  Basket trials are increasingly used for the simultaneous evaluation of a new
treatment in various patient subgroups under one overarching protocol. We
propose a Bayesian approach to sample size determination in basket trials that
permit borrowing of information between commensurate subsets. Specifically, we
consider a randomised basket trial design where patients are randomly assigned
to the new treatment or a control within each trial subset (`subtrial' for
short). Closed-form sample size formulae are derived to ensure each subtrial
has a specified chance of correctly deciding whether the new treatment is
superior to or not better than the control by some clinically relevant
difference. Given pre-specified levels of pairwise (in)commensurability, the
subtrial sample sizes are solved simultaneously. The proposed Bayesian approach
resembles the frequentist formulation of the problem in yielding comparable
sample sizes for circumstances of no borrowing. When borrowing is enabled
between commensurate subtrials, a considerably smaller trial sample size is
required compared to the widely implemented approach of no borrowing. We
illustrate the use of our sample size formulae with two examples based on real
basket trials. A comprehensive simulation study further shows that the proposed
methodology can maintain the true positive and false positive rates at desired
levels.
