Optimal Bayesian hierarchical model to accelerate the development of tissue-agnostic drugs and basket trials

Tissue-agnostic trials and basket trials enroll patients based on their genetic biomarkers, not tumor type, in an attempt to determine if a new drug can successfully treat disease conditions based on biomarkers. The Bayesian hierarchical model (BHM) provides an attractive approach to design phase II tissue-agnostic trials by allowing information borrowing across multiple disease types. In this article, we elucidate two intrinsic and inevitable issues that may limit the use of BHM to tissue-agnostic trials: sensitivity to the prior specification of the shrinkage parameter and the competing "interest" among disease types in increasing power and controlling type I error. To address these issues, we propose the optimal BHM (OBHM) and clustered OBHM (COBHM) approaches. In these approach, we first specify a flexible utility function to quantify the tradeoff between type I error and power across disease types based on the study objectives, and then we select the prior of the shrinkage parameter to optimize the utility function of clinical and regulatory interest. COBHM further utilizes a simple Bayesian rule to cluster tumor types into sensitive and insensitive subgroups to achieve more accurate information borrowing. Simulation study shows that the OBHM and especially COBHM have desirable operating characteristics, outperforming some existing methods. COBHM effectively balances power and type I error, addresses the sensitivity of the prior selection, and reduces the "unwarranted" subjectivity in the prior selection. It provides a systematic, rigorous way to apply BHM and solve the common problem of blindingly using a non-informative inverse-gamma prior (with a large variance) or priors arbitrarily chosen that may lead to problematic statistical properties.