Bayesian Multivariate Probability of Success Using Historical Data with Strict Control of Family-wise Error Rate

Abstract: Given the cost and duration of phase III and phase IV clinical trials, the development of statistical methods for go/no-go decisions is vital. In this paper, we introduce a Bayesian methodology to compute the probability of success based on the current data of a treatment regimen for the multivariate linear model. Our approach utilizes a Bayesian seemingly unrelated regression model, which allows for multiple endpoints to be modeled jointly even if the covariates between the endpoints are different. Correlations between endpoints are explicitly modeled. This Bayesian joint modeling approach unifies single and multiple testing procedures under a single framework. We develop an approach to multiple testing that asymptotically guarantees strict family-wise error rate control, and is more powerful than frequentist approaches to multiplicity. The method effectively yields those of Ibrahim et al. and Chuang-Stein as special cases, and, to our knowledge, is the only method that allows for robust sample size determination for multiple endpoints and/or hypotheses and the only method that provides strict family-wise type I error control in the presence of multiplicity.