Bayesian Variable Selection on Small Sample Trial Data via Adaptive Posterior-Informed Shrinkage Prior

Identifying variables associated with clinical endpoints is of much interest in clinical trials. With the rapid growth of cell and gene therapy (CGT) and therapeutics for ultra-rare diseases, there is an urgent need for statistical methods that can detect meaningful associations under severe sample-size constraints. Motivated by data-borrowing strategies for historical controls, we propose the Adaptive Posterior-Informed Shrinkage Prior (APSP), a Bayesian approach that adaptively borrows information from external sources to improve variable-selection efficiency while preserving robustness across plausible scenarios. APSP builds upon existing Bayesian data borrowing frameworks, incorporating data-driven adaptive information selection, structure of mixture shrinkage informative priors and decision making with empirical null to enhance variable selection performances under small sample size. Extensive simulations show that APSP attains better efficiency relative to traditional and popular data-borrowing and Bayesian variable-selection methods while maintaining robustness under linear relationships. We further applied APSP to identify variables associated with peak C-peptide at Day 75 from the Clinical Islet Transplantation (CIT) Consortium study CIT06 by borrowing information from the study CIT07.