SAM: Self‐adapting mixture prior to dynamically borrow information from historical data in clinical trials

Mixture priors provide an intuitive way to incorporate historical data while accounting for potential prior‐data conflict by combining an informative prior with a noninformative prior. However, prespecifying the mixing weight for each component remains a crucial challenge. Ideally, the mixing weight should reflect the degree of prior‐data conflict, which is often unknown beforehand, posing a significant obstacle to the application and acceptance of mixture priors. To address this challenge, we introduce self‐adapting mixture (SAM) priors that determine the mixing weight using likelihood ratio test statistics or Bayes factors. SAM priors are data‐driven and self‐adapting, favoring the informative (noninformative) prior component when there is little (substantial) evidence of prior‐data conflict. Consequently, SAM priors achieve dynamic information borrowing. We demonstrate that SAM priors exhibit desirable properties in both finite and large samples and achieve information‐borrowing consistency. Moreover, SAM priors are easy to compute, data‐driven, and calibration‐free, mitigating the risk of data dredging. Numerical studies show that SAM priors outperform existing methods in adopting prior‐data conflicts effectively. We developed R package “SAMprior” and web application that are freely available at CRAN and www.trialdesign.org to facilitate the use of SAM priors.