  Clinical trials often evaluate multiple outcome variables to form a
comprehensive picture of the effects of a new treatment. The resulting
multidimensional insight contributes to clinically relevant and efficient
decision-making about treatment superiority. Common statistical procedures to
make these superiority decisions with multiple outcomes have two important
shortcomings however: 1) Outcome variables are often modeled individually, and
consequently fail to consider the relation between outcomes; and 2) superiority
is often defined as a relevant difference on a single, on any, or on all
outcomes(s); and lacks a compensatory mechanism that allows large positive
effects on one or multiple outcome(s) to outweigh small negative effects on
other outcomes. To address these shortcomings, this paper proposes 1) a
Bayesian model for the analysis of correlated binary outcomes based on the
multivariate Bernoulli distribution; and 2) a flexible decision criterion with
a compensatory mechanism that captures the relative importance of the outcomes.
A simulation study demonstrates that efficient and unbiased decisions can be
made while Type I error rates are properly controlled. The performance of the
framework is illustrated for 1) fixed, group sequential, and adaptive designs;
and 2) non-informative and informative prior distributions.
