Robust Bayesian design and analysis of clinical trials via prior partitioning

Unlike traditional approaches, Bayesian methods enable formal combination of expert opinion and objective information into interim and final analyses of clinical trials data. However, in cases where a broad group must be convinced by the results, a practical approach for studying and communicating the robustness of conclusions to prior specification is required. Rather than adopt the traditional method of modifying a single, initial prior and repeating the posterior calculation, in this paper we give a partial characterization of the class of priors leading to a given decision (such as stopping the trial and rejecting the null hypothesis) conditional on the observed data. We employ an interval null hypothesis based on the indifference zone approach of Freedman and Spiegelhalter, and restrict attention to priors having certain prespecified quantiles. We illustrate the application of our approach to interim monitoring using data from a recent AIDS clinical trial. We also indicate the method's usefulness in the design of future trials, creating simulation-based Bayesian analogues of the classical sample size table.