Initialize intercept as logit of outcome rate for logistic regression models

[egillax]

Hi @msuchard ,

I believe currently the intercept is initialized as zero (at least for logistic regression, only model I checked). Given we are often dealing with rare outcomes I think it would be better to use the logit of the outcome rate ( log(p / (1 - p)) ). In this case the model converges faster (as measured in fever iterations, see below) and seems to give the same results. I do think this could end up giving ~ 20-30% speed up for outcome rates of 1-3% which are common in our data. The example below for Eunomia gives a speedup of over 2x with outcome rate of 2%, but it's rather small data (n=1800, p=372). There's also a pure Cyclops reprex at the bottom giving about 30% fewer iterations but I had to change the simulateCyclopsData to give 1-3% outcome rates.

Of course I could supply startingCoefficients myself from the PLP to add this. But if there are no downsides maybe this should be the default in Cyclops ? What do you think ?

reprex:

library(PatientLevelPrediction)
    library(Cyclops)
    
    connectionDetails <- Eunomia::getEunomiaConnectionDetails()
#> attempting to download GiBleed
#> attempting to extract and load: /tmp/RtmpplDETg/GiBleed_5.3.zip to: /tmp/RtmpplDETg/GiBleed_5.3.sqlite
    Eunomia::createCohorts(connectionDetails)
#> Cohorts created in table main.cohort
#>   cohortId       name
#> 1        1  Celecoxib
#> 2        2 Diclofenac
#> 3        3    GiBleed
#> 4        4     NSAIDs
#>                                                                                        description
#> 1    A simplified cohort definition for new users of celecoxib, designed specifically for Eunomia.
#> 2    A simplified cohort definition for new users ofdiclofenac, designed specifically for Eunomia.
#> 3 A simplified cohort definition for gastrointestinal bleeding, designed specifically for Eunomia.
#> 4       A simplified cohort definition for new users of NSAIDs, designed specifically for Eunomia.
#>   count
#> 1  1844
#> 2   850
#> 3   479
#> 4  2694
    outcomeId <- 3 # GIbleed
    seed <- 42
    
    databaseDetails <- createDatabaseDetails(
        connectionDetails = connectionDetails,
        cdmDatabaseSchema = "main",
        cdmDatabaseName = "main",
        cohortDatabaseSchema = "main",
        cohortTable = "cohort",
        outcomeDatabaseSchema = "main",
        outcomeTable =  "cohort",
        targetId = 1,
        outcomeIds = outcomeId,
        cdmVersion = 5)
#> No cdm database id entered so using cdmDatabaseSchema - if cdmDatabaseSchema is the same for multiple different databases, please use cdmDatabaseId to specify a unique identifier for the database and version
    
    covariateSettings <- FeatureExtraction::createDefaultCovariateSettings()
    
    plpData <- getPlpData(databaseDetails = databaseDetails,
                          covariateSettings = covariateSettings,
                          restrictPlpDataSettings = createRestrictPlpDataSettings())
#> Connecting using SQLite driver
#> 
#> Constructing the at risk cohort
#>   |                                                                              |                                                                      |   0%  |                                                                              |=======================                                               |  33%  |                                                                              |===============================================                       |  67%  |                                                                              |======================================================================| 100%
#> Executing SQL took 0.026 secs
#> Fetching cohorts from server
#> Loading cohorts took 0.031 secs
#> Constructing features on server
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#> Executing SQL took 3.26 secs
#> Fetching data from server
#> Fetching data took 0.312 secs
#> Fetching outcomes from server
#> Loading outcomes took 0.0241 secs
    
    population <- createStudyPopulation(
        plpData,
        outcomeId = outcomeId,
        populationSettings = createStudyPopulationSettings(
            minTimeAtRisk = 1,
            riskWindowEnd = 15) # short TAR end for lower outcome rate
    )
#> outcomeId: 3
#> binary: TRUE
#> includeAllOutcomes: TRUE
#> firstExposureOnly: FALSE
#> washoutPeriod: 0
#> removeSubjectsWithPriorOutcome: TRUE
#> priorOutcomeLookback: 99999
#> requireTimeAtRisk: TRUE
#> minTimeAtRisk: 1
#> restrictTarToCohortEnd: FALSE
#> riskWindowStart: 1
#> startAnchor: cohort start
#> riskWindowEnd: 15
#> endAnchor: cohort start
#> restrictTarToCohortEnd: FALSE
#> Removing subjects with prior outcomes (if any)
#> Removing non outcome subjects with insufficient time at risk (if any)
#> Outcome is 0 or 1
#> Population created with: 1800 observations, 1800 unique subjects and 38 outcomes
#> Population created in 0.044 secs
    
    population$y <- population$outcomeCount
    plpData$covariateData$outcomes <- population
    cyclopsData <- convertToCyclopsData(plpData$covariateData$outcomes,
                                        plpData$covariateData$covariates,
                                        modelType = "lr",
                                        addIntercept = TRUE)
    
    prior <- createPrior("laplace", exclude = c(0), useCrossValidation = FALSE)
    
    control <- createControl(noiseLevel = "quiet",
                             cvRepetitions = 1,
                             tolerance = 1e-9,
                             seed = seed)
    
    out <- capture.output(fit <- fitCyclopsModel(cyclopsData, prior, control))
    
