_headings":"","what":"Method sample_ids()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Performs random stratified sampling patient ids (replacement) patient equal weight picked within strata (.e dependent many non-missing visits ).","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-3","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$sample_ids()"},{"path":"/reference/longDataConstructor.html","id":"returns-2","dir":"Reference","previous_headings":"","what":"Returns","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Character vector ids.","code":""},{"path":"/reference/longDataConstructor.html","id":"method-extract-by-id-","dir":"Reference","previous_headings":"","what":"Method extract_by_id()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Returns list key information given subject. convenience wrapper save manually grab element.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-4","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$extract_by_id(id)"},{"path":"/reference/longDataConstructor.html","id":"arguments-3","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"id Character subject id exists within self$data.","code":""},{"path":"/reference/longDataConstructor.html","id":"method-update-strategies-","dir":"Reference","previous_headings":"","what":"Method update_strategies()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Convenience function run self$set_strategies(dat_ice, update=TRUE) kept legacy reasons.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-5","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$update_strategies(dat_ice)"},{"path":"/reference/longDataConstructor.html","id":"arguments-4","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"dat_ice data.frame containing ICE information see impute() format dataframe.","code":""},{"path":"/reference/longDataConstructor.html","id":"method-set-strategies-","dir":"Reference","previous_headings":"","what":"Method set_strategies()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Updates self$strategies, self$is_mar, self$is_post_ice variables based upon provided ICE information.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-6","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$set_strategies(dat_ice = NULL, update = FALSE)"},{"path":"/reference/longDataConstructor.html","id":"arguments-5","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"dat_ice data.frame containing ICE information. See details. update Logical, indicates ICE data used update. See details.","code":""},{"path":"/reference/longDataConstructor.html","id":"details-2","dir":"Reference","previous_headings":"","what":"Details","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"See draws() specification dat_ice update=FALSE. See impute() format dat_ice update=TRUE. update=TRUE function ensures MAR strategies changed non-MAR presence post-ICE observations.","code":""},{"path":"/reference/longDataConstructor.html","id":"method-check-has-data-at-each-visit-","dir":"Reference","previous_headings":"","what":"Method check_has_data_at_each_visit()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Ensures visits least 1 observed \"MAR\" observation. Throws error criteria met. ensure initial MMRM can resolved.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-7","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$check_has_data_at_each_visit()"},{"path":"/reference/longDataConstructor.html","id":"method-set-strata-","dir":"Reference","previous_headings":"","what":"Method set_strata()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Populates self$strata variable. user specified stratification variables first visit used determine value variables. stratification variables specified everyone defined strata 1.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-8","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$set_strata()"},{"path":"/reference/longDataConstructor.html","id":"method-new-","dir":"Reference","previous_headings":"","what":"Method new()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"Constructor function.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-9","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$new(data, vars)"},{"path":"/reference/longDataConstructor.html","id":"arguments-6","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"data longitudinal dataset. vars ivars object created set_vars().","code":""},{"path":"/reference/longDataConstructor.html","id":"method-clone-","dir":"Reference","previous_headings":"","what":"Method clone()","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"objects class cloneable method.","code":""},{"path":"/reference/longDataConstructor.html","id":"usage-10","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"","code":"longDataConstructor$clone(deep = FALSE)"},{"path":"/reference/longDataConstructor.html","id":"arguments-7","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for Storing / Accessing & Sampling Longitudinal Data — longDataConstructor","text":"deep Whether make deep clone.","code":""},{"path":"/reference/ls_design.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate design vector for the lsmeans — ls_design","title":"Calculate design vector for the lsmeans — ls_design","text":"Calculates design vector required generate lsmean standard error. ls_design_equal calculates applying equal weight per covariate combination whilst ls_design_proportional applies weighting proportional frequency covariate combination occurred actual dataset.","code":""},{"path":"/reference/ls_design.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate design vector for the lsmeans — ls_design","text":"","code":"ls_design_equal(data, frm, fix) ls_design_counterfactual(data, frm, fix) ls_design_proportional(data, frm, fix)"},{"path":"/reference/ls_design.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate design vector for the lsmeans — ls_design","text":"data data.frame frm Formula used fit original model fix named list variables fixed values","code":""},{"path":"/reference/lsmeans.html","id":null,"dir":"Reference","previous_headings":"","what":"Least Square Means — lsmeans","title":"Least Square Means — lsmeans","text":"Estimates least square means linear model. exact implementation / interpretation depends weighting scheme; see weighting section information.","code":""},{"path":"/reference/lsmeans.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Least Square Means — lsmeans","text":"","code":"lsmeans( model, ..., .weights = c(\"counterfactual\", \"equal\", \"proportional_em\", \"proportional\") )"},{"path":"/reference/lsmeans.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Least Square Means — lsmeans","text":"model model created lm. ... Fixes specific variables specific values .e. trt = 1 age = 50. name argument must name variable within dataset. .weights Character, either \"counterfactual\" (default), \"equal\", \"proportional_em\" \"proportional\". Specifies weighting strategy used calculating lsmeans. See weighting section details.","code":""},{"path":[]},{"path":"/reference/lsmeans.html","id":"counterfactual","dir":"Reference","previous_headings":"","what":"Counterfactual","title":"Least Square Means — lsmeans","text":"weights = \"counterfactual\" (default) lsmeans obtained taking average predicted values patient assigning patients arm turn. approach equivalent standardization g-computation. comparison emmeans approach equivalent : Note ensure backwards compatibility previous versions rbmi weights = \"proportional\" alias weights = \"counterfactual\". get results consistent emmeans's weights = \"proportional\" please use weights = \"proportional_em\".","code":"emmeans::emmeans(model, specs = \"\", counterfactual = \"\")"},{"path":"/reference/lsmeans.html","id":"equal","dir":"Reference","previous_headings":"","what":"Equal","title":"Least Square Means — lsmeans","text":"weights = \"equal\" lsmeans obtained taking model fitted value hypothetical patient whose covariates defined follows: Continuous covariates set mean(X) Dummy categorical variables set 1/N N number levels Continuous * continuous interactions set mean(X) * mean(Y) Continuous * categorical interactions set mean(X) * 1/N Dummy categorical * categorical interactions set 1/N * 1/M comparison emmeans approach equivalent :","code":"emmeans::emmeans(model, specs = \"\", weights = \"equal\")"},{"path":"/reference/lsmeans.html","id":"proportional","dir":"Reference","previous_headings":"","what":"Proportional","title":"Least Square Means — lsmeans","text":"weights = \"proportional_em\" lsmeans obtained per weights = \"equal\" except instead weighting observation equally weighted proportion given combination categorical values occurred data. comparison emmeans approach equivalent : Note confused weights = \"proportional\" alias weights = \"counterfactual\".","code":"emmeans::emmeans(model, specs = \"\", weights = \"proportional\")"},{"path":"/reference/lsmeans.html","id":"fixing","dir":"Reference","previous_headings":"","what":"Fixing","title":"Least Square Means — lsmeans","text":"Regardless weighting scheme named arguments passed via ... fix value covariate specified value. example, lsmeans(model, trt = \"\") fix dummy variable trtA 1 patients (real hypothetical) calculating lsmeans. See references similar implementations done SAS R via emmeans package.","code":""},{"path":"/reference/lsmeans.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Least Square Means — lsmeans","text":"https://CRAN.R-project.org/package=emmeans https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.3/statug/statug_glm_details41.htm","code":""},{"path":"/reference/lsmeans.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Least Square Means — lsmeans","text":"","code":"if (FALSE) { # \\dontrun{ mod <- lm(Sepal.Length ~ Species + Petal.Length, data = iris) lsmeans(mod) lsmeans(mod, Species = \"virginica\") lsmeans(mod, Species = \"versicolor\") lsmeans(mod, Species = \"versicolor\", Petal.Length = 1) } # }"},{"path":"/reference/make_rbmi_cluster.html","id":null,"dir":"Reference","previous_headings":"","what":"Create a rbmi ready cluster — make_rbmi_cluster","title":"Create a rbmi ready cluster — make_rbmi_cluster","text":"Create rbmi ready cluster","code":""},{"path":"/reference/make_rbmi_cluster.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create a rbmi ready cluster — make_rbmi_cluster","text":"","code":"make_rbmi_cluster(ncores = 1, objects = NULL, packages = NULL)"},{"path":"/reference/make_rbmi_cluster.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create a rbmi ready cluster — make_rbmi_cluster","text":"ncores Number parallel processes use existing cluster make use objects named list objects export sub-processes packages character vector libraries load sub-processes function wrapper around parallel::makePSOCKcluster() takes care configuring rbmi used sub-processes well loading user defined objects libraries setting seed reproducibility. ncores 1 function return NULL. ncores cluster created via parallel::makeCluster() function just takes care inserting relevant rbmi objects existing cluster.","code":""},{"path":"/reference/make_rbmi_cluster.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create a rbmi ready cluster — make_rbmi_cluster","text":"","code":"if (FALSE) { # \\dontrun{ # Basic usage make_rbmi_cluster(5) # User objects + libraries VALUE <- 5 myfun <- function(x) { x + day(VALUE) # From lubridate::day() } make_rbmi_cluster(5, list(VALUE = VALUE, myfun = myfun), c(\"lubridate\")) # Using a already created cluster cl <- parallel::makeCluster(5) make_rbmi_cluster(cl) } # }"},{"path":"/reference/method.html","id":null,"dir":"Reference","previous_headings":"","what":"Set the multiple imputation methodology — method","title":"Set the multiple imputation methodology — method","text":"functions determine methods rbmi use creating imputation models, generating imputed values pooling results.","code":""},{"path":"/reference/method.