Nonparametric Bayesian Group Sequential Design

Abstract

The customary objective of a group sequential design is the comparison of several treatments or populations. The evolutionary nature of such trials encourages the use of the Bayesian paradigm in the design, monitoring and analysis of these trials. Here we focus on the design issue for the case of continuous, possibly multivariate response at each trial. Our approach is descriptive. Given a model specification, a design is characterized by a number of interim evaluations, the group size for each interim look, and a set of stopping criteria which determine our decision at a given look. By simulating replications of the design we can summarize design performance in terms of when the trial was stopped and reason for stopping. Such simulation and evaluation requires a fully Bayesian model specification for each treatment. We take a nonparametric perspective for the likelihood specification by assuming that the data is drawn from a distribution which arises through Dirichlet process mixing. However, we distinguish a sampling or “what if” prior, reflecting illustrative differences between populations, from a fitting or skeptical prior assuming no differences. By drawing trials under the sampling model, while fitting the model under the fitting prior, Bayesian learning moves us from prior indifference to detection of differences. We illustrate with two examples, one having univariate response, the other bivariate response.