Augmenting the Control Arm of Randomized Trials by Incorporating Multiple External Data Sources Using Propensity Score Stratification and Data-Driven Mixture Prior

To enhance efficiency in drug development, interest in augmenting randomized controlled trials by supplementing the control arm with external data has grown rapidly. However, external data may lack between-population exchangeability. To facilitate proper information borrowing, we propose two two-stage strategies: the stratified propensity score self-adaptive mixture (SPS-SAM) prior and stratified propensity score calibrated elastic mixture (SPS-CEM) prior. The mixture prior is composed of an informative meta-analytic predictive (MAP) prior and a vague prior. In the first stage, propensity scores (PS) stratification is performed to select similar subjects from external data. Within each stratum, to mitigate the measured confounding, we calculate the PS overlap coefficient to account for the between-group heterogeneity by adjusting the hyperparameters of the MAP prior. In the second stage, to reduce unmeasured confounding and address potential prior-data conflict, we construct a data-driven mixture prior incorporating an adaptive weight that dynamically controls the proportion of the MAP prior. To obtain the adaptive weight measuring the extent of congruence between the current and the external data, SPS-SAM prior uses the likelihood ratio test and SPS-CEM prior uses the scaled t-test, respectively. Compared with existing methods, simulations studies and illustrative examples demonstrate the superior features of the proposed methods. Both proposed methods outperform existing methods by yielding smaller bias, greater calibrated power, and achieving accurate, efficient, and robust estimation of the treatment effect.