The power prior approach has been widely used in decision-making processes across various fields where historical data is available. However, its application in process validation—a critical step in pharmaceutical manufacturing to ensure product quality and safety—remains limited, particularly in partial borrowing of historical information from early development batches. This manuscript addresses this gap by formulating and evaluating three classes of partial borrowing power priors: (PBPP1) a partial borrowing power prior with a fixed discounting parameter, (PBPP2) an unnormalized partial borrowing power prior with a random discounting parameter, and (PBPP3) a normalized partial borrowing power prior with a random discounting parameter. A Bayesian linear mixed model is employed for each class to account for both intra-batch and inter-batch variability in drug product potency. These methods are illustrated with simulated data based on real drug product data to provide a framework for leveraging historical data in process validation and to determine the number of samples per batch required to adequately characterize intra-batch variability for process performance qualification (PPQ). By modeling relevant data and conducting a simulation study, we confirm the limitations of PBPP1 and PBPP2 in addressing discrepancies between historical and current data, while demonstrating that PBPP3 effectively handles potential incompatibilities between historical and current data and makes inferences regarding the discounting parameter.
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