1. Advanced Epi August 15-19 th 2011 SACEMA Matthew Fox Boston University Center for Global Health and Development Department of Epidemiology Health Economics and Epidemiology Research Office mfox@bu.edu

2. Introductions Who are you? Where do you work/study? What do you study?

3. Welcome About me Week long short course on epi methods  2 Sessions/day each about 3 hours (depending)  Assumes intro/intermediate epi, practical experience with epi and stats Mix of lecture and discussion  Too much material, take good notes, go back to them Finish mid-day on Friday Course works if you read and participate

4. Course Overview Review basic epidemiologic principles  Reinterpret them in a new light Think through problems/implications of what we learned in intro/intermed epi  Develop a causal framework(s) to hang our epidemiologic thinking Learn/apply advanced epi methods

5. Modern Epidemiology III

6. Questions for Today What is epidemiology, what is its goal? What are measures of association and measures of effect?  What do these measures really mean?  Which ones have causal meanings?  What is the odds ratio really about  Why does everyone use it?

7. The goal of epidemiologic research Epidemiology is study of:  The distribution and determinants of disease in human populations and the application of that knowledge to the control of disease But the goal is:  To obtain a valid and precise (and generalizable) estimate of the effect of an exposure on a disease Validity is the opposite of bias, precision is the opposite of random error  Fundamentally concerned with measurement

10. Anyone remember Type I and Type II error? What are they?

11. Basic Statistics Truth about Null EffectNo effect Our study null Effect Correct Type I error (alpha) No effect Type II error (beta) Correct Type I: If we reject the null, what are the chance there is no effect? Type II: If we fail to reject the null, what are the chances there is an effect?

12. How do we know a particular epidemiologic finding is true? Find that the relative risk of exposure to vitamin # on cancer @ is 2.5, p=0.049 Assume we did the perfect study  No bias (confounding, selection, information)  80% power, alpha = 0.05 What is chance there is really no effect of vitamins on cancer?  i.e. True relative risk is 1

13. Syphilis testing in the US In US pre-2005, Massachusetts required a syphilis test before marriage  Assume the test was: 95% sensitive and 95% specific If I test positive, how likely is it that I truly have syphilis?  Answer is that it depends

14. Syphilis Truth +-Total Test + - Total Prevalence is: 1% Se = 95% Sp = 95% 1009900 95 5 495 9405 590 9410 PPV = 16% 10,000

15. Back to our study Truth EffectNo effect Our study Effect Correct Type I error (alpha) No effect Type II error (beta) Correct Alpha and beta use the TRUTH as the denominator and so are like Se and Sp

16. Back to our study Truth EffectNo effect Our study Effect Correct Type I error (alpha) No effect Type II error (beta) Correct Judging the “correctness” of a single study is the PPV, and depends of the prevalence of true hypotheses

17. Back to our study alpha = 5%, (Sp 95%) beta = 5%, (Se 95%) 10009000 950 50 450 8550 1400 8600 68% chance our study is right Truth +-Total Our Study + - Total10,000 Prevalence of true hypotheses is: 10%

18. Take home message: We need to critically examine the way we have been taught to design and interpret epidemiologic research

19. Review of basic concepts Study design, measures of disease frequency, measures of effect/association

21. The Source Population The population that gives rise to cases It is defined:  In time and place  With respect to population characteristics  With respect to external influences (modifiers)  Not as a sample of the general population

22. Cohorts Membership in a cohort requires a person meet admissibility criteria  Have common admissibility-defining events Membership begins once the temporally last criterion is met  Once a member, a person never leaves (membership is static or closed)  A closed cohort adds no new members and loses only to death, an open cohort is adding new members

23. Dynamic population Membership requires a person satisfy the membership status criteria  They have common admissibility-defining characteristics Membership exists so long as all of the status criteria are satisfied A person can enter a dynamic population, leave it, and then re-enter

24. Cohorts vs. Dynamic Populations Framingham heart study  Cohort – the admissibility criteria are enrolling in the study in 1948. Never leave the cohort once you enroll.  Dynamic population – could have instead studied all residents of Framingham from 1948 onwards, the catchment population for a case registry there. Some will leave, new people will join.

