1Apr 18, 2023

Chapter 19Chapter 19Stratified 2-by-2 TablesStratified 2-by-2 Tables

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In Chapter 19:

• 19.1 Preventing Confounding

• 19.2 Simpson’s Paradox (Severe Confounding)

• 19.3 Mantel-Haenszel Methods

• 19.4 Interaction

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§19.1 Confounding• Confounding ≡ a

distortion brought about by extraneous variables

• Word origin: “to mix together”

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Properties of confounding variables

• Associated with exposure

• Independent risk factor

• Not in causal pathway

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Mitigating Confounding1. 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 Averroлs

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Mitigating confounding (cont.)

3. Matching – balances confounders

4. Regression models – mathematically adjusts for confounders

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

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§19.2 Simpson’s Paradox

An extreme form of confounding in which in which the confounding variable reverses

the direction the association

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Example: Death following Accident Evacuation

Died Survived TotalHelicopter 64 136 200

Road 260 840 1100

Crude comparison ≡ head-to-head comparison without adjustment for extraneous factors.

1100/260

20064RR

2364.

3200. 35.1

Can we conclude that helicopter evacuation is 35% riskier?

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Stratify by Severity of AccidentDied Survived Total

Helicopter 64 136 200

Road 260 840 1100

Serious AccidentsDied Survived Total

Helicopter 48 52 100Road 60 40 100

Minor AccidentsDied Survived Total

Helicopter 16 84 100Road 200 800 1000

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Accident Evacuation Highly Serious Accidents

Serious AccidentsDied Survived Total

Helicopter 48 52 100Road 60 40 100

10060

10040RR 80.0

Quite different from crude OR (direction of association reversed)

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Accident Evacuation Less Serious Accidents

Minor AccidentsDied Survived Total

Helicopter 16 84 100Road 200 800 1000

80.01000200

10016RR

2000.

1600.

Again, quite different from crude RR.

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Accident EvacuationProperties 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)

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Notation• Subscript k indicates stratum number

• Strata-specific RR estimates: RR-hatk

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k

kk

k

kk

n

nan

na

RR12

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H-Mˆ

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

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WinPEPI > Compare2 >A.

Output

Input

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

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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

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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

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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

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Inspection Asbestos, Lung Cancer, Smoking

Case-control data

Too heterogeneous to summarize with a single OR

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Test for InteractionOverview

A. H0: no interaction vs. Ha: interaction

B. Various chi-square interaction statistic exist (Text: ad hoc; WinPEPI: Rothman 1986 or Fleiss 1981)

C. Small P-value good evidence against H0 conclude interaction

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Test for InteractionAsbestos Example

A. H0:OR1 = OR2 (no interaction) versus Ha:OR1 ≠ OR2 (interaction)

B. WinPEPI > Compare2 > A. > Stratified

Input

OR-hat1 = 60 OR-hat2 = 2

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Test for InteractionAsbestos Example

C. Output:

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