Chapter 19 Stratified 2-by-2 Tables

1. Chapter 19Stratified 2-by-2 Tables

2. In Chapter 19: • 19.1 Preventing Confounding • 19.2 Simpson’s Paradox (Severe Confounding) • 19.3 Mantel-Haenszel Methods • 19.4 Interaction

3. Confounding≡ adistortion brought about by extraneous variables Word origin: “to mix together” §19.1 Confounding

4. Properties of confounding variables • Associated with exposure • Independent risk factor • Not in causal pathway

5. Randomization (experimentation) –balance group with respect to measured and unmeasured confounders Restriction – impose uniformity in the study base; homogeneity with respect to potential confounders Mitigating Confounding . St. Thomas Aquinas Confounding Averroлs

6. Mitigating confounding (cont.) 3. Matching – balances confounders 4. Regression models – mathematically adjusts for confounders 5. Stratification – subdivides data into homogenous groups (THIS CHAPTER)

7. §19.2 Simpson’s Paradox An extreme form of confounding in which in which the confounding variablereverses the direction the association

8. Example: Death following Accident Evacuation Crude comparison ≡ head-to-head comparison without adjustment for extraneous factors. Can we conclude that helicopter evacuation is 35% riskier?

9. Stratify by Severity of Accident

10. Accident Evacuation Highly Serious Accidents Quite different from crude OR (direction of association reversed)

11. Accident Evacuation Less Serious Accidents Again, quite different from crude RR.

12. Seriousness of accident (C) associated with helicopter evacuation (E) Seriousness of accident (C) is independent risk factor for death (D) Seriousness of accident (C) is not in the causal pathway (i.e., helicopter evaluation does not cause the accident to become more serious) Accident EvacuationProperties of Confounding

13. Notation • Subscript k indicates stratum number • Strata-specific RR estimates: RR-hatk

14. Mantel-Haenszel Summary Relative Risk Combine strata-specific RR^s to derive a single summary measure of effect “adjusted” for the confounding factor Calculate by computer

15. WinPEPI > Compare2 >A. Input Output RR-hatM-H = 0.80 (95% CI for RR: 0.63 – 1.02)

16. Mantel-Haenszel Test Step A: H0: no association (e.g., RRM-H = 1) Step B: WinPEPI > Compare2 > A. > Stratified Step C: Step D: P = .063 or P = .2078 (cont-corrected)  evidence against H0 is marginally significant

17. Other Mantel-Haenszel Summary Estimates Mantel-Haenszel methods are available for odds ratio, rate ratios, and risk difference Same principle apply (stratify & use M-H to summarize and tests Covered in text, but not covered in this presentation

18. 19.4 Interaction • Statistical interaction = heterogeneity in the effect measures, i.e., different effects within subgroups • Do not use Mantel-Haenszel summary statistics when interaction exists  this would hide the non-uniform effects • Assessment of interaction • Inspection! • Hypothesis test

19. Inspection Asbestos, Lung Cancer, Smoking Case-control data Too heterogeneous to summarize with a single OR

20. Test for InteractionOverview • H0: no interaction vs. Ha: interaction • Various chi-square interaction statistic exist (Text: ad hoc; WinPEPI: Rothman 1986 or Fleiss 1981) • Small P-value  good evidence against H0 conclude interaction

21. Test for InteractionAsbestos Example • H0:OR1= OR2(no interaction) versus Ha:OR1≠OR2(interaction) • WinPEPI > Compare2 > A. > Stratified  Input OR-hat2 = 2 OR-hat1 = 60

22. Test for InteractionAsbestos Example C. Output: D. Conclude: Good evidence of interaction  avoid MH and other summary adjustments