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set the multiple imputation methodology — method","text":"","code":"method_bayes( burn_in = 200, burn_between = 50, same_cov = TRUE, n_samples = 20, seed = NULL ) method_approxbayes( covariance = c(\"us\", \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\"), threshold = 0.01, same_cov = TRUE, REML = TRUE, n_samples = 20 ) method_condmean( covariance = c(\"us\", \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\"), threshold = 0.01, same_cov = TRUE, REML = TRUE, n_samples = NULL, type = c(\"bootstrap\", \"jackknife\") ) method_bmlmi( covariance = c(\"us\", \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\"), threshold = 0.01, same_cov = TRUE, REML = TRUE, B = 20, D = 2 )"},{"path":"/reference/method.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set the multiple imputation methodology — method","text":"burn_in numeric specifies many observations discarded prior extracting actual samples. Note sampler initialized maximum likelihood estimates weakly informative prior used thus theory value need high. burn_between numeric specifies \"thinning\" rate .e. many observations discarded sample. used prevent issues associated autocorrelation samples. same_cov logical, TRUE imputation model fitted using single shared covariance matrix observations. FALSE separate covariance matrix fit group determined group argument set_vars(). n_samples numeric determines many imputed datasets generated. case method_condmean(type = \"jackknife\") argument must set NULL. See details. seed deprecated. Please use set.seed() instead. covariance character string specifies structure covariance matrix used imputation model. Must one \"us\" (default), \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\"). See details. threshold numeric 0 1, specifies proportion bootstrap datasets can fail produce valid samples error thrown. See details. REML logical indicating whether use REML estimation rather maximum likelihood. type character string specifies resampling method used perform inference conditional mean imputation approach (set via method_condmean()) used. Must one \"bootstrap\" \"jackknife\". B numeric determines number bootstrap samples method_bmlmi. D numeric determines number random imputations bootstrap sample. Needed method_bmlmi().","code":""},{"path":"/reference/method.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Set the multiple imputation methodology — method","text":"case method_condmean(type = \"bootstrap\") n_samples + 1 imputation models datasets generated first sample based original dataset whilst n_samples samples bootstrapped datasets. Likewise, method_condmean(type = \"jackknife\") length(unique(data$subjid)) + 1 imputation models datasets generated. cases represented n + 1 displayed print message. user able specify different covariance structures using covariance argument. Currently supported structures include: Unstructured (\"us\") (default) Ante-dependence (\"ad\") Heterogeneous ante-dependence (\"adh\") First-order auto-regressive (\"ar1\") Heterogeneous first-order auto-regressive (\"ar1h\") Compound symmetry (\"cs\") Heterogeneous compound symmetry (\"csh\") Toeplitz (\"toep\") Heterogeneous Toeplitz (\"toeph\") full details please see mmrm::cov_types(). Note present Bayesian methods support unstructured. case method_condmean(type = \"bootstrap\"), method_approxbayes() method_bmlmi() repeated bootstrap samples original dataset taken MMRM fitted sample. Due randomness sampled datasets, well limitations optimisers used fit models, uncommon estimates particular dataset generated. instances rbmi designed throw bootstrapped dataset try another. However ensure errors due chance due underlying misspecification data /model tolerance limit set many samples can discarded. tolerance limit reached error thrown process aborted. tolerance limit defined ceiling(threshold * n_samples). Note jackknife method estimates need generated leave-one-datasets error thrown fail fit. Please note time writing (September 2021) Stan unable produce reproducible samples across different operating systems even seed used. care must taken using Stan across different machines. information limitation please consult Stan documentation https://mc-stan.org/docs/2_27/reference-manual/reproducibility-chapter.html","code":""},{"path":"/reference/par_lapply.html","id":null,"dir":"Reference","previous_headings":"","what":"Parallelise Lapply — par_lapply","title":"Parallelise Lapply — par_lapply","text":"Simple wrapper around lapply parallel::clusterApplyLB abstract away logic deciding one use","code":""},{"path":"/reference/par_lapply.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Parallelise Lapply — par_lapply","text":"","code":"par_lapply(cl, fun, x, ...)"},{"path":"/reference/par_lapply.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Parallelise Lapply — par_lapply","text":"cl Cluster created parallel::makeCluster() NULL fun Function run x object looped ... extra arguements passed fun","code":""},{"path":"/reference/parametric_ci.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate parametric confidence intervals — parametric_ci","title":"Calculate parametric confidence intervals — parametric_ci","text":"Calculates confidence intervals based upon parametric distribution.","code":""},{"path":"/reference/parametric_ci.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate parametric confidence intervals — parametric_ci","text":"","code":"parametric_ci(point, se, alpha, alternative, qfun, pfun, ...)"},{"path":"/reference/parametric_ci.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate parametric confidence intervals — parametric_ci","text":"point point estimate. se standard error point estimate. using non-\"normal\" distribution set 1. alpha type 1 error rate, value 0 1. alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\". qfun quantile function assumed distribution .e. qnorm. pfun CDF function assumed distribution .e. pnorm. ... additional arguments passed qfun pfun .e. df = 102.","code":""},{"path":"/reference/pool.html","id":null,"dir":"Reference","previous_headings":"","what":"Pool analysis results obtained from the imputed datasets — pool","title":"Pool analysis results obtained from the imputed datasets — pool","text":"Pool analysis results obtained imputed datasets","code":""},{"path":"/reference/pool.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Pool analysis results obtained from the imputed datasets — pool","text":"","code":"pool( results, conf.level = 0.95, alternative = c(\"two.sided\", \"less\", \"greater\"), type = c(\"percentile\", \"normal\") ) # S3 method for class 'pool' as.data.frame(x, ...) # S3 method for class 'pool' print(x, ...)"},{"path":"/reference/pool.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Pool analysis results obtained from the imputed datasets — pool","text":"results analysis object created analyse(). conf.level confidence level returned confidence interval. Must single number 0 1. Default 0.95. alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\". type character string either \"percentile\" (default) \"normal\". Determines method used calculate bootstrap confidence intervals. See details. used method_condmean(type = \"bootstrap\") specified original call draws(). x pool object generated pool(). ... used.","code":""},{"path":"/reference/pool.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Pool analysis results obtained from the imputed datasets — pool","text":"calculation used generate point estimate, standard errors confidence interval depends upon method specified original call draws(); particular: method_approxbayes() & method_bayes() use Rubin's rules pool estimates variances across multiple imputed datasets, Barnard-Rubin rule pool degree's freedom; see Little & Rubin (2002). method_condmean(type = \"bootstrap\") uses percentile normal approximation; see Efron & Tibshirani (1994). Note percentile bootstrap, standard error calculated, .e. standard errors NA object / data.frame. method_condmean(type = \"jackknife\") uses standard jackknife variance formula; see Efron & Tibshirani (1994). method_bmlmi uses pooling procedure Bootstrapped Maximum Likelihood MI (BMLMI). See Von Hippel & Bartlett (2021).","code":""},{"path":"/reference/pool.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Pool analysis results obtained from the imputed datasets — pool","text":"Bradley Efron Robert J Tibshirani. introduction bootstrap. CRC press, 1994. [Section 11] Roderick J. . Little Donald B. Rubin. Statistical Analysis Missing Data, Second Edition. John Wiley & Sons, Hoboken, New Jersey, 2002. [Section 5.4] Von Hippel, Paul T Bartlett, Jonathan W. Maximum likelihood multiple imputation: Faster imputations consistent standard errors without posterior draws. 2021.","code":""},{"path":"/reference/pool_bootstrap_normal.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrap Pooling via normal approximation — pool_bootstrap_normal","title":"Bootstrap Pooling via normal approximation — pool_bootstrap_normal","text":"Get point estimate, confidence interval p-value using normal approximation.","code":""},{"path":"/reference/pool_bootstrap_normal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrap Pooling via normal approximation — pool_bootstrap_normal","text":"","code":"pool_bootstrap_normal(est, conf.level, alternative)"},{"path":"/reference/pool_bootstrap_normal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrap Pooling via normal approximation — pool_bootstrap_normal","text":"est numeric vector point estimates bootstrap sample. conf.level confidence level returned confidence interval. Must single number 0 1. Default 0.95. alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\".","code":""},{"path":"/reference/pool_bootstrap_normal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bootstrap Pooling via normal approximation — pool_bootstrap_normal","text":"point estimate taken first element est. remaining n-1 values est used generate confidence intervals.","code":""},{"path":"/reference/pool_bootstrap_percentile.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrap Pooling via Percentiles — pool_bootstrap_percentile","title":"Bootstrap Pooling via Percentiles — pool_bootstrap_percentile","text":"Get point estimate, confidence interval p-value using percentiles. Note quantile \"type=6\" used, see stats::quantile() details.","code":""},{"path":"/reference/pool_bootstrap_percentile.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrap Pooling via Percentiles — pool_bootstrap_percentile","text":"","code":"pool_bootstrap_percentile(est, conf.level, alternative)"},{"path":"/reference/pool_bootstrap_percentile.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrap Pooling via Percentiles — pool_bootstrap_percentile","text":"est numeric vector point estimates bootstrap sample. conf.level confidence level returned confidence interval. Must single number 0 1. Default 0.95. alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\".","code":""},{"path":"/reference/pool_bootstrap_percentile.