1. Designing Clinical Research 2009 Confounding and Causal Inference Warren Browner

2. Confounding Guaranteed to be confusing. Guaranteed to be confusing. If you think you understand it, you probably don’t. If you think you understand it, you probably don’t. I often revert to an analogy involving smoking, carrying matches, and lung cancer. I often revert to an analogy involving smoking, carrying matches, and lung cancer.

3. Confounding, Round One A problem in understanding what the association between two variables means. A problem in understanding what the association between two variables means. No association, no confounding to worry about No association, no confounding to worry about Example: A study which finds that people who carry matches are more likely to get lung cancer.

4. Confounding, Round Two Confounding only matters in studies that attempt to show that an association between a predictor and an outcome is causal. Confounding only matters in studies that attempt to show that an association between a predictor and an outcome is causal. Is the association between carrying matches and lung cancer causal? Is the association between carrying matches and lung cancer causal? Or is the association confounded by something else? Or is the association confounded by something else?

5. Confounding, Round Three Confounding is irrelevant in… Confounding is irrelevant in… Diagnostic and prognostic test studies Diagnostic and prognostic test studies Is cough a useful sign for the diagnosis of lung cancer? Is cough a useful sign for the diagnosis of lung cancer? Risk assessment Risk assessment You’re trying to determine whether people who carry matches are at greater risk of lung cancer. You’re trying to determine whether people who carry matches are at greater risk of lung cancer.

6. Confounding, A Picture Lung cancer (outcome) Carrying matches (predictor?)

7. Confounding, A Picture Lung cancer (outcome) Carrying matches (predictor?) Smoking cigarettes (confounder)

8. Confounding, A Picture Lung cancer (outcome) Carrying matches (predictor?) Smoking cigarettes (confounder) Carrying matches does not cause lung cancer; smoking does.

9. Huh, Aren’t All Associations Causal? Nope. Most aren’t! Nope. Most aren’t! Hard for us to believe. We excel at ascribing causes. Hard for us to believe. We excel at ascribing causes. Think about the last time you “just knew” someone who wronged you did so intentionally. Think about the last time you “just knew” someone who wronged you did so intentionally.

10. What are Some Other Explanations? The Big Five The Big Five Chance Chance Bias Bias Effect-cause Effect-cause Confounding Confounding Cause-effect Cause-effect

11. Five Potential Explanations for Associations Made in Observational Studies Spurious (not real) 1) ChanceBottled water and lung cancer (tested 100 exposures, P < 0.05) (tested 100 exposures, P < 0.05) 2) BiasCoffee and lung cancer (controls had GERD) (controls had GERD)

12. Five Potential Explanations for Associations Made in Observational Studies Real, but not causal 3) Effect – causeCough and lung cancer 4)ConfoundingCarrying matches and lung cancer lung cancer

13. Five Potential Explanations for Associations Made in Observational Studies Causal 5) Cause – effectCigarettes and lung cancer

14. Surely This is a Mistake that Pros Don’t Make They do. They do. Famous “proof” that smoking causes cervical cancer (i.e., that confounding was unlikely). Famous “proof” that smoking causes cervical cancer (i.e., that confounding was unlikely). But confounding can result in strong associations. But confounding can result in strong associations.

15. An Example of Confounding CA OR = ??? NO CA MATCHES NO MATCHES Case-control study: 1000 cases of lung cancer, 82% carry matches (or a lighter) 1000 controls (no cancer), 34% carry matches

16. An Example of Confounding CA OR = = 8.84 820x660 180x340 340 180 820 660 NO CA MATCHES NO MATCHES Carrying matches increases the risk (odds) of lung cancer almost 9-fold!

17. What’s the Problem? It is ABSOLUTELY true that people who carry matches are at increased risk of lung cancer It is ABSOLUTELY true that people who carry matches are at increased risk of lung cancer But it is NOT true (right?) that carrying matches causes lung cancer. But it is NOT true (right?) that carrying matches causes lung cancer. What is going on? (Duh…) What is going on? (Duh…)

18. What’s Going On? 90% of lung cancer patients smoke 90% of lung cancer patients smoke 30% of controls smoke 30% of controls smoke 90% of smokers carry matches 90% of smokers carry matches 10% of non-smokers carry matches 10% of non-smokers carry matches Smoking confounds the association between carrying matches and lung cancer Smoking confounds the association between carrying matches and lung cancer

19. Still Skeptical? I mean, the odds ratio was almost 9!

20. Let’s Work This Out 1000 cases, 820 carry matches 900 smoke, 90% of whom carry matches 900 smoke, 90% of whom carry matches 100 don’t smoke, 10% of whom carry matches 100 don’t smoke, 10% of whom carry matches 1000 controls, 340 carry matches 300 smoke, 90% of whom carry matches 300 smoke, 90% of whom carry matches 700 don’t smoke, 10% of whom carry matches 700 don’t smoke, 10% of whom carry matches

21. All You Need to Know Stratify by Exposure to the Confounder (SEC) Stratify by Exposure to the Confounder (SEC) In this case, smoking is the confounder (“Smoking confounds the association between carrying matches and lung cancer.”) In this case, smoking is the confounder (“Smoking confounds the association between carrying matches and lung cancer.”) The analyses should be stratified by smoking. The analyses should be stratified by smoking. Look separately among smokers and non-smokers Look separately among smokers and non-smokers

