Overlapping Indices for Dynamic Information Borrowing in Bayesian Hierarchical Modeling

Information borrowing has received increasing attention in multiple subgroups data analysis. Bayesian hierarchical models (BHMs) are widely used in this field. However, the common exchangeability assumption becomes questionable when heterogeneity exists across subgroups. Although various methods have been developed to address this issue—focusing on two key questions: how to accurately identify heterogeneity and how to appropriately borrow information—two core challenges remain: (a) balancing the tradeoff between increasing subgroup homogeneity (exchangeability) and keeping the efficiency and robustness of information borrowing, and (b) dynamically determining borrowing strength based on the varying levels of homogeneity. To address these challenges, we propose a cluster-based framework called the Bayesian Hierarchical Model with Overlapping Indices (BHMOI). BHMOI incorporates two novel indices: the Overlapping Clustering Index (OCI), which facilitates optimal clustering, and the Overlapping Borrowing Index (OBI), which guides the assignment of borrowing strength based on cluster-specific homogeneity. BHMOI is a flexible framework that can accommodate different data types and enables efficient, robust information borrowing with desirable properties. Simulation studies and real data analysis demonstrate the effectiveness and practical utility of BHMOI. Supplementary materials for this article are available online.