Standardized Dynamic Borrowing: Uniform Control of Information Borrowing

Abstract: Dynamic borrowing can improve efficiency in clinical trials using external information, but existing methods may not offer transparent, prespecified control over borrowing. We introduce Standardized Dynamic Borrowing (SDB), which combines a source-informed component with a no-borrowing component and updates their relative odds using a Bayes factor standardized by its supremum over admissible target data. The posterior density under the no-borrowing component is obtained by normalizing the target-data likelihood. The prespecified source-component initial weight is a sharp uniform upper bound on its posterior weight, providing an interpretable borrowing constraint. When source and target models belong to the same one-parameter canonical exponential family, posterior expected local-information-ratio effective sample size equals target sample size plus borrowed source-prior effective sample size minus a nonnegative heterogeneity penalty. For normally distributed outcomes, borrowing depends on a standardized source-target conflict $Z$-score and decreases according to a standard normal kernel. We also jointly select the initial weight and target sample size to meet prespecified power and Type I error requirements. Normal and binomial illustrations demonstrate how SDB translates source-target compatibility into data-adaptive borrowing and how the calibration procedure prespecifies the source-component initial weight and target sample size under operating-characteristic constraints. These results provide a transparent framework for prespecifying, controlling, and interpreting dynamic borrowing.