  In developing products for rare diseases, statistical challenges arise due to
the limited number of patients available for participation in drug trials and
other clinical research. Bayesian adaptive clinical trial designs offer the
possibility of increased statistical efficiency, reduced development cost and
ethical hazard prevention via their incorporation of evidence from external
sources (historical data, expert opinions, and real-world evidence), and
flexibility in the specification of interim looks. In this paper, we propose a
novel Bayesian adaptive commensurate design that borrows adaptively from
historical information and also uses a particular payoff function to optimize
the timing of the study's interim analysis. The trial payoff is a function of
how many samples can be saved via early stopping and the probability of making
correct early decisions for either futility or efficacy. We calibrate our
Bayesian algorithm to have acceptable long-run frequentist properties (Type I
error and power) via simulation at the design stage. We illustrate our approach
using a pediatric trial design setting testing the effect of a new drug for a
rare genetic disease. The optimIA R package available at
https://github.com/wxwx1993/Bayesian_IA_Timing provides an easy-to-use
implementation of our approach.