25. STUDY DESIGN: How to harvest information from the base Census (cohort) or Sample (case-control) Cases are valuable (information rich)  In SE calcs, these drive your standard error Ex. SE(LN(RR)) = sqrt(1/A–1/N 1 +1/B–1/N 0 )  Include all the cases in the population Information density of population that gave rise to cases is not great  Can include all or sample  Nearly all base’s info is harvested when sample of base is small multiple of the cases

26. Which is the best measure to assess causal effects? 1) Risk Difference 2) Risk Ratio 3) Odds Ratio

27. In a case-control study, from what population do we sample controls? 1) Those with disease 2) Those without disease 3) Everyone, regardless of whether they have the disease

28. Cohort Study

29. Case-control Study

30. Kramer and Bovin 1987 We define a cohort study as a study in which subjects are followed forward from exposure to outcome… Inferential reasoning is from cause to effect. In case- control studies, the directionality is the reverse. Study subjects are investigated backwards from outcome to exposure, and the reasoning is from effect to cause.”

31. Cohort Study: Relative Risks Relative risk: (A/N 1 ) / (B/N 0 )  Risk in exposed / risk in unexposed  Risk is number of cases / total at risk  Numerator is number of cases  Denominator is cases and controls! Index (E+)Reference (E-) CasesAB Non-casesCD TotalN1N1 N0N0

32. Cohort Concept t0t0 t N E+ N E- Exposed Cases A Unexposed Cases B C (N E+ - a) D (N E- - b)

33. Cohort Study: Relative Risks Relative risk:  (A/N 1 )/(B/N 0 ) can be rearranged as (A/B)/(N 1 /N 0 )  A/B is ratio of exposed to unexposed cases  N 1 /N 0 is ratio of exposed to unexposed in population Index (E+)Reference (E-) CasesAB Non-casesCD TotalN1N1 N0N0

34. Relative risk has meaning: average increase in risk produced by exposure

35. Case-control: Cases Members of population who develop disease over the follow-up period  Same cases as the analogous cohort study  Case ascertainment is influenced by design Primary base: population defined first Secondary base: cases defined first

36. Case-control: Controls A sample of the population experience that gave rise to the cases 3 options (paradigms)  Un-diseased experience  Population at risk at beginning of the study  Population experience over follow-up 0 mos6 mos12 mos18 mos24 mos Cases05101520 Non-cases10095908580

37. Case-control Concept t0t0 t N E+ N E- Exposed Cases A Unexposed Cases B C (N E+ - a) D (N E- - b) Option 1: Cumulative Option 2: Case-cohort Option 3: Density Sampling

38. Case-control study IndexReference CasesAB ControlsCD Now we can’t estimate risk A/N 1 and B/N 0 because we don’t know the denominators Left with an odds ratio  But how to interpret?

39. 2 ways to calculate an OR IndexReference CasesAB ControlsCD Cross product ratio:  (A*D)/(B*C)  Not particularly meaningful, but it works

40. 2 ways to calculate an OR IndexReference CasesAB ControlsCD Case ratio/base ratio:  (A/B) / (C/D)  A/B is the ratio of exposed to unexposed cases  C/D is the ratio of exposed to unexposed controls  Remember back to Relative Risk Here C/D fills in for N 1 /N 0

41. The trohoc fallacy IndexReference Cases400100 Non-cases600900 Total1000 IndexReference Cases400100 Non-cases6090 TotalNotsampled The trohoc fallacy is idea that a case-control study is a cohort study done backwards (heteropalindrome) Requires a rare disease assumption for the odds ratio to approximate the relative risk RR = (400/1000) / (100/1000) = 4.0 OR = (400/60) / (100/90) = 6.0 10% sample of non-cases

42. Case-control Concept t0t0 t N E+ N E- Exposed Cases A Unexposed Cases B C (N E+ - a) D (N E- - b) Option 1: Cumulative Option 2: Case-cohort

43. The trohoc fallacy revealed IndexReference Cases400100 Non-cases600900 Total1000 IndexReference Cases400100 Non-casesNotsampled Controls100 Sample total population that gave rise to cases (which includes cases), not undiseased at end  Cases can be their own controls if randomly sampled Requires no rare disease assumption RR = (400/1000) / (100/1000) = 4.0 OR = (400/100) / (100/100) = 4.0 10% sample of population that gave rise to cases

