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Analysis of Case Control Studies

Analysis of Case Control Studies. E – exposure to asbestos D – disease: bladder cancer S – strata: smoking status. 2X2 Table. p = Pr(Exposure) p may depend on D and/or S. A difference between 2 log odds.

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Analysis of Case Control Studies

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  1. Analysis of Case Control Studies E – exposure to asbestos D – disease: bladder cancer S – strata: smoking status

  2. 2X2 Table • p = Pr(Exposure) • p may depend on D and/or S

  3. A difference between 2 log odds • The log of the odds of exposure for those with disease minus the log of the odds of exposure for those without disease • Now…. Brace yourself… The exponent of a difference is a ratio! YAY!

  4. So what… you say? • Lets take the exponent of: • The odds ratio: OR • Remember: exp and log are inverses of one another

  5. Exp and Log • Exp(Log(A)) = A = Log(Exp(A)) • Exp(A-B) = Exp(A)Exp(-B) =Exp(A)/Exp(B) • So the exponent of a difference is a ratio of exponents • Log(A/B) = Log(A) – Log(B) • So the logarithm of a ratio is a difference between logarithms

  6. Stratified analysis via logistic regression • Let’s try:

  7. Effect modification • Test: • This is the same null hypothesis as the ‘test for homogeneity’ in a ‘classical’ analysis. • Evidence against this null hypothesis indicates that there is evidence that the stratum specific odds ratios are different • If there is no evidence against….

  8. …assess confounding • …just like linear regression Since ORs are ratios, ratios of ORs are usually considered (as opposed to differences)

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