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bootstrap Pooling via Percentiles — pool_bootstrap_percentile","text":"point estimate taken first element est. remaining n-1 values est used generate confidence intervals.","code":""},{"path":"/reference/pool_internal.html","id":null,"dir":"Reference","previous_headings":"","what":"Internal Pool Methods — pool_internal","title":"Internal Pool Methods — pool_internal","text":"Dispatches pool methods based upon results object class. See pool() details.","code":""},{"path":"/reference/pool_internal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Internal Pool Methods — pool_internal","text":"","code":"pool_internal(results, conf.level, alternative, type, D) # S3 method for class 'jackknife' pool_internal(results, conf.level, alternative, type, D) # S3 method for class 'bootstrap' pool_internal( results, conf.level, alternative, type = c(\"percentile\", \"normal\"), D ) # S3 method for class 'bmlmi' pool_internal(results, conf.level, alternative, type, D) # S3 method for class 'rubin' pool_internal(results, conf.level, alternative, type, D)"},{"path":"/reference/pool_internal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Internal Pool Methods — pool_internal","text":"results list results .e. x$results element analyse object created analyse()). conf.level confidence level returned confidence interval. Must single number 0 1. Default 0.95. alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\". type character string either \"percentile\" (default) \"normal\". Determines method used calculate bootstrap confidence intervals. See details. used method_condmean(type = \"bootstrap\") specified original call draws(). D numeric representing number imputations bootstrap sample BMLMI method.","code":""},{"path":"/reference/prepare_stan_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Prepare input data to run the Stan model — prepare_stan_data","title":"Prepare input data to run the Stan model — prepare_stan_data","text":"Prepare input data run Stan model. Creates / calculates required inputs required data{} block MMRM Stan program.","code":""},{"path":"/reference/prepare_stan_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prepare input data to run the Stan model — prepare_stan_data","text":"","code":"prepare_stan_data(ddat, subjid, visit, outcome, group)"},{"path":"/reference/prepare_stan_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prepare input data to run the Stan model — prepare_stan_data","text":"ddat design matrix subjid Character vector containing subjects IDs. visit Vector containing visits. outcome Numeric vector containing outcome variable. group Vector containing group variable.","code":""},{"path":"/reference/prepare_stan_data.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prepare input data to run the Stan model — prepare_stan_data","text":"stan_data object. named list per data{} block related Stan file. particular returns: N - number rows design matrix P - number columns design matrix G - number distinct covariance matrix groups (.e. length(unique(group))) n_visit - number unique outcome visits n_pat - total number pattern groups (defined missingness patterns & covariance group) pat_G - Index Sigma pattern group use pat_n_pt - number patients within pattern group pat_n_visit - number non-missing visits pattern group pat_sigma_index - rows/cols Sigma subset pattern group (padded 0's) y - outcome variable Q - design matrix (QR decomposition) R - R matrix QR decomposition design matrix","code":""},{"path":"/reference/prepare_stan_data.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Prepare input data to run the Stan model — prepare_stan_data","text":"group argument determines covariance matrix group subject belongs . want subjects use shared covariance matrix set group \"1\" everyone.","code":""},{"path":"/reference/print.analysis.html","id":null,"dir":"Reference","previous_headings":"","what":"Print analysis object — print.analysis","title":"Print analysis object — print.analysis","text":"Print analysis object","code":""},{"path":"/reference/print.analysis.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print analysis object — print.analysis","text":"","code":"# S3 method for class 'analysis' print(x, ...)"},{"path":"/reference/print.analysis.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print analysis object — print.analysis","text":"x analysis object generated analyse(). ... used.","code":""},{"path":"/reference/print.draws.html","id":null,"dir":"Reference","previous_headings":"","what":"Print draws object — print.draws","title":"Print draws object — print.draws","text":"Print draws object","code":""},{"path":"/reference/print.draws.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print draws object — print.draws","text":"","code":"# S3 method for class 'draws' print(x, ...)"},{"path":"/reference/print.draws.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print draws object — print.draws","text":"x draws object generated draws(). ... used.","code":""},{"path":"/reference/print.imputation.html","id":null,"dir":"Reference","previous_headings":"","what":"Print imputation object — print.imputation","title":"Print imputation object — print.imputation","text":"Print imputation object","code":""},{"path":"/reference/print.imputation.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print imputation object — print.imputation","text":"","code":"# S3 method for class 'imputation' print(x, ...)"},{"path":"/reference/print.imputation.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print imputation object — print.imputation","text":"x imputation object generated impute(). ... used.","code":""},{"path":"/reference/progressLogger.html","id":null,"dir":"Reference","previous_headings":"","what":"R6 Class for printing current sampling progress — progressLogger","title":"R6 Class for printing current sampling progress — progressLogger","text":"Object initalised total number iterations expected occur. User can update object add method indicate many iterations just occurred. Every time step * 100 % iterations occurred message printed console. Use quiet argument prevent object printing anything ","code":""},{"path":"/reference/progressLogger.html","id":"public-fields","dir":"Reference","previous_headings":"","what":"Public fields","title":"R6 Class for printing current sampling progress — progressLogger","text":"step real, percentage iterations allow printing progress console step_current integer, total number iterations completed since progress last printed console n integer, current number completed iterations n_max integer, total number expected iterations completed acts denominator calculating progress percentages quiet logical holds whether print anything","code":""},{"path":[]},{"path":"/reference/progressLogger.html","id":"public-methods","dir":"Reference","previous_headings":"","what":"Public methods","title":"R6 Class for printing current sampling progress — progressLogger","text":"progressLogger$new() progressLogger$add() progressLogger$print_progress() progressLogger$clone()","code":""},{"path":"/reference/progressLogger.html","id":"method-new-","dir":"Reference","previous_headings":"","what":"Method new()","title":"R6 Class for printing current sampling progress — progressLogger","text":"Create progressLogger object","code":""},{"path":"/reference/progressLogger.html","id":"usage","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for printing current sampling progress — progressLogger","text":"","code":"progressLogger$new(n_max, quiet = FALSE, step = 0.1)"},{"path":"/reference/progressLogger.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for printing current sampling progress — progressLogger","text":"n_max integer, sets field n_max quiet logical, sets field quiet step real, sets field step","code":""},{"path":"/reference/progressLogger.html","id":"method-add-","dir":"Reference","previous_headings":"","what":"Method add()","title":"R6 Class for printing current sampling progress — progressLogger","text":"Records n iterations completed add number current step count (step_current) print progress message log step limit (step) reached. function nothing quiet set TRUE","code":""},{"path":"/reference/progressLogger.html","id":"usage-1","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for printing current sampling progress — progressLogger","text":"","code":"progressLogger$add(n)"},{"path":"/reference/progressLogger.html","id":"arguments-1","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for printing current sampling progress — progressLogger","text":"n number successfully complete iterations since add() last called","code":""},{"path":"/reference/progressLogger.html","id":"method-print-progress-","dir":"Reference","previous_headings":"","what":"Method print_progress()","title":"R6 Class for printing current sampling progress — progressLogger","text":"method print current state progress","code":""},{"path":"/reference/progressLogger.html","id":"usage-2","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for printing current sampling progress — progressLogger","text":"","code":"progressLogger$print_progress()"},{"path":"/reference/progressLogger.html","id":"method-clone-","dir":"Reference","previous_headings":"","what":"Method clone()","title":"R6 Class for printing current sampling progress — progressLogger","text":"objects class cloneable method.","code":""},{"path":"/reference/progressLogger.html","id":"usage-3","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for printing current sampling progress — progressLogger","text":"","code":"progressLogger$clone(deep = FALSE)"},{"path":"/reference/progressLogger.html","id":"arguments-2","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for printing current sampling progress — progressLogger","text":"deep Whether make deep clone.","code":""},{"path":"/reference/pval_percentile.html","id":null,"dir":"Reference","previous_headings":"","what":"P-value of percentile bootstrap — pval_percentile","title":"P-value of percentile bootstrap — pval_percentile","text":"Determines (necessarily unique) quantile (type=6) \"est\" gives value 0 , derive p-value corresponding percentile bootstrap via inversion.","code":""},{"path":"/reference/pval_percentile.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"P-value of percentile bootstrap — pval_percentile","text":"","code":"pval_percentile(est)"},{"path":"/reference/pval_percentile.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"P-value of percentile bootstrap — pval_percentile","text":"est numeric vector point estimates bootstrap sample.","code":""},{"path":"/reference/pval_percentile.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"P-value of percentile bootstrap — pval_percentile","text":"named numeric vector length 2 containing p-value H_0: theta=0 vs H_A: theta>0 (\"pval_greater\") p-value H_0: theta=0 vs H_A: theta<0 (\"pval_less\").","code":""},{"path":"/reference/pval_percentile.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"P-value of percentile bootstrap — pval_percentile","text":"p-value H_0: theta=0 vs H_A: theta>0 value alpha q_alpha = 0. least one estimate equal zero returns largest alpha q_alpha = 0. bootstrap estimates > 0 returns 0; bootstrap estimates < 0 returns 1. Analogous reasoning applied p-value H_0: theta=0 vs H_A: theta<0.","code":""},{"path":"/reference/random_effects_expr.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct random effects formula — random_effects_expr","title":"Construct random effects formula — random_effects_expr","text":"Constructs character representation random effects formula fitting MMRM subject visit format required mmrm::mmrm().","code":""},{"path":"/reference/random_effects_expr.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct random effects formula — random_effects_expr","text":"","code":"random_effects_expr( cov_struct = c(\"us\", \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\"), cov_by_group = FALSE )"},{"path":"/reference/random_effects_expr.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct random effects formula — random_effects_expr","text":"cov_struct Character - covariance structure used, must one \"us\" (default), \"ad\", \"adh\", \"ar1\", \"ar1h\", \"cs\", \"csh\", \"toep\", \"toeph\") cov_by_group Boolean - Whenever use separate covariances per group level","code":""},{"path":"/reference/random_effects_expr.