22. Stratify by Exposure to Confounder (SEC) NO CA NO MATCHES CA MATCHES OR smokers = ?? SMOKERS CA MATCHES OR non-smokers = ?? NON-SMOKERS NO CA NO MATCHES 1000 cases, 820 carry matches 900 smoke, 90% of whom carry matches 100 don’t smoke, 10% of whom carry matches 1000 controls, 340 carry matches 300 smoke, 90% of whom carry matches 700 don’t smoke, 10% of whom carry matches

23. Stratify by Exposure to Confounder (SEC) NO CA NO MATCHES CA 90 810 MATCHES OR smokers = ?? SMOKERS CA 90 10 MATCHES OR non-smokers = ?? NON-SMOKERS NO CA NO MATCHES 1000 cases, 820 carry matches 900 smoke, 90% of whom carry matches 100 don’t smoke, 10% of whom carry matches 1000 controls, 340 carry matches 300 smoke, 90% of whom carry matches 700 don’t smoke, 10% of whom carry matches

24. Stratify by Exposure to Confounder (SEC) NO CA NO MATCHES CA 270 90 810 30 MATCHES OR smokers = = 1.0 810x30 90x270 SMOKERS CA 70 90 10 630 MATCHES OR non-smokers = = 1.0 NON-SMOKERS NO CA NO MATCHES 10x630 90x70

25. After Stratifying by Smoking… There is no association between carrying matches and lung cancer in smokers (OR = 1). There is no association between carrying matches and lung cancer in smokers (OR = 1). There is no association between carrying matches and lung cancer in non-smokers (OR = 1). There is no association between carrying matches and lung cancer in non-smokers (OR = 1). Thus the association between carrying matches and lung cancer is completely confounded by smoking. Thus the association between carrying matches and lung cancer is completely confounded by smoking.

26. Confounding and Confounders Confounding occurs when the association between two variables (a predictor and an outcome) is due to a third variable (the confounder). Confounding occurs when the association between two variables (a predictor and an outcome) is due to a third variable (the confounder). The confounder must also be causally related to the outcome. The confounder must also be causally related to the outcome. Subtle point, but true Subtle point, but true

27. Subtle Digression One would NOT say that the association between carrying matches and lung cancer was confounded by having ashtrays in the home. One would NOT say that the association between carrying matches and lung cancer was confounded by having ashtrays in the home. Though the same kind of arithmetic might hold. Though the same kind of arithmetic might hold.

28. My Rules Never assume “it can’t be confounding” in an observational study. Never assume “it can’t be confounding” in an observational study. Be humble and skeptical. Be humble and skeptical.

29. Dealing with Confounding Does carrying matches cause lung cancer? Design phase strategies SpecificationMatching Analysis phase strategies StratificationAdjustment

30. Specification and Matching Both terms refer to the confounder Both terms refer to the confounder Specify: only study those with (or without) the confounder Specify: only study those with (or without) the confounder Look at carrying matches and lung cancer only in non- smokers Look at carrying matches and lung cancer only in non- smokers Match: make sure that a case who does (not) smoke is matched to a control who does (not). Match: make sure that a case who does (not) smoke is matched to a control who does (not). Then compare the frequency of carrying matches Then compare the frequency of carrying matches

31. Stratification and Adjustment Again, both terms refer to the confounder Again, both terms refer to the confounder Stratify the analyses by exposure to the confounder Stratify the analyses by exposure to the confounder Adjust the analyses for exposure to the confounder Adjust the analyses for exposure to the confounder

32. It’s Not Just Ruling Things Out Even if you eliminate (or make unlikely) chance, bias, confounding, and effect-cause, it’s nice to have “positive evidence” of causality Even if you eliminate (or make unlikely) chance, bias, confounding, and effect-cause, it’s nice to have “positive evidence” of causality

33. “Positive” Evidence of Causality TemporalityConsistencyDose-responsePlausibility

34. I Misled You Before There can be confounding when there’s no association. There can be confounding when there’s no association. If a confounder weakens the association between the predictor and the outcome. If a confounder weakens the association between the predictor and the outcome. Sometimes called suppression or reverse confounding. Sometimes called suppression or reverse confounding. Don’t lose sleep about this for all (and often any) of your null findings. Don’t lose sleep about this for all (and often any) of your null findings.

35. Interaction and Effect Modification Almost nobody understands these (they’re the same thing!) Almost nobody understands these (they’re the same thing!) But what it means is not that complicated. But what it means is not that complicated. The effect of one predictor on an outcome varies by the presence of another predictor. The effect of one predictor on an outcome varies by the presence of another predictor.

36. Interaction, Example from the 70’s The effect of social class on survival depended on country. The effect of social class on survival depended on country. In Viet Nam, higher social class was associated with better survival. In Viet Nam, higher social class was associated with better survival. In Cambodia, higher social class was associated with worse survival. In Cambodia, higher social class was associated with worse survival.

37. Interaction, Example from the 70’s The effect of country on survival depended on social class. The effect of country on survival depended on social class. Among the rich, being in Viet Nam was associated with better survival. Among the rich, being in Viet Nam was associated with better survival. Among the poor, being in Cambodia was associated with better survival. Among the poor, being in Cambodia was associated with better survival.

38. That’s the End… Confounded?