Bayesian subset analysis

As a means of assessing the importance of variation in treatment effect among patient subsets, we derived posterior distributions for subset-specific treatment effects. The effects are represented by combinations of terms for treatment and treatment-by-covariate interaction effects in familiar regression models. Exchange-ability among the interactions is a key assumption; thus, the results are of interest primarily in the context of examining a collection of subsets with no definite a priori distinction relative to treatment effect. Exchangeability leads to a shrinking of the posterior distributions of the interaction terms toward the natural origin of 0, offsetting the tendency of the estimated effects to disperse. The method is applied to parameter estimates from a proportional hazards regression analysis of survival data from a clinical trial, invoking the approximate multivariate normal distribution of the estimates. No subjective prior distributions are required. Vague priors are used for all of the regression coefficients except the treatment-by-covariate interactions, which are assumed to follow a normal distribution.