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Construct random effects formula — random_effects_expr","text":"example assuming user specified covariance structure \"us\" groups provided return cov_by_group set FALSE indicates separate covariance matrices required per group following returned:","code":"us(visit | subjid) us( visit | group / subjid )"},{"path":"/reference/rbmi-package.html","id":null,"dir":"Reference","previous_headings":"","what":"rbmi: Reference Based Multiple Imputation — rbmi-package","title":"rbmi: Reference Based Multiple Imputation — rbmi-package","text":"rbmi package used perform reference based multiple imputation. package provides implementations common, patient-specific imputation strategies whilst allowing user select various standard Bayesian frequentist approaches. package designed around 4 core functions: draws() - Fits multiple imputation models impute() - Imputes multiple datasets analyse() - Analyses multiple datasets pool() - Pools multiple results single statistic learn rbmi, please see quickstart vignette: vignette(topic= \"quickstart\", package = \"rbmi\")","code":""},{"path":[]},{"path":"/reference/rbmi-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"rbmi: Reference Based Multiple Imputation — rbmi-package","text":"Maintainer: Craig Gower-Page craig.gower-page@roche.com Authors: Alessandro Noci alessandro.noci@roche.com Isaac Gravestock isaac.gravestock@roche.com contributors: Marcel Wolbers marcel.wolbers@roche.com [contributor] F. Hoffmann-La Roche AG [copyright holder, funder]","code":""},{"path":"/reference/rbmi-settings.html","id":null,"dir":"Reference","previous_headings":"","what":"rbmi settings — rbmi-settings","title":"rbmi settings — rbmi-settings","text":"Define settings modify behaviour rbmi package following name options can set via:","code":"options( = )"},{"path":"/reference/rbmi-settings.html","id":"rbmi-cache-dir","dir":"Reference","previous_headings":"","what":"rbmi.cache_dir","title":"rbmi settings — rbmi-settings","text":"Default = tools::R_user_dir(\"rbmi\", = \"cache\") Directory store compiled Stan model . set, temporary directory used given R session. Can also set via environment variable RBMI_CACHE_DIR.","code":""},{"path":"/reference/rbmi-settings.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"rbmi settings — rbmi-settings","text":"","code":"set_options()"},{"path":"/reference/rbmi-settings.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"rbmi settings — rbmi-settings","text":"","code":"if (FALSE) { # \\dontrun{ options(rbmi.cache_dir = \"some/directory/path\") } # }"},{"path":"/reference/record.html","id":null,"dir":"Reference","previous_headings":"","what":"Capture all Output — record","title":"Capture all Output — record","text":"function silences warnings, errors & messages instead returns list containing results (error) + warning error messages character vectors.","code":""},{"path":"/reference/record.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Capture all Output — record","text":"","code":"record(expr)"},{"path":"/reference/record.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Capture all Output — record","text":"expr expression executed","code":""},{"path":"/reference/record.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Capture all Output — record","text":"list containing results - object returned expr list() error thrown warnings - NULL character vector warnings thrown errors - NULL string error thrown messages - NULL character vector messages produced","code":""},{"path":"/reference/record.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Capture all Output — record","text":"","code":"if (FALSE) { # \\dontrun{ record({ x <- 1 y <- 2 warning(\"something went wrong\") message(\"O nearly done\") x + y }) } # }"},{"path":"/reference/recursive_reduce.html","id":null,"dir":"Reference","previous_headings":"","what":"recursive_reduce — recursive_reduce","title":"recursive_reduce — recursive_reduce","text":"Utility function used replicated purrr::reduce. Recursively applies function list elements 1 element remains","code":""},{"path":"/reference/recursive_reduce.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"recursive_reduce — recursive_reduce","text":"","code":"recursive_reduce(.l, .f)"},{"path":"/reference/recursive_reduce.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"recursive_reduce — recursive_reduce","text":".l list values apply function .f function apply element list turn .e. .l[[1]] <- .f( .l[[1]] , .l[[2]]) ; .l[[1]] <- .f( .l[[1]] , .l[[3]])","code":""},{"path":"/reference/remove_if_all_missing.html","id":null,"dir":"Reference","previous_headings":"","what":"Remove subjects from dataset if they have no observed values — remove_if_all_missing","title":"Remove subjects from dataset if they have no observed values — remove_if_all_missing","text":"function takes data.frame variables visit, outcome & subjid. removes rows given subjid non-missing values outcome.","code":""},{"path":"/reference/remove_if_all_missing.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Remove subjects from dataset if they have no observed values — remove_if_all_missing","text":"","code":"remove_if_all_missing(dat)"},{"path":"/reference/remove_if_all_missing.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Remove subjects from dataset if they have no observed values — remove_if_all_missing","text":"dat data.frame","code":""},{"path":"/reference/rubin_df.html","id":null,"dir":"Reference","previous_headings":"","what":"Barnard and Rubin degrees of freedom adjustment — rubin_df","title":"Barnard and Rubin degrees of freedom adjustment — rubin_df","text":"Compute degrees freedom according Barnard-Rubin formula.","code":""},{"path":"/reference/rubin_df.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Barnard and Rubin degrees of freedom adjustment — rubin_df","text":"","code":"rubin_df(v_com, var_b, var_t, M)"},{"path":"/reference/rubin_df.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Barnard and Rubin degrees of freedom adjustment — rubin_df","text":"v_com Positive number representing degrees freedom complete-data analysis. var_b -variance point estimate across multiply imputed datasets. var_t Total-variance point estimate according Rubin's rules. M Number imputations.","code":""},{"path":"/reference/rubin_df.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Barnard and Rubin degrees of freedom adjustment — rubin_df","text":"Degrees freedom according Barnard-Rubin formula. See Barnard-Rubin (1999).","code":""},{"path":"/reference/rubin_df.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Barnard and Rubin degrees of freedom adjustment — rubin_df","text":"computation takes account limit cases missing data (.e. -variance var_b zero) complete-data degrees freedom set Inf. Moreover, v_com given NA, function returns Inf.","code":""},{"path":"/reference/rubin_df.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Barnard and Rubin degrees of freedom adjustment — rubin_df","text":"Barnard, J. Rubin, D.B. (1999). Small sample degrees freedom multiple imputation. Biometrika, 86, 948-955.","code":""},{"path":"/reference/rubin_rules.html","id":null,"dir":"Reference","previous_headings":"","what":"Combine estimates using Rubin's rules — rubin_rules","title":"Combine estimates using Rubin's rules — rubin_rules","text":"Pool together results M complete-data analyses according Rubin's rules. See details.","code":""},{"path":"/reference/rubin_rules.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Combine estimates using Rubin's rules — rubin_rules","text":"","code":"rubin_rules(ests, ses, v_com)"},{"path":"/reference/rubin_rules.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Combine estimates using Rubin's rules — rubin_rules","text":"ests Numeric vector containing point estimates complete-data analyses. ses Numeric vector containing standard errors complete-data analyses. v_com Positive number representing degrees freedom complete-data analysis.","code":""},{"path":"/reference/rubin_rules.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Combine estimates using Rubin's rules — rubin_rules","text":"list containing: est_point: pooled point estimate according Little-Rubin (2002). var_t: total variance according Little-Rubin (2002). df: degrees freedom according Barnard-Rubin (1999).","code":""},{"path":"/reference/rubin_rules.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Combine estimates using Rubin's rules — rubin_rules","text":"rubin_rules applies Rubin's rules (Rubin, 1987) pooling together results multiple imputation procedure. pooled point estimate est_point average across point estimates complete-data analyses (given input argument ests). total variance var_t sum two terms representing within-variance -variance (see Little-Rubin (2002)). function also returns df, estimated pooled degrees freedom according Barnard-Rubin (1999) can used inference based t-distribution.","code":""},{"path":"/reference/rubin_rules.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Combine estimates using Rubin's rules — rubin_rules","text":"Barnard, J. Rubin, D.B. (1999). Small sample degrees freedom multiple imputation. Biometrika, 86, 948-955 Roderick J. . Little Donald B. Rubin. Statistical Analysis Missing Data, Second Edition. John Wiley & Sons, Hoboken, New Jersey, 2002. [Section 5.4]","code":""},{"path":[]},{"path":"/reference/sample_ids.html","id":null,"dir":"Reference","previous_headings":"","what":"Sample Patient Ids — sample_ids","title":"Sample Patient Ids — sample_ids","text":"Performs stratified bootstrap sample IDS ensuring return vector length input vector","code":""},{"path":"/reference/sample_ids.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sample Patient Ids — sample_ids","text":"","code":"sample_ids(ids, strata = rep(1, length(ids)))"},{"path":"/reference/sample_ids.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sample Patient Ids — sample_ids","text":"ids vector sample strata strata indicator, ids sampled within strata ensuring numbers strata maintained","code":""},{"path":"/reference/sample_ids.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Sample Patient Ids — sample_ids","text":"","code":"if (FALSE) { # \\dontrun{ sample_ids( c(\"a\", \"b\", \"c\", \"d\"), strata = c(1,1,2,2)) } # }"},{"path":"/reference/sample_list.html","id":null,"dir":"Reference","previous_headings":"","what":"Create and validate a sample_list object — sample_list","title":"Create and validate a sample_list object — sample_list","text":"Given list sample_single objects generate sample_single(), creates sample_list objects validate .","code":""},{"path":"/reference/sample_list.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create and validate a sample_list object — sample_list","text":"","code":"sample_list(...)"},{"path":"/reference/sample_list.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create and validate a sample_list object — sample_list","text":"... list sample_single objects.","code":""},{"path":"/reference/sample_mvnorm.html","id":null,"dir":"Reference","previous_headings":"","what":"Sample random values from the multivariate normal distribution — sample_mvnorm","title":"Sample random values from the multivariate normal distribution — sample_mvnorm","text":"Sample random values multivariate normal distribution","code":""},{"path":"/reference/sample_mvnorm.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sample random values from the multivariate normal distribution — sample_mvnorm","text":"","code":"sample_mvnorm(mu, sigma)"},{"path":"/reference/sample_mvnorm.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sample random values from the multivariate normal distribution — sample_mvnorm","text":"mu mean vector sigma covariance matrix Samples multivariate normal variables multiplying univariate random normal variables cholesky decomposition covariance matrix. mu length 1 just uses rnorm instead.","code":""},{"path":"/reference/sample_single.html","id":null,"dir":"Reference","previous_headings":"","what":"Create object of sample_single class — sample_single","title":"Create object of sample_single class — sample_single","text":"Creates object class sample_single named list containing input parameters validate .","code":""},{"path":"/reference/sample_single.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create object of sample_single class — sample_single","text":"","code":"sample_single( ids, beta = NA, sigma = NA, theta = NA, failed = any(is.na(beta)), ids_samp = ids )"},{"path":"/reference/sample_single.