3 §19.1 ConfoundingConfounding ≡ a distortion in an association brought about by extraneous variablesVariables E = exposure variable D = disease variable C = confounding variableConfounder word origin: “to mix together,” the effects of the confounder gets mixed up with the effects of the exposure
4 Properties of confounding variables Associated with exposureIndependent risk factorNot in causal pathway
5 Mitigating Confounding Randomization balances groups with respect to measured and unmeasured confoundersRestriction of the study base imposes uniformity within groups. St. Thomas Aquinas Confounding Averroлs
6 Mitigating confounding (cont.) 3. Matching – balances confounders4. Regression models – mathematically adjusts for confounders5. Stratification – subdivide data into homogenous groups (THIS CHAPTER)
7 §19.2 Simpson’s ParadoxAn extreme form of confounding in which in which the confounding variable reverses the direction the associationAny 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
8 Can we conclude that helicopter evacuation is 35% riskier? ExampleDoes helicopter evaluations (“exposure”) decrease the risk of death (“disease”) following accidents?Crude comparison ≡ head-to-head comparison without consideration of extraneous factors.DiedSurvivedTotalHelicopter64136200Road2608401100Can we conclude that helicopter evacuation is 35% riskier?
9 Confounder = Severity of Accident DiedSurvivedTotalHelicopter64136200Road2608401100Serious AccidentsDiedSurvivedTotalHelicopter4852100Road6040Stratify by the confounding variable:Minor AccidentsDiedSurvivedTotalHelicopter1684100Road2008001000
10 Accident Evacuation Serious Accidents DiedSurvivedTotalHelicopter4852100Road6040Among serious accidents, the risk of death was decreased by 20% with helicopter evacuation.
11 Accident Evacuation Minor Accidents DiedSurvivedTotalHelicopter1684100Road2008001000Among minor accidents, the risk of death was also decreased by 20%.
12 Accident Evacuation Properties of Confounding Seriousness of accidentEvacuation methodDeath
13 Summary Relative RiskSince 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 circumstancesThis summary RR has “adjusted” for severity of accident
14 Summary Relative RiskIn practice, the strata-specific results won’t be so easily summarizedMost common method for summarizing multiple 2-by-2 tables is the Mantel-Haenszel methodFormulas in textUse SPSS or WinPEPI > Compare2 for data analysisWilliam HaenszelNathan Mantel
15 Summary Estimates with WinPEPI > Compare2 >A. InputOutputRR-hatM-H = 0.80 (95% CI for RR: 0.63 – 1.02)
16 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 inputInterpretation: the usual, i.e., P value as measure of evidenceχ2 = 3.46, df = 1, P = .063 pretty good evidence for difference in survival rates
17 M-H Methods for Other Measures of Association Mantel-Haenszel methods are available for odds ratio, rate ratios, and risk differenceSame principles of confounder analysis and stratification applyCovered in text, but not in this presentationI’m backI’m back
18 Interaction (Effect Measure Modification) When we see different effects within subgroups, a statistical interaction is said to existInteraction = Heterogeneity of the effect measuresDo not use M-H summaries with heterogeneity would hide the non-uniformity
19 Example: Case-Cntl Data E= Asbestos D = Lung CA C = Smoking Too heterogeneous to summarize with a single OR
20 Test for Interaction Hypothesis Statements H0: no interaction vs. Ha: interactionFor case-control study with two strata H0:OR1 = OR2 vs. Ha:OR1 ≠ OR2
21 Test for Interaction Test Statistics Use WinPEPI > Compare2 > A. > Stratified …OR-hat1 = 60OR-hat2 = 2Output:
22 Test for Interaction Interpretation The test of H0:OR1 = OR2 vs. Ha:OR1 ≠ OR2χ2 = 21.38, df = 1, P = Conclude: Good evidence for interactionReport strata-specific results:OR is smokers is 60OR in nonsmokers is 2
23 StrategyLet MA ≡ Measure of Association (RR, OR, etc.)