  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.