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create object of sample_single class — sample_single","text":"ids Vector characters containing ids subjects included original dataset. beta Numeric vector estimated regression coefficients. sigma List estimated covariance matrices (one level vars$group). theta Numeric vector transformed covariances. failed Logical. TRUE model fit failed. ids_samp Vector characters containing ids subjects included given sample.","code":""},{"path":"/reference/sample_single.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create object of sample_single class — sample_single","text":"named list class sample_single. contains following: ids vector characters containing ids subjects included original dataset. beta numeric vector estimated regression coefficients. sigma list estimated covariance matrices (one level vars$group). theta numeric vector transformed covariances. failed logical. TRUE model fit failed. ids_samp vector characters containing ids subjects included given sample.","code":""},{"path":"/reference/scalerConstructor.html","id":null,"dir":"Reference","previous_headings":"","what":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"Scales design matrix non-categorical columns mean 0 standard deviation 1.","code":""},{"path":"/reference/scalerConstructor.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"object initialisation used determine relevant mean SD's scale scaling (un-scaling) performed relevant object methods. Un-scaling done linear model Beta Sigma coefficients. purpose first column dataset scaled assumed outcome variable variables assumed post-transformation predictor variables (.e. dummy variables already expanded).","code":""},{"path":"/reference/scalerConstructor.html","id":"public-fields","dir":"Reference","previous_headings":"","what":"Public fields","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"centre Vector column means. first value outcome variable, variables predictors. scales Vector column standard deviations. first value outcome variable, variables predictors.","code":""},{"path":[]},{"path":"/reference/scalerConstructor.html","id":"public-methods","dir":"Reference","previous_headings":"","what":"Public methods","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"scalerConstructor$new() scalerConstructor$scale() scalerConstructor$unscale_sigma() scalerConstructor$unscale_beta() scalerConstructor$clone()","code":""},{"path":"/reference/scalerConstructor.html","id":"method-new-","dir":"Reference","previous_headings":"","what":"Method new()","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"Uses dat determine relevant column means standard deviations use scaling un-scaling future datasets. Implicitly assumes new datasets column order dat","code":""},{"path":"/reference/scalerConstructor.html","id":"usage","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"","code":"scalerConstructor$new(dat)"},{"path":"/reference/scalerConstructor.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"dat data.frame matrix. columns must numeric (.e dummy variables, must already expanded ).","code":""},{"path":"/reference/scalerConstructor.html","id":"details-1","dir":"Reference","previous_headings":"","what":"Details","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"Categorical columns (determined values entirely 1 0) scaled. achieved setting corresponding values centre 0 scale 1.","code":""},{"path":"/reference/scalerConstructor.html","id":"method-scale-","dir":"Reference","previous_headings":"","what":"Method scale()","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"Scales dataset continuous variables mean 0 standard deviation 1.","code":""},{"path":"/reference/scalerConstructor.html","id":"usage-1","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"","code":"scalerConstructor$scale(dat)"},{"path":"/reference/scalerConstructor.html","id":"arguments-1","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"dat data.frame matrix whose columns numeric (.e. dummy variables expanded ) whose columns order dataset used initialization function.","code":""},{"path":"/reference/scalerConstructor.html","id":"method-unscale-sigma-","dir":"Reference","previous_headings":"","what":"Method unscale_sigma()","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"Unscales sigma value (matrix) estimated linear model using design matrix scaled object. function works first column initialisation data.frame outcome variable.","code":""},{"path":"/reference/scalerConstructor.html","id":"usage-2","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"","code":"scalerConstructor$unscale_sigma(sigma)"},{"path":"/reference/scalerConstructor.html","id":"arguments-2","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"sigma numeric value matrix.","code":""},{"path":"/reference/scalerConstructor.html","id":"returns","dir":"Reference","previous_headings":"","what":"Returns","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"numeric value matrix","code":""},{"path":"/reference/scalerConstructor.html","id":"method-unscale-beta-","dir":"Reference","previous_headings":"","what":"Method unscale_beta()","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"Unscales beta value (vector) estimated linear model using design matrix scaled object. function works first column initialization data.frame outcome variable.","code":""},{"path":"/reference/scalerConstructor.html","id":"usage-3","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"","code":"scalerConstructor$unscale_beta(beta)"},{"path":"/reference/scalerConstructor.html","id":"arguments-3","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"beta numeric vector beta coefficients estimated linear model.","code":""},{"path":"/reference/scalerConstructor.html","id":"returns-1","dir":"Reference","previous_headings":"","what":"Returns","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"numeric vector.","code":""},{"path":"/reference/scalerConstructor.html","id":"method-clone-","dir":"Reference","previous_headings":"","what":"Method clone()","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"objects class cloneable method.","code":""},{"path":"/reference/scalerConstructor.html","id":"usage-4","dir":"Reference","previous_headings":"","what":"Usage","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"","code":"scalerConstructor$clone(deep = FALSE)"},{"path":"/reference/scalerConstructor.html","id":"arguments-4","dir":"Reference","previous_headings":"","what":"Arguments","title":"R6 Class for scaling (and un-scaling) design matrices — scalerConstructor","text":"deep Whether make deep clone.","code":""},{"path":"/reference/set_simul_pars.html","id":null,"dir":"Reference","previous_headings":"","what":"Set simulation parameters of a study group. — set_simul_pars","title":"Set simulation parameters of a study group. — set_simul_pars","text":"function provides input arguments study group needed simulate data simulate_data(). simulate_data() generates data two-arms clinical trial longitudinal continuous outcomes two intercurrent events (ICEs). ICE1 may thought discontinuation study treatment due study drug condition related (SDCR) reasons. ICE2 may thought discontinuation study treatment due uninformative study drop-, .e. due study drug condition related (NSDRC) reasons outcome data ICE2 always missing.","code":""},{"path":"/reference/set_simul_pars.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set simulation parameters of a study group. — set_simul_pars","text":"","code":"set_simul_pars( mu, sigma, n, prob_ice1 = 0, or_outcome_ice1 = 1, prob_post_ice1_dropout = 0, prob_ice2 = 0, prob_miss = 0 )"},{"path":"/reference/set_simul_pars.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set simulation parameters of a study group. — set_simul_pars","text":"mu Numeric vector describing mean outcome trajectory visit (including baseline) assuming ICEs. sigma Covariance matrix outcome trajectory assuming ICEs. n Number subjects belonging group. prob_ice1 Numeric vector specifies probability experiencing ICE1 (discontinuation study treatment due SDCR reasons) visit subject observed outcome visit equal mean baseline (mu[1]). single numeric provided, probability applied visit. or_outcome_ice1 Numeric value specifies odds ratio experiencing ICE1 visit corresponding +1 higher value observed outcome visit. prob_post_ice1_dropout Numeric value specifies probability study drop-following ICE1. subject simulated drop-ICE1, outcomes ICE1 set missing. prob_ice2 Numeric specifies additional probability post-baseline visit affected study drop-. Outcome data subject's first simulated visit affected study drop-subsequent visits set missing. generates second intercurrent event ICE2, may thought treatment discontinuation due NSDRC reasons subsequent drop-. subject, ICE1 ICE2 simulated occur, assumed earlier counts. case ICEs simulated occur time, assumed ICE1 counts. means single subject can experience either ICE1 ICE2, . prob_miss Numeric value specifies additional probability given post-baseline observation missing. can used produce \"intermittent\" missing values associated ICE.","code":""},{"path":"/reference/set_simul_pars.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Set simulation parameters of a study group. — set_simul_pars","text":"simul_pars object named list containing simulation parameters.","code":""},{"path":"/reference/set_simul_pars.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Set simulation parameters of a study group. — set_simul_pars","text":"details, please see simulate_data().","code":""},{"path":[]},{"path":"/reference/set_vars.html","id":null,"dir":"Reference","previous_headings":"","what":"Set key variables — set_vars","title":"Set key variables — set_vars","text":"function used define names key variables within data.frame's provided input arguments draws() ancova().","code":""},{"path":"/reference/set_vars.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set key variables — set_vars","text":"","code":"set_vars( subjid = \"subjid\", visit = \"visit\", outcome = \"outcome\", group = \"group\", covariates = character(0), strata = group, strategy = \"strategy\" )"},{"path":"/reference/set_vars.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set key variables — set_vars","text":"subjid name \"Subject ID\" variable. length 1 character vector. visit name \"Visit\" variable. length 1 character vector. outcome name \"Outcome\" variable. length 1 character vector. group name \"Group\" variable. length 1 character vector. covariates name covariates used context modeling. See details. strata name stratification variable used context bootstrap sampling. See details. strategy name \"strategy\" variable. length 1 character vector.","code":""},{"path":"/reference/set_vars.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Set key variables — set_vars","text":"draws() ancova() covariates argument can specified indicate variables included imputation analysis models respectively. wish include interaction terms need manually specified .e. covariates = c(\"group*visit\", \"age*sex\"). Please note use () function inhibit interpretation/conversion objects supported. Currently strata used draws() combination method_condmean(type = \"bootstrap\") method_approxbayes() order allow specification stratified bootstrap sampling. default strata set equal value group assumed users want preserve group size samples. See draws() details. Likewise, currently strategy argument used draws() specify name strategy variable within data_ice data.frame. See draws() details.","code":""},{"path":[]},{"path":"/reference/set_vars.