PS-SAM: propensity-score-integrated self-adapting mixture prior to dynamically and efficiently borrow information from historical data.

There has been growing interest in incorporating historical data to improve the efficiency of randomized controlled trials (RCTs) or reduce their required sample size. A key challenge is that the patient characteristics of the historical data may differ from those of the current RCT. To address this issue, a well-known approach is to employ propensity score matching or inverse probability weighting to adjust for baseline heterogeneity, enabling the incorporation of historical data into the inference of RCT. However, this approach is subject to bias when there are unmeasured confounders. We address this issue by incorporating a self-adapting mixture (SAM) prior with propensity score matching and inverse probability weighting to enable additional adaptation for information borrowing in the presence of unmeasured confounders. The resulting propensity score-integrated SAM (PS-SAM) priors are robust in the sense that if there are no unmeasured confounders, they result in an unbiased causal estimate of the treatment effect; and if there are unmeasured confounders, they provide a notably less biased treatment effect with better-controlled type I error. Simulation studies demonstrate that the PS-SAM prior exhibits desirable operating characteristics enabling adaptive information borrowing. The proposed methodology is freely available as the R package "SAMprior".