Scale‐Transformed Power Priors for External Data Integration in Longitudinal Studies

Incorporating external data can improve precision in longitudinal studies, but effective borrowing requires that information from different studies be comparable. Within a Bayesian framework, power priors are widely used for external data integration through likelihood discounting. However, they assume that parameters are on a common information scale. In longitudinal settings, differences in follow-up duration, measurement variability, and correlation structure, along with random effects, can lead to differences in effective Fisher information across studies. This complicates parameter comparability and poses challenges for existing methods, which can result in biased or inefficient inference. We propose a scale-transformed power prior for external data integration in longitudinal studies. The method is developed within a linear mixed-effects modeling framework and rescales historical parameters to the current study scale using Fisher information before borrowing. Conditional Fisher information accounts for unobserved random effects and adjusts for study-specific variability. To address differences in variability and correlation structure, we implement a partial borrowing strategy that applies borrowing to fixed effects while allowing variance components to remain study-specific. We introduce a generalized formulation with an additive adjustment component to allow for remaining differences after scaling. Theoretical results characterize how differences in information scale lead to bias under conventional power priors and establish conditions under which the proposed method improves bias and precision. Simulation studies demonstrate improved performance and provide guidance on settings where scale transformation is beneficial. An application to prostate cancer clinical trial data demonstrates the importance of the proposed method.