Presentations in this series Overview and Randomization Self-matching Proxies Intermediates

1. Avoiding Bias Due toUnmeasured Covariates Presentations in this series Overview and Randomization Self-matching Proxies Intermediates Instruments Equipoise Alec Walker

2. X T D

3. X Randomization T D

4. X Randomization Self-matching T D

5. X Randomization Self-matching T D Proxies Proxies

6. A textbook definition from econometrics.

7. Let O be an outcome (either T treatment or D disease) P be a proxy X be an unmeasured covariate P is a proxy for X with respect to O if thedistribution of O given Pis identical to the distribution of O given P and X A textbook definition from econometrics. • Which is to say that X adds no information about O, if you know P.

8. Let O be an outcome (either T treatment or D disease) P be a proxy X be an unmeasured covariate P is a proxy for X with respect to O if thedistribution of O given Pis identical to the distribution of O given P and X A textbook definition from econometrics. • Which is to say that X adds no information about O, if you know P. Note that O, PandX could all be multidimensional, that is vectors of outcomes, proxies and unmeasured covariates, respectively. This definition could also be conditioned on other, measured covariates.

9. Proxy variables are Correlates of an unmeasured covariate That are useful to the extent that they capture the influence of the unmeasured covariate on a third characteristic Control for a proxy replaces control for the unmeasured covariate

10. Interview responses may be proxies for Historical measurements (diet, smoking, alcohol …) Internal states Genetic traits Biological markers are proxies for biological processes Age, sex, SES are stand-ins for their many correlates . Examples of proxies

11. Interview responses may be proxies for Historical measurements (diet, smoking, alcohol …) Internal states Genetic traits Biological markers are proxies for biological processes Age, sex, SES are stand-ins for their many correlates . Examples of proxies In diabetics, retinal vascular disease is a proxy for vascular disease more generally and is easily ascertained by funduscopic examination.In looking at determinants of myocardial infarction, control for retinal vascular disease could represent control for coexisting vascular pathology.

12. Source: US Department of Veterans Affairs Early diabetic retinopathy https://www.myhealth.va.gov/mhv-portal-web/anonymous.portal?_nfpb=true&_pageLabel=commonConditions&contentPage=va_health_library/diabetic_retinopathy_advanced_info.html

13. Source: US Department of Veterans Affairs Early diabetic retinopathy microaneurysms https://www.myhealth.va.gov/mhv-portal-web/anonymous.portal?_nfpb=true&_pageLabel=commonConditions&contentPage=va_health_library/diabetic_retinopathy_advanced_info.html

14. Source: US Department of Veterans Affairs Advanced diabetic retinopathy https://www.myhealth.va.gov/mhv-portal-web/anonymous.portal?_nfpb=true&_pageLabel=commonConditions&contentPage=va_health_library/diabetic_retinopathy_advanced_info.html

15. X D T

16. X P D T

17. X X P T D D

18. X X P UD T D D UT

19. X X P UD T D D UT

20. UX X P UD T D UT

21. UX X X P UD T D D UT

22. UX X X P UD T D D UT

23. (Unmeasured) Severity of Diabetes Coronary artery disease Retinal vascular disease UD Acute myocardial infarction Thialozinediones for diabetes UT

24. Without mechanistic information, for each of these situations, ( covariate causes proxyproxy causes covariateboth caused by a third factor ) … the proxy looks like a transformation of the predictor, with added error. Proxy value = f(Predictor value) + error

25. An accurate proxy

26. An accurate proxy Treated Untreated The true value of the unmeasured covariate is a predictor of treatment

27. An accurate proxy The proxy predicts treatment almost as well as does the true value. Treated Untreated The true value of the unmeasured covariate is a predictor of treatment

28. An accurate proxy The proxy almost perfectly represents the value of the unmeasured covariate. Treated Untreated

29. An accurate proxy Treated Untreated

30. An accurate proxy Treated Untreated

31. An accurate proxy

32. An accurate proxy The proportion of treated among subjects in a particular small range of proxy values

33. An accurate proxy The proportion of treated among subjects in a particular small range of proxy values

34. An accurate proxy The proportion of treated among subjects in a particular small range of proxy values … is the same as the proportion of treated among subjects in the corresponding small range of true values.

35. An accurate proxy The true value does not provide further information, if you know the proxy.

36. Two accurate proxies Treated Untreated

37. Two accurate proxies Treated Untreated Two good proxies are highly correlated with one another.

38. Two accurate proxies Either proxy provides good prediction of treatment. Treated Untreated

39. Proxies with substantial random error Treated Untreated Untreated

40. Proxies with substantial random error Treated The proxy is still correlated with the unknown measure. Untreated Untreated

41. Treatment is still associated with higher values of the proxy, but thediscriminationis muchworse. Proxies with substantial random error

42. Proxies with substantial random error Treated Untreated

43. Proxies with substantial random error Treated The correlation between the two proxy measures is still evident. Untreated

44. Both proxies show poor discrimination between treated and untreated. Proxies with substantial random error Treated Untreated

45. Proxies with substantial random error The two proxies can be combined into a function that discriminates better than either proxy alone. Treated Untreated

46. A textbook definition from econometrics.

47. Let O be an outcome (either T treatment or D disease) P be a proxy X be an unmeasured covariate P is a proxy for X with respect to O if thedistribution of O given Pis identical to the distribution of O given P and X. A textbook definition from econometrics.