Measures of association

1. Measures of association October 12 2004 Epidemiology 511 W. A. Kukull

2. Epidemiologic Studies Observational Experimental Randomized trials, Clinical Trials Analytic Descriptive Cross- sectional Case-Control Cohort Ecologic

3. Is Disease associated with Exposure? • Foodborne outbreak: compare attack rates • ratio of attack rates • difference of attack rates • Relative Risk = Incidence (exp) / Incidence (not exp) • In a Cohort Study we observe incidence directly • RR is a measure of the STRENGTH of the association

4. Cohort Studies Defined Population Exposed Not Exposed Disease No Disease Disease No Disease

5. Cohort Studies • First select “Exposed” and “Non Exposed” (must be free of disease at start) • Follow over time to see who develops disease • Compare disease incidence in “Exposed” vs “Non Exposed” • Cumulative or incidence density • Can be “retrospective” or “concurrent”

6. Cohort StudiesExamples • British Physicians: smoking and lung cancer (Doll ) • Framingham Heart Study • Nurses Health Study • Cardiovascular Health Study

7. 2 x 2 Table Disease Yes No Yes Exposure No

8. Relative Risk for cohort studies I(exposed) a / a+b CI(e) = RR = = c / c+d I(not) CI(0) I(exposed) ID(e) a / PY1 RR = = = I(not) c / PY2 ID(0)

9. Interpreting RR • RR = 1.0 • incidence in exposed = incidence in unexposed no association: The null value of RR • RR > 1 • incidence in exposed is greater • RR < 1 • incidence in exposed is less (protective)

10. Interpreting RR • “Protective” RRs approach Zero • “Risky” RRs approach “infinity” • An RR of 2.0 and an RR of 0.5 are equal in magnitude but opposite in direction • Choice of reference (unexposed ) category

11. Relative risk “estimates” Increasing risk Decreasing risk (protective) Zero Infinity 1.0 “Null” lower incidence in exposed or fewer exposed among cases higher incidence in exposed or more exposed among cases

12. 2 x 2 Table(cohort) Disease Yes No a b a + b Yes Exposure c d c + d No RR = [a / (a+b)] [c / (c + d)]

13. Calculating RR for CI cohort study Bacteruria Yes No OC use 455 27 Yes (exposure) 77 1831 No

14. Person-year calculation 1/86 1/87 1/88 1/89 1/90 1/91 Total Subject A 2.0 Subject B 3.0 X Subject C 5.0 Subject D 4.0 Subject E 2.5 X Subject F 3.5 Total Years at risk 20.0 X = disease onset

15. Calculating RR (cohort) CHD Yes Person-years No HRT Yes 54,308.7 30 -- -- 51,477.5 60 No

16. Case-Control Studies Past Exposed Not Exposed Exposed Not Exposed Disease Present No Disease “Cases” “Controls”

17. Case-Control Studies • First select “cases” with disease and “controls” without disease • Determine history of exposure before onset of disease • interviews, records, stored specimens • Compare proportions of cases and controls who had been exposed

18. Case-Control • Can we find the incidence in exposed and unexposed? • We selected cases and controls • What will we do to estimate RR? • The Odds Ratio • ratio of the odds that the cases were exposed , to the odds that the controls were exposed: [a/c] / [b/d] = [ad] / [bc] (2 x 2 table)

19. Odds Ratio • An “estimate” of the Relative Risk • When cases are representative re: exposure of all diseased persons in the population • When controls are representative re:exposure of all non diseased in the population • When the disease under study is not “Frequent” • per Gordis, p.184

20. “Representativeness” • Ambiguous term • External validity; generalizability • Are the results limited only to the subjects included in this study? • What about animal model studies? • Internal validity • Were the subjects selected in a way that influenced the result?

21. 2 x 2 TableCase-control study Disease Yes No b a Yes Exposure c d No OR = ad / bc

22. Two Cohort studies: comparison of OR and RR with “rare disease” 35 22 3500 22 14 14 56 5600 OR=2.5 OR=2.5 RR=1.9 RR=2.5

23. Confidence Intervals(non-computational view) • The true measure of effect lies between these bounds, with X% confidence • “we are 95% sure that the true odds ratio lies between 1.2 and 6.7” • Wide confidence interval indicates greater variability, smaller sample size • Small sample size may be inadequate to exclude chance as an explanation

24. 2 x 2 Table Lung Ca Yes No 300 70 Yes Hx of Smoking 30 700 No OR =

25. Calculating OR Myocardial Infarction

26. Canine lymphoma and residence wire codes (Reif et al)

27. Example From the entire population of King Co. in 1998, all 375 hemorrhagic stroke patients were studied. 34.7% of those patients had a history of heavy alcohol use (5-6 drinks /day) during the 3 years prior to the stroke. In a comparison group (n=750), of similar age and sex, drawn from the same population, 125 had hx of heavy alcohol use. What is the strength of association between stroke and heavy alcohol use?

28. Example Of 2364 painters, 578 were identified as exposed to toluene in 1965-69. By 1999 (12427 p-yr) 39 exposed painters had developed bladder cancer while 123 cases had developed in their unexposed colleagues, who contributed 41971 person-years to follow-up by 1999. Is toluene exposure associated with increased risk of bladder Ca? Compare RRs and OR.

29. Disease No Disease Exposed Not Exposed

30. Matched Pairs Case - Control Studies • The “Pair” is the unit of analysis • Concordant pair: when both or neither the case and control are exposed • Discordant pair: when either the case or control are exposed (not both) • A different 2 x 2 table layout

31. Matched pair case-control 2x2 table Control not exp exp exp a b Case OR=b/c d c not exp

32. Matched Pairs data: E= exposedN=not exposed

33. Matched pair case-control 2 x 2 table Control not exp exp exp Case OR=b/c not exp

34. Matched Design Control exp Not exp 50 60 exp Case 20 300 Not exp 430 Pairs OR =

35. Breaking the matching case ctrl exp 110 70 320 360 Not exp 860 subjects OR=

36. Summary • Cohort Studies • calculating RR • Case - Control Studies • Odds Ratio • Matched pair OR • Next time : more scintillating calculations