Calibrated Optimal Decision Making with Multiple Data Sources and Limited Outcome

We consider the optimal decision-making problem in a primary sample of interest with multiple auxiliary sources available. The outcome of interest is limited in the sense that it is only observed in the primary sample. In reality, such multiple data sources may belong to different populations and thus cannot be combined directly. This paper proposes a novel calibrated optimal decision rule (CODR) to address the limited outcome, by leveraging the shared pattern in multiple data sources. Under a mild and testable assumption that the conditional means of intermediate outcomes in different samples are equal given baseline covariates and the treatment information, we can show that the calibrated mean outcome of interest under the CODR is unbiased and more efficient than using the primary sample solely. Extensive experiments on simulated datasets demonstrate empirical validity and improvement of the proposed CODR, followed by a real application on the MIMIC-III as the primary sample with auxiliary data from eICU.