    
    
    # Now fit the same model with starting coefficients
    cyclopsData <- convertToCyclopsData(plpData$covariateData$outcomes,
                                        plpData$covariateData$covariates,
                                        modelType = "lr",
                                        addIntercept = TRUE)
    prior <- createPrior("laplace", exclude = c(0), useCrossValidation = FALSE)
    control <- createControl(noiseLevel = "quiet",
                             cvRepetitions = 1,
                             seed = seed,
                             tolerance = 1e-9)
    ncovars <- length(summary(cyclopsData)$covariateId)
    startingCoefficients <- rep(0, ncovars)
    outcomeRate <- mean(population$y)
    startingCoefficients[1] <- log(outcomeRate / (1 - outcomeRate))
    out2 <- capture.output(fit2 <- fitCyclopsModel(cyclopsData,
                                                   prior,
                                                   control,
                                                   startingCoefficients = startingCoefficients))
    message("Original Cyclops fit complete in ", round(fit$timeFit, 4), " seconds. And ",
            fit$iterations, " iterations. With logLikelihood: ", fit$log_likelihood)
#> Original Cyclops fit complete in 0.018 seconds. And 125 iterations. With logLikelihood: -166.622177178957
    
    message("Modified Cyclops fit complete in ", round(fit2$timeFit, 4), " seconds. And ",
            fit2$iterations, " iterations. With logLikelihood: ", fit2$log_likelihood)
#> Modified Cyclops fit complete in 0.0077 seconds. And 67 iterations. With logLikelihood: -166.622177181422

^{Created on 2025-01-29 with reprex v2.1.1}

Pure Cyclops reprex:

library(Cyclops)
    
    # modify https://github.com/OHDSI/Cyclops/blob/develop/R/Simulation.R#L80C1-L80C63
    # strataBackgroundProb <- runif(nstrata,min=0.01,max=0.03)
    
    seed <- 666
    set.seed(seed)
    
    nrows <- 10000
    ncovars <- 500
    
    data <- simulateCyclopsData(nstrata = 1,
                                nrows = nrows,
                                ncovars = ncovars,
                                model = "logistic")
#> Sparseness = 98.99538 %
    
    cyclopsData <- convertToCyclopsData(data$outcomes,
                                        data$covariates,
                                        modelType = "lr",
                                        addIntercept = TRUE)
#> Sorting covariates by covariateId and rowId
    
    prior <- createPrior("laplace", exclude = c(0), useCrossValidation = FALSE)
    
    control <- createControl(noiseLevel = "quiet",
                             cvType = "auto",
                             cvRepetitions = 1,
                             seed = seed)
    out <- capture.output(fit <- fitCyclopsModel(cyclopsData, prior, control))
    
    
    # Now fit the same model with starting coefficients
    cyclopsData <- convertToCyclopsData(data$outcomes,
                                        data$covariates,
                                        modelType = "lr",
                                        addIntercept = TRUE)
#> Sorting covariates by covariateId and rowId
    prior <- createPrior("laplace", exclude = c(0), useCrossValidation = FALSE)
    control <- createControl(noiseLevel = "quiet",
                             cvRepetitions = 1,
                             seed = seed)
    startingCoefficients <- rep(0, ncovars + 1)
    outcomeRate <- mean(data$outcomes$y)
    startingCoefficients[1] <- log(outcomeRate / (1 - outcomeRate))
    out2 <- capture.output(fit2 <- fitCyclopsModel(cyclopsData,
                                                   prior,
                                                   control,
                                                   startingCoefficients = startingCoefficients))
    
    message("Original Cyclops fit complete in ", round(fit$timeFit, 4), " seconds. And ",
            fit$iterations, " iterations. With logLikelihood: ", fit$log_likelihood)
#> Original Cyclops fit complete in 0.0686 seconds. And 17 iterations. With logLikelihood: -756.202262114616
    
    message("Modified Cyclops fit complete in ", round(fit2$timeFit, 4), " seconds. And ",
            fit2$iterations, " iterations. With logLikelihood: ", fit2$log_likelihood)
#> Modified Cyclops fit complete in 0.0472 seconds. And 12 iterations. With logLikelihood: -756.202248337887

^{Created on 2025-01-29 with reprex v2.1.1}