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**Chapter 19 Stratified 2-by-2 Tables**

4/15/2017 Chapter 19 Stratified 2-by-2 Tables April 17 Basic Biostat 1

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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 in an association brought about by extraneous variables Variables E = exposure variable D = disease variable C = confounding variable Confounder word origin: “to mix together,” the effects of the confounder gets mixed up with the effects of the exposure

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**Properties of confounding variables**

Associated with exposure Independent risk factor Not in causal pathway

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**Mitigating Confounding**

Randomization balances groups with respect to measured and unmeasured confounders Restriction of the study base imposes uniformity within groups . 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 – subdivide 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 Any statistical relationship between two variables may be reversed by including additional factors in the analysis. Application: Which factors should be included in the analysis? Wrong Simpson

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**Can we conclude that helicopter evacuation is 35% riskier?**

Example Does helicopter evaluations (“exposure”) decrease the risk of death (“disease”) following accidents? Crude comparison ≡ head-to-head comparison without consideration of extraneous factors. Died Survived Total Helicopter 64 136 200 Road 260 840 1100 Can we conclude that helicopter evacuation is 35% riskier?

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**Confounder = Severity of Accident**

Died Survived Total Helicopter 64 136 200 Road 260 840 1100 Serious Accidents Died Survived Total Helicopter 48 52 100 Road 60 40 Stratify by the confounding variable: Minor Accidents Died Survived Total Helicopter 16 84 100 Road 200 800 1000

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**Accident Evacuation Serious Accidents**

Died Survived Total Helicopter 48 52 100 Road 60 40 Among serious accidents, the risk of death was decreased by 20% with helicopter evacuation.

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**Accident Evacuation Minor Accidents**

Died Survived Total Helicopter 16 84 100 Road 200 800 1000 Among minor accidents, the risk of death was also decreased by 20%.

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**Accident Evacuation Properties of Confounding**

Seriousness of accident Evacuation method Death

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Summary Relative Risk Since the RRs were the same in the both subgroups (RR1 = RR2 = 0.8), combine the strata-specific RR to derive a single summary measure of association, i.e., the summary RR for helicopter evacuation is 0.80, since it decreases the risk of death by 20% in both circumstances This summary RR has “adjusted” for severity of accident

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Summary Relative Risk In practice, the strata-specific results won’t be so easily summarized Most common method for summarizing multiple 2-by-2 tables is the Mantel-Haenszel method Formulas in text Use SPSS or WinPEPI > Compare2 for data analysis William Haenszel Nathan Mantel

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**Summary Estimates with WinPEPI > Compare2 >A.**

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

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**Summary Hypothesis Test with WinPEPI > Compare2 >A.**

Null hypothesis H0: no association in population (e.g., RRM-H = 1) Test statistics: WinPEPI > Compare2 > A. > Stratified see prior slide for data input Interpretation: the usual, i.e., P value as measure of evidence χ2 = 3.46, df = 1, P = .063 pretty good evidence for difference in survival rates

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**M-H Methods for Other Measures of Association**

Mantel-Haenszel methods are available for odds ratio, rate ratios, and risk difference Same principles of confounder analysis and stratification apply Covered in text, but not in this presentation I’m back I’m back

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**Interaction (Effect Measure Modification)**

When we see different effects within subgroups, a statistical interaction is said to exist Interaction = Heterogeneity of the effect measures Do not use M-H summaries with heterogeneity would hide the non-uniformity

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**Example: Case-Cntl Data E= Asbestos D = Lung CA C = Smoking**

Too heterogeneous to summarize with a single OR

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**Test for Interaction Hypothesis Statements**

H0: no interaction vs. Ha: interaction For case-control study with two strata H0:OR1 = OR2 vs. Ha:OR1 ≠ OR2

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**Test for Interaction Test Statistics**

Use WinPEPI > Compare2 > A. > Stratified … OR-hat1 = 60 OR-hat2 = 2 Output:

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**Test for Interaction Interpretation**

The test of H0:OR1 = OR2 vs. Ha:OR1 ≠ OR2 χ2 = 21.38, df = 1, P = Conclude: Good evidence for interaction Report strata-specific results: OR is smokers is 60 OR in nonsmokers is 2

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Strategy Let MA ≡ Measure of Association (RR, OR, etc.)

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