1. Lecture 8: Selection Bias, Matching, & Control Selection Matthew Fox Advanced Epidemiology

2. What is selection bias?

3. Which studies can have selection bias: cohort or case control?

4. Selection bias or confounding? • Comparison of mortality among office workers and longshoremen from MI • Comparison is biased because those who self-select into longshoremen are fitter which leads to less MI • What is the bias?

5. In a case control study, can we match cases to controls based on exposure?

6. If we match, do we need to adjust for the matched factor?

7. What is overmatching?

8. Misclassification Summary I #1 Non-differential and independent misclassification of dichotomous exposure or disease (usually) creates an expectation that estimates of effect are biased towards the null. #2 Non-differential and independent misclassification of a covariate creates an expectation that the relative risk due to confounding is biased towards the null, yielding residual confounding.

9. Misclassification Summary II #3 Errors due to misclassification can be corrected algebraically #4 Differential misclassification yields an unpredictable bias of the estimates of effect (still correctable). #5 There are important exceptions to the mantra that “non-differential misclassification biases towards the null.”

10. This Session • Selection bias • Definition & control • Matching • Cohort vs. Case-control studies • When to adjust, when not to adjust • Control selection • Adjustment • Is it possible?

11. Selection bias — definition • Distortions of the estimate of effect arising from procedures to select subjects and from factors that influence participation • Common element is that the exposure-disease relation is different among participants than among those theoretically eligible • Observed estimate of effect reflects a mixture of forces affecting participation and forces affecting disease occurrence

12. Separate from Confounding • Cohort studies don’t have selection bias at entry even if subjects self select • Selection into cohort can create confounding, but this can be undone by adjustment • Or becomes an issue of generalizablity • Cohort studies/RCTs can have selection bias at end through differential LTFU • Some can be undone if we know enough about the selection mechanism

13. Selection bias — Fallacy • Formerly frequently viewed as disease-dependent selection forces • Exposure-dependent selection forces were thought to be confounders or part of the population definition. • Sometimes selection factors can be controlled as if they were confounders • For example, matched factors in case-control studies and two-stage studies. • However, not all selection factors related to exposure can be so treated

14. Selection biasAdjust for selection proportions

15. Selection bias — Simple method

16. Selection bias

17. OR = [50/4000] / [40/8000] = 2.5 Selection bias

18. Selection bias

19. Selection bias

20. https://sites.google.com/site/biasanalysis/

21. Structure of Selection Bias

22. Selection forces don’t create bias if they are not related to both exposure and disease

23. Selection bias — Simple method

24. Selection bias

25. OR = [50/4000] / [100/8000] = 1 Selection bias

26. Selection bias

27. Selection bias

28. OR = [50/4000] / [50/4000] = 1 Selection bias

29. Selection bias

30. Selection bias

31. Selection bias

32. OR = [50/10000] / [40/8000] = 1 Selection bias

33. Selection bias

34. Selection Bias Occurs When Selection is Related to Both the Exposure and the Outcome Sounds like confounding, but this time E and D affect Selection

35. Remember back to common causes and common effects (Hernán 2004)

36. Selection Bias in a Case Control Study: • Case controls study of the relationship between estrogens and myocardial infarction • Cases are those hospitalized for MI • Controls are those hospitalized for hip fracture • Could this cause selection bias?

37. Selection Bias in a Case Control Study: • E= estrogens D = myocardial infarction • F= hip fracture C = selection into study Selection bias occurs because we condition on a common effect of both E and D

38. Selection Bias in a Cohort Study: • Cohort study of relationship between HAART and progression to AIDS • LTFU occurs more among those with low CD4 • LTFU occurs more among those with AIDS • But now selection out occurs before AIDS • Could this cause selection bias?

39. Selection Bias in a Cohort Study: Differential LTFU • E = ART, D = AIDS, L = vector of symptoms • U = True immunosuppression (unmeasured) • C= Drop out (LTFU) Selection bias occurs because we condition on a common effect of both E and a common cause C and D

40. Selection Bias in a Cohort Study: Differential LTFU • E = ART, D = AIDS, L = vector of symptoms • U = True immunosuppression (unmeasured) • C= Drop out

41. Selection Bias vs. Confounding • Bias is a systematic difference between the truth and the observed • Pr[Ya=1=1] - Pr[Ya=0=1] ≠ Pr[Y=1|a=1] - Pr[Y=1|a=0] • Separate from random error which is not structural • Using DAGs we can see the common structures • Confounding = common causes (directly or through other mechanisms) • Selection bias = conditioning on common effects

42. To see the difference • Comparison of mortality among office workers and longshoremen from MI • Comparison is biased because those who self-select into longshoremen are fitter which leads to less MI • What is the DAG? Occupation MI Fitness

43. Adjustment for Selection Bias

44. Adjustment for loss to follow up through weighting • Because selection bias means we are only looking at those included in the study we can’t adjust through stratification • We don’t have the data on those not included • Can use weighting, because this does not require us to have data on those missing • Inverse probability of censoring weighting • Assumes we have enough data to predict the drop out

45. Now we ask, what if the censored were not censored?

46. Now we ask, what if the censored were not censored?

47. Now we ask, what if the censored were not censored?

48. Now we ask, what if the censored were not censored?

49. Further stratify IPC weights for predictors of censoring • As shown assumes those lost are same as those retained • Not likely to be true • Calculate weights within levels of predictors of censoring • Valid if we can produce conditional exchangeability between those lost and those not lost • Weights can be multiplied by IPTW weights to simultaneously adjust for confounding

50. Matching