brendan j kelly - measures in clinical epidemiology 20181113.txt

Measures of Disease in Clinical Epidemiology
Brendan J. Kelly, MD, MSCE
Infectious Diseases & Epidemiology
Perelman School of Medicine
University of Pennsylvania

Learning Objectives
Be able to:
Use population data in the description of health and disease.
Describe types of data and data distributions.
Calculate prevalence, incidence (warning: a few different types), relative risk, and odds ratios from study data.
Explain the meaning of prevalence, incidence, relative risk, and odds ratios.

Learning Objectives
Why?
Understand distributions and determinants of diseases.
inform differential diagnoses
counsel patients
design public health interventions
direct new diagnostics and therapies
How?
Lots of definitions.
A bit of arithmetic.

Suess 1965.

Definitions: A Reference for Later
Point Prevalence: # with disease / # population, at a single moment
Period Prevalence: # with disease / # population, over time interval
Cumulative Incidence: # new cases / # at risk @ start (long) time interval
“Incidence Rate”: # new cases / # at risk @ start (short) time interval
Incidence Density or “Rate”: # new cases / person-time at risk *more precise*
Relative Risk: (# cases exposed / # exposed) / (# cases unexposed / # unexposed)
Absolute Risk: risk of developing disease over time period (cumulative incidence)
AR Reduction: (# cases exposed / # exposed) - (# cases unexposed / # unexposed)
Number Needed to Treat: # treated for 1 to benefit = 1 / ARR
Odds Ratio: (# exp cases / # unexp cases) / (# exp controls / # unexp controls)

Case from 1981: HIV and PCP
36-year-old man presents with a 4-month history of fever, dyspnea, and cough...
Differential diagnosis must be grounded in understanding:
distributions of disease (prevalence / incidence)
determinants of disease (associations / risk factors)
(in infectious diseases, the differential is always evolving)

Case from 1981: HIV and PCP
36-year-old man presents with a 4-month history of fever, dyspnea, and cough...
Differential diagnosis must be grounded in understanding:
distributions of disease (prevalence / incidence)
determinants of disease (associations / risk factors)
(in infectious diseases, the differential is always evolving)

https://www.hiv.gov/hiv-basics/overview/history/hiv-and-aids-timeline

MMWR June 5, 1981
“All the above observations suggest the possibility of a cellular-immune dysfunction related to a common exposure that predisposes individuals to opportunistic infections such as pneumocystosis and candidiasis. Although the role of CMV infection in the pathogenesis of pneumocystosis remains unknown, the possibility of P. carinii infection must be carefully considered in a differential diagnosis for previously healthy homosexual males with dyspnea and pneumonia.”

Measures of Disease Occurrence

Prevalence
How common is Pneumocystis pneumonia?
Prevalence: 
# with the disease / # in specified population
“point prevalence” - at a specific point in time
“period prevalence” - during a given period (e.g., 12-month prevalence)
a proportion: unitless, ranges from 0-1
numerator includes all people who have the disease, both new and ongoing cases, so represents a cross-sectional “snapshot” of the population

Prevalence of Pneumocystis pneumonia
In 1967, CDC became the sole supplier of pentamidine in the United States and began collecting data on cases of PCP.
Period prevalence published in 1974: 579 cases (194 confirmed) over 3 years.
What’s the denominator?
What’s the prevalence?
Walzer PD et al Annals Int Med 1974

Prevalence != Risk
Prevalence: numerator includes all people who have the disease, both new and ongoing cases, so represents a cross-sectional “snapshot” of the population. 
Prevalence does NOT estimate the risk of developing the disease because prevalence does not fully account for time (are the measured cases old cases or new cases?).

