A Bayesian decision-theoretic approach to multiple testing in basket trials

Basket trials evaluate a single treatment across multiple patient subpopulations, posing important multiple testing problems. Motivated by this setting, we propose a novel Bayesian decision-theoretic approach based on a family of loss functions. These functions adaptively penalize false positives and false negatives based on the numbers of true null and alternative hypotheses, making a basket more likely to be identified as promising when others show promise. Estimation of treatment effects remains independent across baskets, avoiding the computational burden of existing hierarchical modeling approaches and allowing straightforward generalization to trials with different endpoints. The degree of borrowing and the conservativeness of decisions are controlled by tuning parameters, which can be calibrated to achieve desired control of frequentist error rates. The optimal Bayes decision rule is derived by minimizing the posterior expected loss and is computationally efficient. Simulation studies demonstrate that the proposed approach exhibits desirable operating characteristics, performing competitively with widely used alternatives. We illustrate its practical utility through an application to a basket trial of vemurafenib.