Mitigating propensity score model misspecification with multiply robust weights when leveraging external data

Propensity score-integrated Bayesian dynamic borrowing methods offer an effective approach for covariate adjustment when using external data to augment randomized controlled trials (RCTs). However, identifying the correct propensity score model can be challenging due to unknown treatment selection processes, potentially leading to model misspecification and biased estimates. To improve robustness to model misspecification, we propose an innovative Bayesian inference procedure that incorporates multiply robust weights into the construction of informative power priors. Specifically, we specify a set of candidate propensity score models to derive multiply robust weights, balancing covariates between the current data and external data. The weighted external data is then incorporated into the analysis using a Bayesian power prior method. We further extend this approach to leverage multiple external datasets. Simulation studies indicate that when the set of postulated propensity score models include a correctly specified model, the proposed method achieves desirable operating characteristics, including low bias, low root mean squared error (RMSE), controlled type I error rate at the predetermined nominal level, and high statistical power. This method also provides a robust strategy for researchers who may have a difficult time developing or selecting a single propensity score model.