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Set key variables — set_vars","text":"","code":"if (FALSE) { # \\dontrun{ # Using CDISC variable names as an example set_vars( subjid = \"usubjid\", visit = \"avisit\", outcome = \"aval\", group = \"arm\", covariates = c(\"bwt\", \"bht\", \"arm * avisit\"), strategy = \"strat\" ) } # }"},{"path":"/reference/simulate_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate data — simulate_data","title":"Generate data — simulate_data","text":"Generate data two-arms clinical trial longitudinal continuous outcome two intercurrent events (ICEs). ICE1 may thought discontinuation study treatment due study drug condition related (SDCR) reasons. ICE2 may thought discontinuation study treatment due uninformative study drop-, .e. due study drug condition related (NSDRC) reasons outcome data ICE2 always missing.","code":""},{"path":"/reference/simulate_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate data — simulate_data","text":"","code":"simulate_data(pars_c, pars_t, post_ice1_traj, strategies = getStrategies())"},{"path":"/reference/simulate_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate data — simulate_data","text":"pars_c simul_pars object generated set_simul_pars(). specifies simulation parameters control arm. pars_t simul_pars object generated set_simul_pars(). specifies simulation parameters treatment arm. post_ice1_traj string specifies observed outcomes occurring ICE1 simulated. Must target function included strategies. Possible choices : Missing Random \"MAR\", Jump Reference \"JR\", Copy Reference \"CR\", Copy Increments Reference \"CIR\", Last Mean Carried Forward \"LMCF\". User-defined strategies also added. See getStrategies() details. strategies named list functions. Default equal getStrategies(). See getStrategies() details.","code":""},{"path":"/reference/simulate_data.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate data — simulate_data","text":"data.frame containing simulated data. includes following variables: id: Factor variable specifies id subject. visit: Factor variable specifies visit assessment. Visit 0 denotes baseline visit. group: Factor variable specifies treatment group subject belongs . outcome_bl: Numeric variable specifies baseline outcome. outcome_noICE: Numeric variable specifies longitudinal outcome assuming ICEs. ind_ice1: Binary variable takes value 1 corresponding visit affected ICE1 0 otherwise. dropout_ice1: Binary variable takes value 1 corresponding visit affected drop-following ICE1 0 otherwise. ind_ice2: Binary variable takes value 1 corresponding visit affected ICE2. outcome: Numeric variable specifies longitudinal outcome including ICE1, ICE2 intermittent missing values.","code":""},{"path":"/reference/simulate_data.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Generate data — simulate_data","text":"data generation works follows: Generate outcome data visits (including baseline) multivariate normal distribution parameters pars_c$mu pars_c$sigma control arm parameters pars_t$mu pars_t$sigma treatment arm, respectively. Note randomized trial, outcomes distribution baseline treatment groups, .e. one set pars_c$mu[1]=pars_t$mu[1] pars_c$sigma[1,1]=pars_t$sigma[1,1]. Simulate whether ICE1 (study treatment discontinuation due SDCR reasons) occurs visit according parameters pars_c$prob_ice1 pars_c$or_outcome_ice1 control arm pars_t$prob_ice1 pars_t$or_outcome_ice1 treatment arm, respectively. Simulate drop-following ICE1 according pars_c$prob_post_ice1_dropout pars_t$prob_post_ice1_dropout. Simulate additional uninformative study drop-probabilities pars_c$prob_ice2 pars_t$prob_ice2 visit. generates second intercurrent event ICE2, may thought treatment discontinuation due NSDRC reasons subsequent drop-. simulated time drop-subject's first visit affected drop-data visit subsequent visits consequently set missing. subject, ICE1 ICE2 simulated occur, assumed earlier counts. case ICEs simulated occur time, assumed ICE1 counts. means single subject can experience either ICE1 ICE2, . Adjust trajectories ICE1 according given assumption expressed post_ice1_traj argument. Note post-ICE1 outcomes intervention arm can adjusted. Post-ICE1 outcomes control arm adjusted. Simulate additional intermittent missing outcome data per arguments pars_c$prob_miss pars_t$prob_miss. probability ICE visit modeled according following logistic regression model: ~ 1 + (visit == 0) + ... + (visit == n_visits-1) + ((x-alpha)) : n_visits number visits (including baseline). alpha baseline outcome mean. term ((x-alpha)) specifies dependency probability ICE current outcome value. corresponding regression coefficients logistic model defined follows: intercept set 0, coefficients corresponding discontinuation visit subject outcome equal mean baseline set according parameters pars_c$prob_ice1 (pars_t$prob_ice1), regression coefficient associated covariate ((x-alpha)) set log(pars_c$or_outcome_ice1) (log(pars_t$or_outcome_ice1)). Please note baseline outcome missing affected ICEs.","code":""},{"path":"/reference/simulate_dropout.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate drop-out — simulate_dropout","title":"Simulate drop-out — simulate_dropout","text":"Simulate drop-","code":""},{"path":"/reference/simulate_dropout.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate drop-out — simulate_dropout","text":"","code":"simulate_dropout(prob_dropout, ids, subset = rep(1, length(ids)))"},{"path":"/reference/simulate_dropout.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate drop-out — simulate_dropout","text":"prob_dropout Numeric specifies probability post-baseline visit affected study drop-. ids Factor variable specifies id subject. subset Binary variable specifies subset affected drop-. .e. subset binary vector length equal length ids takes value 1 corresponding visit affected drop-0 otherwise.","code":""},{"path":"/reference/simulate_dropout.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate drop-out — simulate_dropout","text":"binary vector length equal length ids takes value 1 corresponding outcome affected study drop-.","code":""},{"path":"/reference/simulate_dropout.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulate drop-out — simulate_dropout","text":"subset can used specify outcome values affected drop-. default subset set 1 values except values corresponding baseline outcome, since baseline supposed affected drop-. Even subset specified user, values corresponding baseline outcome still hard-coded 0.","code":""},{"path":"/reference/simulate_ice.html","id":null,"dir":"Reference","previous_headings":"","what":"Simulate intercurrent event — simulate_ice","title":"Simulate intercurrent event — simulate_ice","text":"Simulate intercurrent event","code":""},{"path":"/reference/simulate_ice.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Simulate intercurrent event — simulate_ice","text":"","code":"simulate_ice(outcome, visits, ids, prob_ice, or_outcome_ice, baseline_mean)"},{"path":"/reference/simulate_ice.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Simulate intercurrent event — simulate_ice","text":"outcome Numeric variable specifies longitudinal outcome single group. visits Factor variable specifies visit assessment. ids Factor variable specifies id subject. prob_ice Numeric vector specifies visit probability experiencing ICE current visit subject outcome equal mean baseline. single numeric provided, probability applied visit. or_outcome_ice Numeric value specifies odds ratio ICE corresponding +1 higher value outcome visit. baseline_mean Mean outcome value baseline.","code":""},{"path":"/reference/simulate_ice.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Simulate intercurrent event — simulate_ice","text":"binary variable takes value 1 corresponding outcome affected ICE 0 otherwise.","code":""},{"path":"/reference/simulate_ice.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Simulate intercurrent event — simulate_ice","text":"probability ICE visit modeled according following logistic regression model: ~ 1 + (visit == 0) + ... + (visit == n_visits-1) + ((x-alpha)) : n_visits number visits (including baseline). alpha baseline outcome mean set via argument baseline_mean. term ((x-alpha)) specifies dependency probability ICE current outcome value. corresponding regression coefficients logistic model defined follows: intercept set 0, coefficients corresponding discontinuation visit subject outcome equal mean baseline set according parameter or_outcome_ice, regression coefficient associated covariate ((x-alpha)) set log(or_outcome_ice).","code":""},{"path":"/reference/simulate_test_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Create simulated datasets — simulate_test_data","title":"Create simulated datasets — simulate_test_data","text":"Creates longitudinal dataset format rbmi designed analyse.","code":""},{"path":"/reference/simulate_test_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create simulated datasets — simulate_test_data","text":"","code":"simulate_test_data( n = 200, sd = c(3, 5, 7), cor = c(0.1, 0.7, 0.4), mu = list(int = 10, age = 3, sex = 2, trt = c(0, 4, 8), visit = c(0, 1, 2)) ) as_vcov(sd, cor)"},{"path":"/reference/simulate_test_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create simulated datasets — simulate_test_data","text":"n number subjects sample. Total number observations returned thus n * length(sd) sd standard deviations outcome visit. .e. square root diagonal covariance matrix outcome cor correlation coefficients outcome values visit. See details. mu coefficients use construct mean outcome value visit. Must named list elements int, age, sex, trt & visit. See details.","code":""},{"path":"/reference/simulate_test_data.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Create simulated datasets — simulate_test_data","text":"number visits determined size variance covariance matrix. .e. 3 standard deviation values provided 3 visits per patient created. covariates simulated dataset produced follows: Patients age sampled random N(0,1) distribution Patients sex sampled random 50/50 split Patients group sampled random fixed group n/2 patients outcome variable sampled multivariate normal distribution, see details mean outcome variable derived : coefficients intercept, age sex taken mu$int, mu$age mu$sex respectively, must length 1 numeric. Treatment visit coefficients taken mu$trt mu$visit respectively must either length 1 (.e. constant affect across visits) equal number visits (determined length sd). .e. wanted treatment slope 5 visit slope 1 specify: correlation matrix constructed cor follows. Let cor = c(, b, c, d, e, f) correlation matrix :","code":"outcome = Intercept + age + sex + visit + treatment mu = list(..., \"trt\" = c(0,5,10), \"visit\" = c(0,1,2)) 1 a b d a 1 c e b c 1 f d e f 1"},{"path":"/reference/sort_by.html","id":null,"dir":"Reference","previous_headings":"","what":"Sort data.frame — sort_by","title":"Sort data.frame — sort_by","text":"Sorts data.frame (ascending default) based upon variables within dataset","code":""},{"path":"/reference/sort_by.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Sort data.frame — sort_by","text":"","code":"sort_by(df, vars = NULL, decreasing = FALSE)"},{"path":"/reference/sort_by.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Sort data.frame — sort_by","text":"df data.frame vars character vector variables decreasing logical whether sort order descending ascending (default) order. Can either single logical value (case applied variables) vector length vars","code":""},{"path":"/reference/sort_by.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Sort data.frame — sort_by","text":"","code":"if (FALSE) { # \\dontrun{ sort_by(iris, c(\"Sepal.Length\", \"Sepal.Width\"), decreasing = c(TRUE, FALSE)) } # }"},{"path":"/reference/split_dim.html","id":null,"dir":"Reference","previous_headings":"","what":"Transform array into list of arrays — split_dim","title":"Transform array into list of arrays — split_dim","text":"Transform array list arrays listing performed given dimension.","code":""},{"path":"/reference/split_dim.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Transform array into list of arrays — split_dim","text":"","code":"split_dim(a, n)"},{"path":"/reference/split_dim.