Bayesian Decision Theoretic Design for Group Sequential Medical Trials having Multivariate Patient R

In the conduct of sequential clinical trials primary statistical issues include design, monitoring and reporting. Here we focus on design issues. Group sequential designs have been developed to link patient accrual to when interim analysis should occur. In practice, trials with multiple arms and multivariate patient response are important. We present an approach for implementing and assessing optimal group sequential designs for such trials. We envision trials where patient response is obtained shortly after treatment and is recorded as a categorical outcome represented by a cell in a multi-way contingency table. Study objectives involve comparison of sums of selected cell probabilities across arms. Actions expressing opinions on these comparisons motivate 0 appropriate decision-theoretic structure. Optimal bounded designs are obtained using backward induction, implemented via Monte Carlo integration. While required random generation grows geometrically in the number of interim looks, i.e., number of patient groups, we provide computationally feasible bounds for the needed continuation risks as well as expected sample sizes. We work with a running example on bone marrow transplantation using marrow cells from a human leucocyte antigen identical sibling, taken from Thall et al. (1995).