Stratification issues with binary endpoints

This note addresses four interrelated issues for a stratified comparative trial with a binary endpoint: 1. How to define the true overall treatment effect parameter 2. How the strata should be weighted when conducting inference and estimation involving the overall treatment effect, 3. How to (and how not to) test for a treatment by stratum (T x S) interaction, and 4. When, why, and how the outcome of the T x S test should influence the weights assigned to each stratum. Numerical example; are provided to reinforce the key points.