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Transform array into list of arrays — split_dim","text":"Array number dimensions least 2. n Positive integer. Dimension listed.","code":""},{"path":"/reference/split_dim.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Transform array into list of arrays — split_dim","text":"list length n arrays number dimensions equal number dimensions minus 1.","code":""},{"path":"/reference/split_dim.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Transform array into list of arrays — split_dim","text":"example, 3 dimensional array n = 1, split_dim(,n) returns list 2 dimensional arrays (.e. list matrices) element list [, , ], takes values 1 length first dimension array. Example: inputs: <- array( c(1,2,3,4,5,6,7,8,9,10,11,12), dim = c(3,2,2)), means : n <- 1 output res <- split_dim(,n) list 3 elements:","code":"a[1,,] a[2,,] a[3,,] [,1] [,2] [,1] [,2] [,1] [,2] --------- --------- --------- 1 7 2 8 3 9 4 10 5 11 6 12 res[[1]] res[[2]] res[[3]] [,1] [,2] [,1] [,2] [,1] [,2] --------- --------- --------- 1 7 2 8 3 9 4 10 5 11 6 12"},{"path":"/reference/split_imputations.html","id":null,"dir":"Reference","previous_headings":"","what":"Split a flat list of imputation_single() into multiple imputation_df()'s by ID — split_imputations","title":"Split a flat list of imputation_single() into multiple imputation_df()'s by ID — split_imputations","text":"Split flat list imputation_single() multiple imputation_df()'s ID","code":""},{"path":"/reference/split_imputations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Split a flat list of imputation_single() into multiple imputation_df()'s by ID — split_imputations","text":"","code":"split_imputations(list_of_singles, split_ids)"},{"path":"/reference/split_imputations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Split a flat list of imputation_single() into multiple imputation_df()'s by ID — split_imputations","text":"list_of_singles list imputation_single()'s split_ids list 1 element per required split. element must contain vector \"ID\"'s correspond imputation_single() ID's required within sample. total number ID's must equal length list_of_singles","code":""},{"path":"/reference/split_imputations.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Split a flat list of imputation_single() into multiple imputation_df()'s by ID — split_imputations","text":"function converts list imputations structured per patient structured per sample .e. converts :","code":"obj <- list( imputation_single(\"Ben\", numeric(0)), imputation_single(\"Ben\", numeric(0)), imputation_single(\"Ben\", numeric(0)), imputation_single(\"Harry\", c(1, 2)), imputation_single(\"Phil\", c(3, 4)), imputation_single(\"Phil\", c(5, 6)), imputation_single(\"Tom\", c(7, 8, 9)) ) index <- list( c(\"Ben\", \"Harry\", \"Phil\", \"Tom\"), c(\"Ben\", \"Ben\", \"Phil\") ) output <- list( imputation_df( imputation_single(id = \"Ben\", values = numeric(0)), imputation_single(id = \"Harry\", values = c(1, 2)), imputation_single(id = \"Phil\", values = c(3, 4)), imputation_single(id = \"Tom\", values = c(7, 8, 9)) ), imputation_df( imputation_single(id = \"Ben\", values = numeric(0)), imputation_single(id = \"Ben\", values = numeric(0)), imputation_single(id = \"Phil\", values = c(5, 6)) ) )"},{"path":"/reference/str_contains.html","id":null,"dir":"Reference","previous_headings":"","what":"Does a string contain a substring — str_contains","title":"Does a string contain a substring — str_contains","text":"Returns vector TRUE/FALSE element x contains element subs .e.","code":"str_contains( c(\"ben\", \"tom\", \"harry\"), c(\"e\", \"y\")) [1] TRUE FALSE TRUE"},{"path":"/reference/str_contains.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Does a string contain a substring — str_contains","text":"","code":"str_contains(x, subs)"},{"path":"/reference/str_contains.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Does a string contain a substring — str_contains","text":"x character vector subs character vector substrings look ","code":""},{"path":"/reference/strategies.html","id":null,"dir":"Reference","previous_headings":"","what":"Strategies — strategies","title":"Strategies — strategies","text":"functions used implement various reference based imputation strategies combining subjects distribution reference distribution based upon visits failed meet Missing--Random (MAR) assumption.","code":""},{"path":"/reference/strategies.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Strategies — strategies","text":"","code":"strategy_MAR(pars_group, pars_ref, index_mar) strategy_JR(pars_group, pars_ref, index_mar) strategy_CR(pars_group, pars_ref, index_mar) strategy_CIR(pars_group, pars_ref, index_mar) strategy_LMCF(pars_group, pars_ref, index_mar)"},{"path":"/reference/strategies.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Strategies — strategies","text":"pars_group list parameters subject's group. See details. pars_ref list parameters subject's reference group. See details. index_mar logical vector indicating visits meet MAR assumption subject. .e. identifies observations non-MAR intercurrent event (ICE).","code":""},{"path":"/reference/strategies.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Strategies — strategies","text":"pars_group pars_ref must list containing elements mu sigma. mu must numeric vector sigma must square matrix symmetric covariance matrix dimensions equal length mu index_mar. e.g. Users can define strategy functions include via strategies argument impute() using getStrategies(). said following strategies available \"box\": Missing Random (MAR) Jump Reference (JR) Copy Reference (CR) Copy Increments Reference (CIR) Last Mean Carried Forward (LMCF)","code":"list( mu = c(1,2,3), sigma = matrix(c(4,3,2,3,5,4,2,4,6), nrow = 3, ncol = 3) )"},{"path":"/reference/string_pad.html","id":null,"dir":"Reference","previous_headings":"","what":"string_pad — string_pad","title":"string_pad — string_pad","text":"Utility function used replicate str_pad. Adds white space either end string get equal desired length","code":""},{"path":"/reference/string_pad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"string_pad — string_pad","text":"","code":"string_pad(x, width)"},{"path":"/reference/string_pad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"string_pad — string_pad","text":"x string width desired length","code":""},{"path":"/reference/transpose_imputations.html","id":null,"dir":"Reference","previous_headings":"","what":"Transpose imputations — transpose_imputations","title":"Transpose imputations — transpose_imputations","text":"Takes imputation_df object transposes e.g.","code":"list( list(id = \"a\", values = c(1,2,3)), list(id = \"b\", values = c(4,5,6) ) )"},{"path":"/reference/transpose_imputations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Transpose imputations — transpose_imputations","text":"","code":"transpose_imputations(imputations)"},{"path":"/reference/transpose_imputations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Transpose imputations — transpose_imputations","text":"imputations imputation_df object created imputation_df()","code":""},{"path":"/reference/transpose_imputations.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Transpose imputations — transpose_imputations","text":"becomes","code":"list( ids = c(\"a\", \"b\"), values = c(1,2,3,4,5,6) )"},{"path":"/reference/transpose_results.html","id":null,"dir":"Reference","previous_headings":"","what":"Transpose results object — transpose_results","title":"Transpose results object — transpose_results","text":"Transposes Results object (created analyse()) order group estimates together vectors.","code":""},{"path":"/reference/transpose_results.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Transpose results object — transpose_results","text":"","code":"transpose_results(results, components)"},{"path":"/reference/transpose_results.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Transpose results object — transpose_results","text":"results list results. components character vector components extract (.e. \"est\", \"se\").","code":""},{"path":"/reference/transpose_results.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Transpose results object — transpose_results","text":"Essentially function takes object format: produces:","code":"x <- list( list( \"trt1\" = list( est = 1, se = 2 ), \"trt2\" = list( est = 3, se = 4 ) ), list( \"trt1\" = list( est = 5, se = 6 ), \"trt2\" = list( est = 7, se = 8 ) ) ) list( trt1 = list( est = c(1,5), se = c(2,6) ), trt2 = list( est = c(3,7), se = c(4,8) ) )"},{"path":"/reference/transpose_samples.html","id":null,"dir":"Reference","previous_headings":"","what":"Transpose samples — transpose_samples","title":"Transpose samples — transpose_samples","text":"Transposes samples generated draws() grouped subjid instead sample number.","code":""},{"path":"/reference/transpose_samples.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Transpose samples — transpose_samples","text":"","code":"transpose_samples(samples)"},{"path":"/reference/transpose_samples.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Transpose samples — transpose_samples","text":"samples list samples generated draws().","code":""},{"path":"/reference/validate.analysis.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate analysis objects — validate.analysis","title":"Validate analysis objects — validate.analysis","text":"Validates return object analyse() function.","code":""},{"path":"/reference/validate.analysis.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate analysis objects — validate.analysis","text":"","code":"# S3 method for class 'analysis' validate(x, ...)"},{"path":"/reference/validate.analysis.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate analysis objects — validate.analysis","text":"x analysis results object (class \"jackknife\", \"bootstrap\", \"rubin\"). ... used.","code":""},{"path":"/reference/validate.draws.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate draws object — validate.draws","title":"Validate draws object — validate.draws","text":"Validate draws object","code":""},{"path":"/reference/validate.draws.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate draws object — validate.draws","text":"","code":"# S3 method for class 'draws' validate(x, ...)"},{"path":"/reference/validate.draws.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate draws object — validate.draws","text":"x draws object generated as_draws(). ... used.","code":""},{"path":"/reference/validate.html","id":null,"dir":"Reference","previous_headings":"","what":"Generic validation method — validate","title":"Generic validation method — validate","text":"function used perform assertions object conforms expected structure basic assumptions violated. throw error checks pass.","code":""},{"path":"/reference/validate.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generic validation method — validate","text":"","code":"validate(x, ...)"},{"path":"/reference/validate.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generic validation method — validate","text":"x object validated. ... additional arguments pass specific validation method.","code":""},{"path":"/reference/validate.is_mar.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate is_mar for a given subject — validate.is_mar","title":"Validate is_mar for a given subject — validate.is_mar","text":"Checks longitudinal data patient divided MAR followed non-MAR data; non-MAR observation followed MAR observation allowed.","code":""},{"path":"/reference/validate.is_mar.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate is_mar for a given subject — validate.is_mar","text":"","code":"# S3 method for class 'is_mar' validate(x, ...)"},{"path":"/reference/validate.is_mar.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate is_mar for a given subject — validate.is_mar","text":"x Object class is_mar. Logical vector indicating whether observations MAR. ... used.","code":""},{"path":"/reference/validate.is_mar.