  In current clinical trial development, historical information is receiving
more attention as it provides utility beyond sample size calculation.
Meta-analytic-predictive (MAP) priors and robust MAP priors have been proposed
for prospectively borrowing historical data on a single endpoint. To
simultaneously synthesize control information from multiple endpoints in
confirmatory clinical trials, we propose to approximate posterior probabilities
from a Bayesian hierarchical model and estimate critical values by deep
learning to construct pre-specified strategies for hypothesis testing. This
feature is important to ensure study integrity by establishing prospective
decision functions before the trial conduct. Simulations are performed to show
that our method properly controls family-wise error rate (FWER) and preserves
power as compared with a typical practice of choosing constant critical values
given a subset of null space. Satisfactory performance under prior-data
conflict is also demonstrated. We further illustrate our method using a case
study in Immunology.