Prevalence: Question #1
How can an infection have high prevalence if it occurs infrequently?
(1) the infection is rapidly fatal
(2) the infection rapidly resolves
(3) a few children get the infection every year, but the infection persists for the rest of their lives
(4) the infection results in lifelong protective immunity


Incidence
Among MSM, Pneumocystis pneumonia is occurring more frequently...
Incidence: occurrence of new cases over a given period of time
cumulative incidence = # new cases / # population at risk @ start time interval
incidence density = # new cases / person-time at risk (more precise)

Notes on Cumulative Incidence
Cumulative incidence:
must specify population consisting of at-risk individuals
must specify a time period of observation
numerator = all new cases during a specified time period 
denominator = all individuals at risk in the specified population at the start of the specified time period (does NOT account for deaths due to other causes)
ranges from 0 to 1 (a.k.a., “incidence proportion”)
like prevalence, is a proportion and therefore has no units (but only makes sense if you specify the time period of observation, e.g., % per year)

Notes on Incidence Density
Incidence density:
in a specified population consisting of at risk individuals over a specified period of observation, more precisely quantifies the person-time at risk
numerator = all new cases during a specified time period 
denominator = the sum, over all individuals in the population, of time at risk until the event of interest, death, loss to follow-up, the end of the study, or when they are no longer at risk for whatever reason
not a proportion; range depends on the units of person-time (0 to infinity)
accounts for death from other causes!

Notes on Population at Risk
In a population, individuals are at risk of disease if they: 
(1) do not have the disease at baseline
(2) are capable of developing the disease(e.g., have the organ of interest; have not been successfully immunized against the disease;haven’t developed lifelong immunity)
The difference between cumulative incidence and incidence density is that the latter attempts a more precise quantification of population at risk -- it’s harder to evaluate, but more informative if you can.

Caution with “Incidence Rate”
“Incidence rate” is used to mean two different things:
# new cases / # population at risk @ start (short) time interval (e.g., “annual incidence rate” to mean cumulative incidence over one year)
# new cases / person-time at risk (i.e., incidence density, the precise rate)

Incidence: Which Denominator?
To understand the difference between cumulative incidence and incidence density, imagine a study of persons with HIV at risk for PCP:
10 subjects enrolled at the start of a two-year observation period
5 cases of PCP (red on plot); each receives 3 weeks of antibiotic treatment
2 subjects started on PCP prophylaxis during follow-up (blue on plot)


Incidence: Which Denominator?
To understand the difference between cumulative incidence and incidence density, imagine a study of persons with HIV at risk for PCP:
10 subjects enrolled at the start of a two year period
5 cases of PCP (red on plot); each receives 3 weeks of antibiotic treatment
3 subjects started on PCP prophylaxis during follow-up (yellow on plot)
What’s the annual cumulative incidence of PCP?
If you don’t count time on prophylaxis or treatment antibiotics as “time at risk”, how does the incidence density compare to the annual cumulative incidence?
What if the end of the black line is death / loss to follow-up?

Incidence: Question #2
Your patient with HIV is considering starting prophylactic antibiotics for PCP. You have PCP prevalence, cumulative incidence, and incidence density data available. Which data provide the most precise information on the patient’s risk of PCP off of prophylaxis?
(1) prevalence
(2) cumulative incidence
(3) incidence density

Morris A et al. EID 2004.

Can you tell prevalence from incidence?
Prevalence
Incidence
Death or Recovery
Former Cases
Birth - Death | Migration

Prevalence vs Incidence: Examples
Pancreatic cancer versus leukemia:
new cases per year: pancreatic 24,120; leukemia 23,370
deaths per year: pancreatic 19,850; leukemia 10,240
which is more prevalent?
HIV in Rakai, Uganda 1994-2003:
intensive “ABC” intervention (Abstinence, Be faithful, Condoms)
prevalence declined, but incidence remained constant at 1.5% per year
what happened?
Wawer M et al CROI 2005. Roehr B BMJ 2005.

Morris A et al. EID 2004.
What’s the most prevalent OI???

