1June 15

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

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

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

5 Mitigating Confounding 1.Randomization (experimentation) – balance group with respect to measured and unmeasured confounders 2.Restriction – impose uniformity in the study base; homogeneity with respect to potential confounders. St. Thomas Aquinas Confounding AverroлsSt. 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 variable reverses the direction the association

8 Example: Death following Accident Evacuation DiedSurvivedTotal Helicopter Road 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 DiedSurvivedTotal Helicopter Road Serious Accidents DiedSurvivedTotal Helicopter Road Minor Accidents DiedSurvivedTotal Helicopter Road

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

11 Accident Evacuation Less Serious Accidents Minor Accidents DiedSurvivedTotal Helicopter Road Again, quite different from crude RR.

12 Accident Evacuation Properties of Confounding 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)

13 Notation Subscript k indicates stratum number Strata-specific RR estimates: RR-hat k

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

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

16 Mantel-Haenszel Test Step A: H 0 : no association (e.g., RR M-H = 1) Step B: WinPEPI > Compare2 > A. > Stratified Step C: Step D: P =.063 or P =.2078 (cont-corrected)  evidence against H 0 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

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 Interaction Overview A.H 0 : no interaction vs. H a : interaction B.Various chi-square interaction statistic exist (Text: ad hoc; WinPEPI: Rothman 1986 or Fleiss 1981) C.Small P-value  good evidence against H 0  conclude interaction

21 Test for Interaction Asbestos Example A.H 0 :OR 1 = OR 2 (no interaction) versus H a :OR 1 ≠ OR 2 (interaction) B.WinPEPI > Compare2 > A. > Stratified  Input OR-hat 1 = 60 OR-hat 2 = 2

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

23 Interaction Statistic – Hand Calculation Ad hoc interaction statistic