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We consider the optimal decision-making problem in a primary sample ofinterest with multiple auxiliary sources available. The outcome of interest islimited in the sense that it is only observed in the primary sample. Inreality, such multiple data sources may belong to heterogeneous studies andthus cannot be combined directly. This paper proposes a new framework to handleheterogeneous samples and address the limited outcome simultaneously through anovel calibrated optimal decision-making method, by leveraging the commonintermediate outcomes in multiple data sources. Specifically, our method allowsthe baseline covariates across different samples to have either homogeneous orheterogeneous distributions. Under the equal conditional means of intermediateoutcomes in different samples given baseline covariates and the treatmentinformation, we show that the proposed estimator of the conditional meanoutcome is asymptotically normal and more efficient than using the primarysample solely. Extensive experiments on simulated datasets demonstrateempirical validity and improved efficiency using our approach, followed by areal application to electronic health records.

Calibrated Optimal Decision Making with Multiple Data Sources and Limited Outcome