1. Case-Control Studies September 2014 Alexander M. Walker MD, DrPH With Sonia Hernández-Díaz MD, DrPH

2. Case-Control Studies  Cohort studies with sampling  Instead of the full population denominator, we take a sample, called the “controls” At random from the cohort members with no event At random from the cohort members At random times from random members Or optionally matched to cases  Personal characteristics  Time of follow-up  Captures covariates that would be too expensive to ascertain for the full cohort Time-varying Resource intensive data collection

3. Prevalence and Person-Time Person-Time The prevalence of a characteristic in person-time is the fraction of person- time in which the characteristic is present.. Person-time prevalence is a weighted average of point prevalence over all instances of time, with the prevalent number of persons at risk as the weight.

4. Sampling Person-Time Person-Time If we only sample days taken at random during the period of accrual of person-time, we can still recover the person-time prevalence Person-time prevalence is a weighted average of point prevalence over all instances of time, with the prevalent number of persons at risk as the first part of the weight, and the inverse of the sampling fraction of days as the second part of the weight.

5. Sampling Person-Time Person-Time If for each day selected at random, we take a person at random, we sampling person-days. If the person selected is under observation on the selected date, that person-day is a control.

6. Sampling Person-Time YesPT Yesast 1 Nocst 0 Outcome Exposure Person-Time If for each day selected at random, we take a person at random, we sampling person-days. If the person selected is under observation on the selected date, that person-day is a control. The sampling rate of person-days (controls sampled divided by the number of person-days eligible) is the rate of control generation. It is a rate in the same sense that disease incidence is a rate, except that the control-sampling rate is by construction unrelated to exposure. Call this sampling rate s.

7. The Odds Ratio with Cases and Sampled Person-Time CasesControls Yes λ1t1λ1t1 st 1 No λ0t0λ0t0 st 0 Outcome Exposure Person-Time Consider the table of expected values, below. The odds ratio of this case- control table of expected values is From which it follows that an estimate of the OR is an estimate of ρ. Note that there is no “rare disease” assumption.

8. A Case-Control Study with Sampled Person-Time 8 The question at hand was whether inhaled corticosteroids had the effect of weakening bone to the point of making women more susceptible to fracture. Nonvertebral fracture was chosen because vertebral fracture is so often asymptomatic.

9. Random Sampling of Person-Time 9

10. Cases, Controls, OR 10

11. Risk Sets Persons over Time Risk Set Each case is compared to all the people who were at risk to become cases at the time the case occurred. This collection of persons at risk is called the “Risk Set.”

12. Risk Set Sampling in Case-Control Studies Proportional Hazards analysis Each case is compared to a sample of the people who were at risk to become cases at the time the case occurred. This sampled persons called matched controls. They have been matched on time and possibly other factors. Matched case-control analysis

13. Graham et al. 2005 For every case, we randomly selected four controls from individuals under observation in the study cohort on the date of the case event (index date), and matched them for age (year of birth), sex, and health plan region (north or south). A given cohort member selected as a control for a case on one date could become a control for another case occurring on a later index date, as long as he or she remained in the study cohort and was therefore also at risk of becoming a case. Graham DJ, Campen D, Hui R, Spence M, Cheetham C, Levy G, Shoor S, Ray WA. Risk of acute myocardial infarction and sudden cardiac death in patients treated with cyclo-oxygenase 2 selective and non-selective non- steroidal anti-inflammatory drugs: nested case-control study. Lancet 2005;365475-81Lancet 2005;365475-81 13

14. Graham et al. 2005 For every case, we randomly selected four controls from individuals under observation in the study cohort on the date of the case event (index date), and matched them for age (year of birth), sex, and health plan region (north or south). A given cohort member selected as a control for a case on one date could become a control for another case occurring on a later index date, as long as he or she remained in the study cohort and was therefore also at risk of becoming a case. Graham DJ, Campen D, Hui R, Spence M, Cheetham C, Levy G, Shoor S, Ray WA. Risk of acute myocardial infarction and sudden cardiac death in patients treated with cyclo-oxygenase 2 selective and non-selective non- steroidal anti-inflammatory drugs: nested case-control study. Lancet 2005;365475-81Lancet 2005;365475-81 14 Risk set sampling

15. Graham et al. 2005 For every case, we randomly selected four controls from individuals under observation in the study cohort on the date of the case event (index date), and matched them for age (year of birth), sex, and health plan region (north or south). A given cohort member selected as a control for a case on one date could become a control for another case occurring on a later index date, as long as he or she remained in the study cohort and was therefore also at risk of becoming a case. Graham DJ, Campen D, Hui R, Spence M, Cheetham C, Levy G, Shoor S, Ray WA. Risk of acute myocardial infarction and sudden cardiac death in patients treated with cyclo-oxygenase 2 selective and non-selective non- steroidal anti-inflammatory drugs: nested case-control study. Lancet 2005;365475-81Lancet 2005;365475-81 15 Matching in risk-set sampling is equivalent to sampling from strata, where the strata definitions are the levels of the matching factors.

16. Graham et al. 2005 For every case, we randomly selected four controls from individuals under observation in the study cohort on the date of the case event (index date), and matched them for age (year of birth), sex, and health plan region (north or south). A given cohort member selected as a control for a case on one date could become a control for another case occurring on a later index date, as long as he or she remained in the study cohort and was therefore also at risk of becoming a case. Graham DJ, Campen D, Hui R, Spence M, Cheetham C, Levy G, Shoor S, Ray WA. Risk of acute myocardial infarction and sudden cardiac death in patients treated with cyclo-oxygenase 2 selective and non-selective non- steroidal anti-inflammatory drugs: nested case-control study. Lancet 2005;365475-81Lancet 2005;365475-81 16

17. Take Home Lessons: Cohort Sampling  All case-control studies can be seen as being samples drawn from specifiable cohorts.  Different modes of cohort analysis give rise to corresponding case-control designs. Closed cohort, fixed folow-up  Sample noncases Variable follow-up time, time-varying exposure, stable baseline incidence  Sample person-time Variable baseline incidence  Sample risk sets  Case-control analysis are directly tied to the corresponding cohort analysis, with further allowance for sampling  “Case-control” studies that do not use cohort sampling are valid only to the extent that the procedures used approximate cohort sampling. 17

18. Case-Control Advantages  Relatively inexpensive  Relatively quick  Particularly useful for rare outcomes  Closely logical connection to cohort designs However, you have to bear in mind that  Focus on a single outcome can be very misleading when overall cost and benefit is the real questions  Poorly conceptualized studies can taint the field  Negative attitudes that are a holdover from old hierarchies of evidence that do not reflect modern understanding

19. Thank You!