Leveraging external evidence using Bayesian hierarchical model and propensity score in the presence of covariates

In recent decades, there has been growing interest in leveraging external data information for clinical devel-opment as it improves the efficiency of the design and inference of clinical trials when utilized properly and more importantly, alleviates potential ethical and recruitment challenges. When it is of interest to augment the con-current study's control arm using external control data, the potential outcome heterogeneity across data sources, also known as prior-data conflict, should be accounted for. In addition, in the outcome modeling, inclusion of prognostic covariates that may have impact on the outcome can avoid efficiency loss or potential bias. In this paper, we propose a Bayesian hierarchical modeling strategy incorporating covariate-adjusted meta-analytic predictive approach (cMAP) and also introduce a propensity score (PS) based sequential procedure that in-tegrates the cMAP. In the simulation study, the proposed methods are found to have advantages in the esti-mation, power, and type I error control over the standard methods such as PS matching alone and hierarchical modeling that ignores the covariates. An illustrative example is used to illustrate the procedure.