Abstract
Subgroups occur naturally in a large variety of data sets and data analysis. For example, how do we estimate the efficacy of immunotherapy in different molecular subtypes of lung cancer? How do we estimate the response rate of a targeted therapy in a basket trial with different types of cancer? Bayesian hierarchical model (BHM) has been widely used in synthesizing information across subgroups. The typical assumption of exchangeability is very restricted and often does not hold. Efforts have been made in clustering the subgroups first, then, assuming exchangeability within cluster and borrowing information across subgroups within the same cluster. The two-step procedure has two main challenges: (1) How to determine the number of clusters? And (2) How much information to borrow within each cluster? To address these two interconnected challenges, we propose two distribution-free overlapping indices, namely, the overlapping clustering index for identifying the optimal clustering result and the overlapping borrowing index for assigning proper borrowing strength to clusters. Accordingly, we develop a new method BHMOI (Bayesian hierarchical model with overlapping indices). BHMOI includes a novel weighted K-Means clustering algorithm to obtain optimal clustering results, and an innate way to dynamically determining the borrowing strength in each cluster. BHMOI can achieve efficient and robust information borrowing with desirable properties. Examples and simulation studies are provided to demonstrate the effectiveness of BHMOl in heterogeneity identification and dynamic information borrowing.