Prevalence vs Incidence: When Used?
Prevalence:
public health planning
diagnostic test evaluation
Cumulative Incidence: 
prognosis
evaluation of therapies
Incidence Density:
rate of appearance of new cases
changes can reflect the effect of risk factors

Data Types & Data Descriptions

Case: HIV and PCP
36-year-old man presents with a 4-month history of fever, dyspnea, and cough...
What do you want to know and why?
vital signs and physical exam
laboratory test values
radiology

What Data Types?
Vital signs and physical exam:
Temperature (degrees) - continuous
Heart / respiratory rate (beats or breaths / min) - continuous
Oxygen saturation (%) - continuous
Laboratory values:
WBC / CD4 (cells / uL) - continuous
HIV viral load (copies / mL) - continuous
Radiology:
Ground glass - dichotomous

Types of Data - Exposures
Dichotomous: history of diabetes, history of breast cancer, etc
Continuous: age, height, weight, blood pressure, etc
Nominal: race, ethnicity, state of residence 
Ordinal: age category, weight category

Types of Data - Outcomes
Dichotomous: survival, pneumonia, MI
Continuous: probability of treatment result 
Ordinal: patient satisfaction* NOTE: diagnoses and clinical decisions are dichotomous *

Describing Continuous Data - Normal
Normally distributed data can be well characterized by its mean and standard deviation:
Mean: 				m	Standard Deviation:(N = total number in the population; μ = mean)

Describing Continuous Data - Normal
To calculate standard deviation (SD):(1) for each value, subtract the mean of the group and square the result; (2) find the mean of these squared (this is the variance); (3) SD is square root of variance  

Describing Continuous Data - Normal
What makes standard deviation greater?
Mean: 				m	Standard Deviation:(N = total number in the population; μ = mean)


Standard Deviation: Question #3
What makes standard deviation increase?
(1) More subjects?
(2) Higher mean value?
(3) Higher maximum value?
(4) Greater difference between extreme and mean values? 

Describing Continuous Data - NOT Normal
“Non-parametric” data have a mean and standard deviation, but these do NOT characterize the data well.
For uniform or skewed data, we prefer to use median and interquartile range (IQR) to describe the distribution of a continuous variable. (Note: for normal data, mean and median have the same value).

Describing Continuous Data - NOT Normal
Mean, Median, Mode:

Median and mode depend on ranking the values: median is the “middle value” when data are ordered; mode is most frequently occurring value.
(n = # of data values)

Describing Continuous Data - NOT Normal
Which is least affected by outliers? Mean, median, or mode?
(n = # of data values)

Study Types & Inference from Data

Case from 1981: HIV and PCP
36-year-old man presents with a 4-month history of fever, dyspnea, and cough. On admission he is found to have fever to 101.2F, tachycardia, tachypnea, and hypoxemia, which worsens with ambulation. He is also noted to have oral thrush and distant breath sounds on exam. A lung biopsy confirms Pneumocystis pneumonia.
Differential diagnosis must be grounded in understanding:
distributions of disease (prevalence / incidence)
determinants of disease (associations / risk factors)

Masur et al Ann Int Med 1989

Basics of Study Types
We want to understand the relationship between risk factors (exposures) and disease (outcomes). For example, between CD4 count and PCP in HIV.
To calculate incidence need to know how many are in a population:
randomized trials: pick the population, randomize, control the treatment, and measure the outcome
cohort studies: pick the population, divide into preselected exposure (treatment or risk factor) groups, and measure the outcome
But do NOT know this generally in case control studies: pick the cases and control groups, then measure rates of exposure (do NOT know how many in population).

“2x2” Table
Dichotomous exposures and outcomes.
Examine relationships between exposures and outcomes.
Caution!!!
you need to know whether study is trial/cohort vs case-control
you can always calculate a relative risk (RR) from 2x2 table, but only appropriate for trial/cohort study
you can always calculate an odds ratio (OR) from 2x2 table, but only appropriate for case-control study (can do better with RR if trial/cohort)

“2x2” Table: Calculation for Cohort/Trial
Relative Risk (RR)= [A/(A+B) / C/(C+D)]
Absolute Risk Reduction (ARR) = [A/(A+B) – C/(C+D)]
Number Needed to Treat (NNT)= 1/ARR
Outcome Yes
Outcome No
Totals
Risk of Outcome
Exposure Yes
A
B
(A+B)
A/(A+B)
Exposure No
C
D
(C+D)
C/C+D)
Totals
(A+C)
(B+D)
A+B+C+D


