  The effects of treatments may differ between persons with different
characteristics. Addressing such treatment heterogeneity is crucial to
investigate whether patients with specific characteristics are likely to
benefit from a new treatment. The current paper presents a novel Bayesian
method for superiority decision-making in the context of randomized controlled
trials with multivariate binary responses and heterogeneous treatment effects.
The framework is based on three elements: a) Bayesian multivariate logistic
regression analysis with a P\'olya-Gamma expansion; b) a transformation
procedure to transfer obtained regression coefficients to a more intuitive
multivariate probability scale (i.e., success probabilities and the differences
between them); and c) a compatible decision procedure for treatment comparison
with prespecified decision error rates. Procedures for a priori sample size
estimation under a non-informative prior distribution are included. A numerical
evaluation demonstrated that decisions based on a priori sample size estimation
resulted in anticipated error rates among the trial population as well as
subpopulations. Further, average and conditional treatment effect parameters
could be estimated unbiasedly when the sample was large enough. Illustration
with the International Stroke Trial dataset revealed a trend towards
heterogeneous effects among stroke patients: Something that would have remained
undetected when analyses were limited to average treatment effects.
