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 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!

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

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

Stratified analysis via logistic regression Let’s try:

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….

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