Strategies for comparing treatments on a binary response with multi-centre data

This paper surveys methods for comparing treatments on a binary response when observations occur for several strata. A common application is multi-centre clinical trials, in which the strata refer to a sample of centres or sites of some type. Questions of interest include how one should summarize the difference between the treatments, how one should make inferential comparisons, how one should investigate whether treatment-by-centre interaction exists, how one should describe effects when interaction exists, whether one should treat centres and centre-specific treatment effects as fixed or random, and whether centres that have either 0 successes or 0 failures should contribute to the analysis. This article discusses these matters in the context of various strategies for analysing such data, in particular focusing on special problems presented by sparse data.