Chapter 19 Stratified 2-by-2 Tables

Chapter 19Stratified 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≡ adistortion in an association brought about by extraneous variables Variables E = exposure variableD = disease variableC = confounding variable Confounder word origin: “to mix together,” the effects of the confounder gets mixed up with the effects of the exposure §19.1 Confounding

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

Example Does helicopter evaluations (“exposure”) decrease the risk of death (“disease”) following accidents? Crude comparison ≡ head-to-head comparison without consideration of extraneous factors. Can we conclude that helicopter evacuation is 35% riskier?

Confounder = Severity of Accident Stratify by the confounding variable:

Accident Evacuation Serious Accidents Among serious accidents, the risk of death was decreased by 20% with helicopter evacuation.

Accident Evacuation Minor Accidents Among minor accidents, the risk of death was also decreased by 20%.

Accident EvacuationProperties of Confounding Seriousness of accident Death Evacuation method

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 Summary Relative Risk This summary RR has “adjusted” for severity of accident

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

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

Summary Hypothesis Test with WinPEPI > Compare2 >A. • Null hypothesisH0: 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

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 M-H Methods for Other Measures of Association I’m back I’m back

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

Example: Case-Cntl Data E= Asbestos D = Lung CA C = Smoking Too heterogeneous to summarize with a single OR

Test for InteractionHypothesis Statements • H0: no interaction vs. Ha: interaction • For case-control study with two strataH0:OR1= OR2vs. Ha:OR1 ≠OR2

Test for InteractionTest Statistics Use WinPEPI > Compare2 > A. > Stratified  … OR-hat2 = 2 OR-hat1 = 60 Output:

Test for InteractionInterpretation The test of H0:OR1= OR2vs. Ha:OR1 ≠OR2 χ2 = 21.38, df = 1, P = 0.0000038.  Conclude: Good evidence for interaction Report strata-specific results: OR is smokers is 60 OR in nonsmokers is 2

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

Chapter 19 Stratified 2-by-2 Tables