Large medical data collected from clinical trials and observational studies often exhibit heterogeneity due to various reasons, such as difference in geographical locations as commonly seen in multi-center studies. Due to the heterogeneity in data, the optimal treatment decision might vary across patients from different study populations. As such, it becomes crucial to appropriately account for data heterogeneity when deriving the optimal treatment regime for achieving the best clinical outcome of interest. In this work, we propose a novel maximin-projection learning for estimating a single treatment decision rule that works reliably for patients across different subgroups. Based on the estimated optimal treatment regime for all subgroups, the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming (QCLP) problem, which can be efficiently computed by the interior-point method. Consistency and asymptotic normality of the estimator are established. Numerical examples show the reliability and effectiveness of the proposed methodology.