Relative Risk (RR)
Compares risk between two groups of people:
if 2 in 10 are cured in the control group and 3 in 10 in the treatment group, the RR is (2/10)/(3/10) = 0.66 (i.e. 0.33 less likely to have the disease after treatment) 
Can also be calculated as the inverse:
if 3 in 10 are cured in the treatment group and 2 in 10 in the control group, the RR is (3/10)/(2/10) = 1.5 (i.e. 0.5 times more likely to be cured if treated)

Relative Risk (RR)

Absolute Risk (AR) & Reduction (ARR)
Absolute risk (AR): risk of developing a given disease over a period of time
this is the incidence!
if you have a 1 in 10 chance of developing skin cancer in your lifetime, you are said to have a 10% absolute risk
Absolute risk reduction (ARR): difference in risk between the treatment/ exposure group and the control group
if 2 in 10 are cured in the control group and 3 in 10 in the treatment group, the ARR is 3/10 – 2/10 = 10%

Number Needed to Treat (NNT)
Number needed to treat (NNT): Number of patients who need to be treated for one person to benefit from the treatment  (= 1/ARR)
using ARR numbers above, NNT = 1/ARR = 1/0.1 = 10
in this example, you need to treat 10 people to prevent one bad outcome


Number Needed to Treat (NNT)
Number needed to treat (NNT): Number of patients who need to be treated for one person to benefit from the treatment  (= 1/ARR)
using ARR numbers above, NNT = 1/ARR = 1/0.1 = 10
in this example, you need to treat 10 people to prevent one bad outcome
Return to example of CD4 count and PCP… imagine a pill that can maintain CD4 count above 250… what’s the NNT to prevent one case of PCP?
RR = (26 / 50) / (2 / 50) = 13
ARR = (26 / 50) - (2 / 50) = 0.48
NNT = 1 / 0.48 = 2.08


“2x2” Table: Calculation for Case-Control
Odds Ratio (OR)= (A/C)/(B/D) = AD / BC
Absolute Risk Reduction (ARR) = not appropriate to calculate
Number Needed to Treat (NNT) = not appropriate to calculate
Outcome Yes
Outcome No
Totals
Exposure Yes
A
B
NA
Exposure No
C
D
NA
Odds
A/C
B/D

Relative Risk vs Odds Ratio

Utility of Odds Ratio (OR) & Case-Control
If the disease incidence is low, then:
A + B ~ B & C + D ~ D
RR = (A / A + B) / (C / C + D) ~ (A / B) / (C / D) = AD / BC = OR
Outcome Yes
Outcome No
Totals
Exposure Yes
A
B
NA
Exposure No
C
D
NA
Odds
A/C
B/D

Utility of Odds Ratio (OR) & Case-Control
OR will be close to RR if outcome occurs infrequently (<15%).
If outcome is more common, OR will differ increasingly from RR:

Summary

Wickramasekaran et al Mycoses 2017

Suess 1965.

Definitions: A Reference for Later
Point Prevalence: # with disease / # population, at a single moment
Period Prevalence: # with disease / # population, over time interval
Cumulative Incidence: # new cases / # at risk @ start (long) time interval
“Incidence Rate”: # new cases / # at risk @ start (short) time interval
Incidence Density or “Rate”: # new cases / person-time at risk *more precise*
Relative Risk: (# cases exposed / # exposed) / (# cases unexposed / # unexposed)
Absolute Risk: risk of developing disease over time period (cumulative incidence)
AR Reduction: (# cases exposed / # exposed) - (# cases unexposed / # unexposed)
Number Needed to Treat: # treated for 1 to benefit = 1 / ARR
Odds Ratio: (# exp cases / # unexp cases) / (# exp controls / # unexp controls)

Summary
Prevalence is determined by incidence and survival time.
Distribution of data determines how we describe them:
mean and SD vs median and IQR
Relative risk (RR) and odds ratio (OR) are measures of a difference between the incidence of the outcome for two or more exposures or treatments.
RR and OR approximate each other when outcome is rare.
NNT can be a clinically useful number.