Bayesian subset analysis in a colorectal cancer clinical trial

Subset analysis is the examination of treatment comparisons within groups of patients with restricted levels of patient characteristics. Such analyses are vulnerable to multiplicity effects. We examine the problem in the context of a proportional hazards model with terms for treatment, each of several dichotomous covariates representing the patient characteristics of interest, and treatment-by-covariate interaction effects. Parametrically, a subset-specific treatment effect is equal to the treatment effect term plus a linear combination of the interaction terms. We present Bayesian point and interval estimates under the assumption that the interaction terms are exchangeable and the prior distributions for the other regression parameters are locally uniform. This produces a shrinking of the estimated interaction effects towards zero, thereby discounting them and dealing in a natural way with multiplicity. We illustrate the method using results of a recent North Central Cancer Treatment Group/Mayo Clinic study in advanced colorectal cancer.