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Chapter 19 Stratified 2-by-2 Tables. In Chapter 19:. 19.1 Preventing Confounding 19.2 Simpson’s Paradox (Severe Confounding) 19.3 Mantel-Haenszel Methods 19.4 Interaction. Confounding ≡ a distortion brought about by extraneous variables Word origin: “to mix together”. §19.1 Confounding.

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Chapter 19 Stratified 2-by-2 Tables

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in chapter 19
In Chapter 19:
  • 19.1 Preventing Confounding
  • 19.2 Simpson’s Paradox (Severe Confounding)
  • 19.3 Mantel-Haenszel Methods
  • 19.4 Interaction
properties of confounding variables
Properties of confounding variables
  • Associated with exposure
  • Independent risk factor
  • Not in causal pathway
mitigating confounding
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

mitigating confounding cont
Mitigating confounding (cont.)

3. Matching – balances confounders

4. Regression models – mathematically adjusts for confounders

5. Stratification – subdivides data into homogenous groups (THIS CHAPTER)

19 2 simpson s paradox
§19.2 Simpson’s Paradox

An extreme form of confounding in which in which the confounding variablereverses the direction the association

example death following accident evacuation
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?

accident evacuation highly serious accidents
Accident Evacuation Highly Serious Accidents

Quite different from crude OR

(direction of association reversed)

accident evacuation less serious accidents
Accident Evacuation Less Serious Accidents

Again, quite different from crude RR.

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)

Accident EvacuationProperties of Confounding
  • Subscript k indicates stratum number
  • Strata-specific RR estimates: RR-hatk
mantel haenszel summary relative risk
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

winpepi compare2 a
WinPEPI > Compare2 >A.



RR-hatM-H = 0.80 (95% CI for RR: 0.63 – 1.02)

mantel haenszel test
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

other mantel haenszel summary estimates
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

19 4 interaction
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
inspection asbestos lung cancer smoking
Inspection Asbestos, Lung Cancer, Smoking

Case-control data

Too heterogeneous to summarize with a single OR

test for interaction overview
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
test for interaction asbestos example
Test for InteractionAsbestos Example
  • H0:OR1= OR2(no interaction) versus Ha:OR1≠OR2(interaction)
  • WinPEPI > Compare2 > A. > Stratified 


OR-hat2 = 2

OR-hat1 = 60

test for interaction asbestos example22
Test for InteractionAsbestos Example

C. Output:

D. Conclude: Good evidence of interaction  avoid MH and other summary adjustments