44. Miettinen on the trohoc fallacy “Consider the clinical trial: the concern is, as always, to contrast categories of treatment as to subsequent occurrence of some outcome phenomenon, whereas comparing different categories of the outcome as to the antecedent distribution of treatment is uninteresting if not downright perverse.” Preferred terms like “case-referent” and “case- base” studies as “the base sample is no more a control series than a census of the base is”

45. Why it works OR = [A*D] / [B*C] = [A/B] / [C/D]  If we sample 10% of the base then the odds ratio is: OR = [A/B] /[(10%*N 1 )/(10%*N 0 )] = [A/B]/(N 1 /N 0 ) = RR IndexRef CasesAB Non- case CD TotalN1N1 N0N0

46. Cohort studies exclude those who are not at risk for disease (though they don’t need to). In a case control study. Should we exclude those not at risk for exposure? Ex. In a study of hormonal contraception and heart disease, should we exclude nuns?

47. With appropriate sampling, odds ratio is interpreted as estimate of relative risk, which has meaning. Case control studies are cohort studies done efficiently, not cohort studies done backwards.

48. Measures of Disease Frequency Provide an estimate of the occurrence of disease in a population  Typically we study first occurrence as later occurrences are often affected by first Incorporates:  Disease state  Time  Population definition

49. Measures of Disease Frequency Prevalence:  Proportion of population with disease at a particular time  Cross-sectional  Reflects rate of disease occurrence and survival with disease

50. Measures of Disease Frequency Cumulative Incidence (Simple)  Proportion of a population that develops disease over a follow-up period  Also called incidence proportion or risk  Bounded by 0 and 1  Time not part of measure but must report  Difficult to measure in dynamic populations CI (t0,t) = I (t0,t) /N 0

51. Measures of Disease Frequency Incidence rate (density)  Number of newly developed cases divided by accumulated person time Time is part of the denominator  Can be used in dynamic populations/cohorts  Ignores distinction between individuals (2/100 py could be 2 followed 50 yrs each, both get event or 100 followed 1 yr each, 2 get event) IR (t 0,t) = I (t0,t) /∑PT where

52. Measures of Disease Frequency Rules for counting person time  Start disease free, free of history of disease at entry  At risk for outcome? Not necessary, but wasteful  Start after exposure is complete (not during) and after minimum induction period  Stop when disease occurs (date or midpoint)  Stop if withdrawn (lost to follow up, death from another cause, study ends, no longer at risk) Only those eligible to be counted in numerator are in denominator  Ask, if became a case, would I have counted them?

53. Person Time Issues I We conduct a cohort study of continuous smoking vs. no smoking and prostate cancer  Enroll 1000 smokers and 1000 non-smokers At end, find 100 non-smokers became smokers. Should we exclude them?  Can’t because if they became cases while not smoking we would have included them

54. Person Time Issues II Study HAART regimens and death  But much death and LTFU in first 6-months and we care about long term mortality Exclude any deaths in first 6-months  OK if all we care about is long-term effects When should person time start?  Immortal person-time biases towards null

55. Black triangle Prevalence = 2/8 = 0.25

56. Black triangle Cum Inc = 2/9

57. Black triangle Inc Rate = 2/42 5 5 5 5 5 5 5 5 2

58. Measure of Effect Comparison of occurrence of outcome in the same population at same time under two different conditions  Only one can be observed  Second is “counterfactual” (we will come back to this) Theoretical, as such we substitute measure of association  But as an approximation to measure of effect

59. Measures of Association Comparison of incidence in 2+ populations Relative:  Comparison by division  Null (no effect) is 1  Log scale (distance from 0-1 is same as 1 to infinity) Difference:  Comparison by subtraction  Null (no effect) is 0  Distance above and below null is equivalent

60. Calculations

61. Conclusion Objective is a VALID and PRECISE estimate of the effect of an exposure on an outcome Need to think critically about the logic of the methods we have been taught  Make sure we understand how to validly design studies and how to correctly interpret study findings Odds ratios are odd  Correct sampling means can reduce reliance on them