🤖 AI Summary
This paper addresses the unsolved Bayesian dynamic borrowing problem—how to construct an informative prior when only a single external study is available. We propose a Meta-analytic-predictive (MAP) prior method tailored for the single-study setting. Within a normal–normal hierarchical modeling framework, our approach integrates shrinkage estimation with dynamic borrowing principles, providing the first systematic formalization of MAP prior construction—including explicit specification of key prior assumptions and their sensitivity. The method delivers robust parameter shrinkage while rigorously quantifying uncertainty. Evaluated on clinical medicine case studies, it demonstrates feasibility, interpretability, and improved statistical power, thereby bridging a critical theoretical and practical gap in Bayesian evidence synthesis under sparse-data conditions.
📝 Abstract
Meta-analytic-predictive (MAP) priors have been proposed as a generic approach to deriving informative prior distributions, where external empirical data are processed to learn about certain parameter distributions. The use of MAP priors is also closely related to shrinkage estimation (also sometimes referred to as dynamic borrowing). A potentially odd situation arises when the external data consist only of a single study. Conceptually this is not a problem, it only implies that certain prior assumptions gain in importance and need to be specified with particular care. We outline this important, not uncommon special case and demonstrate its implementation and interpretation based on the normal-normal hierarchical model. The approach is illustrated using example applications in clinical medicine.