Adaptive Constrained Weighted Estimation for Incorporating Multiple External Information Sources

There is growing interest in hybrid control approaches that augment concurrent control data in clinical trials. This study proposes a frequentist method based on constrained weighted maximum likelihood estimation with a concept of effective sample size to borrow information from multiple external sources. The proposed method manages heterogeneity across information sources, while ensuring that the power and the Type I error rate are controlled precisely at nominal levels when all information sources are comparable. The method does not require tuning parameters to be prespecified; instead, the weights assigned to each external information source are dynamically optimized. This study evaluates the operating characteristics of the proposed method under various scenarios through simulations and demonstrates its weighting behavior by numerical examples and an application to clinical trial data. The simulation results show that the proposed method outperforms existing methods and demonstrates greater robustness in many situations. Furthermore, the numerical examples and application highlight its ability to achieve adaptive weighting while maintaining the effective sample size at a prespecified target level.