Bayesian variable selection on small sample trial data via adaptive posterior-informed shrinkage prior

Identifying variables associated with clinical endpoints is a central objective in clinical trials. With the rapid expansion of cell and gene therapies (CGTs) and therapeutics for ultra-rare diseases, there is an urgent demand for statistical methods capable of detecting 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 framework that adaptively leverages external information to improve variable-selection efficiency while preserving robustness across diverse scenarios. APSP extends existing Bayesian borrowing methods by incorporating data-driven adaptive information selection, mixture shrinkage informative priors, and empirical-null-based decision rules, thereby enhancing variable-selection performance in small-sample settings. Extensive simulations demonstrated that APSP consistently matches or exceeds the efficiency of traditional and widely used Bayesian data-borrowing and variable-selection approaches. Notably, it exhibits strong robustness against possible discrepancies between internal and external data across a broad range of simulation scenarios. Finally, we applied APSP to the Clinical Islet Transplantation (CIT) Consortium, identifying variables associated with peak C-peptide at Day 75 in study CIT-06 by borrowing information from study CIT-07.