Nonparametric Bayesian clinical trials design for multivariate patient response

In the conduct of sequential clinical trials, primary statistical issues include design, monitoring and reporting. Currently, approaches built upon frequentist inference methodology predominate. Focusing on the design aspect, our objective is the development of a very general Bayesian framework permitting multiple arms with multiple patient endpoints and multiple stopping criteria. Specification of a sequential Bayesian design requires a likelihood, a prior and a stopping rule. We take a nonparametric perspective for the likelihood specification. We do so by representing discrete patient response as a categorical outcome described through cells in a multiway contingency table, while we assume that continuous data is drawn from a distribution which arises through Dirichlet process mixing. To address the subjectivity in the prior specification we can consider a range of priors from skeptical to enthusiastic to capture our views. Historical data available on the standard or placebo arm are used to form the prior for that arm the multiple stopping criteria are employed to define the stopping rule. We propose two different approaches: The first one 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. We then simulate replications of the design and use these replicates to summarize design performance in terms of when the trial was stopped and reason for stopping. The second approach is decision-theoretic. We obtain optimal bounded designs using backward induction, implemented via Monte Carlo integration. While required random generation grows geometrically in the number of interim looks we provide computationally feasible bounds for the needed continuation risks as well as the expected sample sizes. We offer some qualitative results on the behavior of such designs and then present examples to illustrate the entire development.