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate is_mar for a given subject — validate.is_mar","text":"error issue otherwise return TRUE.","code":""},{"path":"/reference/validate.ivars.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate inputs for vars — validate.ivars","title":"Validate inputs for vars — validate.ivars","text":"Checks required variable names defined within vars appropriate datatypes","code":""},{"path":"/reference/validate.ivars.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate inputs for vars — validate.ivars","text":"","code":"# S3 method for class 'ivars' validate(x, ...)"},{"path":"/reference/validate.ivars.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate inputs for vars — validate.ivars","text":"x named list indicating names key variables source dataset ... used","code":""},{"path":"/reference/validate.references.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate user supplied references — validate.references","title":"Validate user supplied references — validate.references","text":"Checks ensure user specified references expect values (.e. found within source data).","code":""},{"path":"/reference/validate.references.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate user supplied references — validate.references","text":"","code":"# S3 method for class 'references' validate(x, control, ...)"},{"path":"/reference/validate.references.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate user supplied references — validate.references","text":"x named character vector. control factor variable (group variable source dataset). ... used.","code":""},{"path":"/reference/validate.references.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate user supplied references — validate.references","text":"error issue otherwise return TRUE.","code":""},{"path":"/reference/validate.sample_list.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate sample_list object — validate.sample_list","title":"Validate sample_list object — validate.sample_list","text":"Validate sample_list object","code":""},{"path":"/reference/validate.sample_list.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate sample_list object — validate.sample_list","text":"","code":"# S3 method for class 'sample_list' validate(x, ...)"},{"path":"/reference/validate.sample_list.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate sample_list object — validate.sample_list","text":"x sample_list object generated sample_list(). ... used.","code":""},{"path":"/reference/validate.sample_single.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate sample_single object — validate.sample_single","title":"Validate sample_single object — validate.sample_single","text":"Validate sample_single object","code":""},{"path":"/reference/validate.sample_single.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate sample_single object — validate.sample_single","text":"","code":"# S3 method for class 'sample_single' validate(x, ...)"},{"path":"/reference/validate.sample_single.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate sample_single object — validate.sample_single","text":"x sample_single object generated sample_single(). ... used.","code":""},{"path":"/reference/validate.simul_pars.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate a simul_pars object — validate.simul_pars","title":"Validate a simul_pars object — validate.simul_pars","text":"Validate simul_pars object","code":""},{"path":"/reference/validate.simul_pars.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate a simul_pars object — validate.simul_pars","text":"","code":"# S3 method for class 'simul_pars' validate(x, ...)"},{"path":"/reference/validate.simul_pars.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate a simul_pars object — validate.simul_pars","text":"x simul_pars object generated set_simul_pars(). ... used.","code":""},{"path":"/reference/validate.stan_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate a stan_data object — validate.stan_data","title":"Validate a stan_data object — validate.stan_data","text":"Validate stan_data object","code":""},{"path":"/reference/validate.stan_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate a stan_data object — validate.stan_data","text":"","code":"# S3 method for class 'stan_data' validate(x, ...)"},{"path":"/reference/validate.stan_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate a stan_data object — validate.stan_data","text":"x stan_data object. ... used.","code":""},{"path":"/reference/validate_analyse_pars.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate analysis results — validate_analyse_pars","title":"Validate analysis results — validate_analyse_pars","text":"Validates analysis results generated analyse().","code":""},{"path":"/reference/validate_analyse_pars.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate analysis results — validate_analyse_pars","text":"","code":"validate_analyse_pars(results, pars)"},{"path":"/reference/validate_analyse_pars.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate analysis results — validate_analyse_pars","text":"results list results generated analysis fun used analyse(). pars list expected parameters analysis. lists .e. c(\"est\", \"se\", \"df\").","code":""},{"path":"/reference/validate_datalong.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate a longdata object — validate_datalong","title":"Validate a longdata object — validate_datalong","text":"Validate longdata object","code":""},{"path":"/reference/validate_datalong.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate a longdata object — validate_datalong","text":"","code":"validate_datalong(data, vars) validate_datalong_varExists(data, vars) validate_datalong_types(data, vars) validate_datalong_notMissing(data, vars) validate_datalong_complete(data, vars) validate_datalong_unifromStrata(data, vars) validate_dataice(data, data_ice, vars, update = FALSE)"},{"path":"/reference/validate_datalong.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate a longdata object — validate_datalong","text":"data data.frame containing longitudinal outcome data + covariates multiple subjects vars vars object created set_vars() data_ice data.frame containing subjects ICE data. See draws() details. update logical, indicates ICE data set first time update applied","code":""},{"path":"/reference/validate_datalong.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Validate a longdata object — validate_datalong","text":"functions used validate various different parts longdata object used draws(), impute(), analyse() pool(). particular: validate_datalong_varExists - Checks variable listed vars actually exists data validate_datalong_types - Checks types key variable expected .e. visit factor variable validate_datalong_notMissing - Checks none key variables (except outcome variable) contain missing values validate_datalong_complete - Checks data complete .e. 1 row subject * visit combination. e.g. nrow(data) == length(unique(subjects)) * length(unique(visits)) validate_datalong_unifromStrata - Checks make sure variables listed stratification variables vary time. e.g. subjects switch stratification groups.","code":""},{"path":"/reference/validate_strategies.html","id":null,"dir":"Reference","previous_headings":"","what":"Validate user specified strategies — validate_strategies","title":"Validate user specified strategies — validate_strategies","text":"Compares user provided strategies required (reference). throw error values reference defined.","code":""},{"path":"/reference/validate_strategies.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Validate user specified strategies — validate_strategies","text":"","code":"validate_strategies(strategies, reference)"},{"path":"/reference/validate_strategies.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Validate user specified strategies — validate_strategies","text":"strategies named list strategies. reference list character vector strategies need defined.","code":""},{"path":"/reference/validate_strategies.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Validate user specified strategies — validate_strategies","text":"throw error issue otherwise return TRUE.","code":""},{"path":"/news/index.html","id":"rbmi-131","dir":"Changelog","previous_headings":"","what":"rbmi 1.3.1","title":"rbmi 1.3.1","text":"Fixed bug stale caches rstan model correctly cleared (#459)","code":""},{"path":"/news/index.html","id":"rbmi-130","dir":"Changelog","previous_headings":"","what":"rbmi 1.3.0","title":"rbmi 1.3.0","text":"CRAN release: 2024-10-16","code":""},{"path":"/news/index.html","id":"breaking-changes-1-3-0","dir":"Changelog","previous_headings":"","what":"Breaking Changes","title":"rbmi 1.3.0","text":"Convert rstan suggested package simplify installation process. means Bayesian imputation functionality available default. use feature, need install rstan separately (#441) Deprecated seed argument method_bayes() favour using base set.seed() function (#431)","code":""},{"path":"/news/index.html","id":"new-features-1-3-0","dir":"Changelog","previous_headings":"","what":"New Features","title":"rbmi 1.3.0","text":"Added vignette implement retrieved dropout models time-varying intercurrent event (ICE) indicators (#414) Added vignette obtain frequentist information-anchored inference conditional mean imputation using rbmi (#406) Added FAQ vignette including statement validation (#407 #440) Renamed lsmeans(..., weights = \"proportional\") lsmeans(..., weights = \"counterfactual\")accurately reflect weights used calculation. Added lsmeans(..., weights = \"proportional_em\") provides consistent results emmeans(..., weights = \"proportional\") lsmeans(..., weights = \"proportional\") left package backwards compatibility alias lsmeans(..., weights = \"counterfactual\") now gives message prompting users use either “proptional_em” “counterfactual” instead. 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ensure future compatibility (@andrjohns, #390) Updated package description include relevant references (#393) Fixed documentation typos (#393)","code":""},{"path":"/news/index.html","id":"rbmi-123","dir":"Changelog","previous_headings":"","what":"rbmi 1.2.3","title":"rbmi 1.2.3","text":"CRAN release: 2022-11-14 Minor internal tweaks ensure compatibility packages rbmi depends ","code":""},{"path":"/news/index.html","id":"rbmi-121","dir":"Changelog","previous_headings":"","what":"rbmi 1.2.1","title":"rbmi 1.2.1","text":"CRAN release: 2022-10-25 Removed native pipes |> testing code package backwards compatible older servers Replaced glmmTMB dependency mmrm package. resulted package stable (less model fitting convergence issues) well speeding run times 3-fold.","code":""},{"path":"/news/index.html","id":"rbmi-114","dir":"Changelog","previous_headings":"","what":"rbmi 1.1.4","title":"rbmi 1.1.4","text":"CRAN release: 2022-05-18 Updated urls references vignettes Fixed bug visit factor levels re-constructed incorrectly delta_template() Fixed bug wrong visit displayed error message specific visit doesn’t data draws() Fixed bug wrong input parameter displayed error message simulate_data()","code":""},{"path":"/news/index.html","id":"rbmi-111--113","dir":"Changelog","previous_headings":"","what":"rbmi 1.1.1 & 1.1.3","title":"rbmi 1.1.1 & 1.1.3","text":"CRAN release: 2022-03-08 change functionality 1.1.0 Various minor tweaks address CRAN checks messages","code":""},{"path":"/news/index.html","id":"rbmi-110","dir":"Changelog","previous_headings":"","what":"rbmi 1.1.0","title":"rbmi 1.1.0","text":"CRAN release: 2022-03-02 Initial public release","code":""}] diff --git a/v1.3.1/sitemap.xml b/v1.3.1/sitemap.xml new file mode 100644 index 000000000..4275d79e7 --- /dev/null +++ b/v1.3.1/sitemap.xml @@ -0,0 +1,155 @@ + +/404.html +/CONTRIBUTING.html +/LICENSE.html +/articles/CondMean_Inference.html +/articles/FAQ.html +/articles/advanced.html +/articles/index.html 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