A Generalized Bayesian Hierarchical Model in Basket Trials

Basket trials in oncology assess one treatment simultaneously on multiple cancer histologies that share a common genomic aberration. A Bayesian hierarchical model (BHM) first proposed by Thall et al. is widely used to borrow information across multiple cancer types in a basket trial. However, this BHM fails to adaptively determine the strength of borrowing and can lead to substantial inflation of Type I error when treatment effects vary by subgroups. Variations of the BHM accounting for heterogeneity have been proposed, some of which are through modifications of the exchangeability assumption of BHM or calibrations of the variance parameter in the BHM. We propose a generalized Bayesian hierarchical model (GBHM), which relaxes the assumption for the variance parameter in the BHM. We perform extensive comparisons to existing BHM variants under four simulation studies, which are based on the same setup as in the respective articles where the BHM variants were proposed. We investigate GBHM employing Inverse-Gamma (IG) and Cauchy priors with various hyperparameters. Simulation studies show that GBHM with certain choices of priors is robust to treatment effect heterogeneity. We recommend GBHM with IG(0.01,0.01) prior for slightly liberal information borrowing if Type I error control is not the main concern and GBHM with Cauchy(25) prior for conservative borrowing otherwise. A tremendous advantage of the GBHM is that it is very simple to implement and complicated prior specification is not needed, whereas current existing approaches may require careful tuning of the prior hyperparameters.