Consider optimal decision-making problems in a primary sample of interest using multiple available supporting sources. The results of interest are restricted in the sense that they are only observed in primary samples. In practice, multiple such data sources may belong to disparate studies and cannot be directly combined. This paper presents a novel framework for processing heterogeneous samples and simultaneously addressing limited outcomes through new coordinated optimal decision-making methods by leveraging common intermediate results across multiple data sources. I suggest Specifically, our method allows baseline covariates for different samples to have uniform or non-uniform distributions. Under equal conditional means of intermediate outcomes for different samples given baseline covariates and treatment information, the proposed estimator of the conditional average outcome is asymptotically normal, and is better than using only primary samples. is also efficient. Extensive experiments on simulated datasets demonstrate empirical validity and efficiency gains using our approach, followed by practical application to electronic health records.
