The field of precision medicine aims to tailor treatment based on patient-specific factors in a reproducible way. To this end, estimating an optimal individualized treatment regime (ITR) that recommends treatment decisions based on patient characteristics to maximize the mean of a pre-specified outcome is of particular interest. Several methods have been proposed for estimating an optimal ITR from clinical trial data in the parallel group setting where each subject is randomized to a single intervention. However, little work has been done in the area of estimating the optimal ITR from crossover study designs. Such designs naturally lend themselves to precision medicine, because they allow for observing the response to multiple treatments for each patient. In this paper, we introduce a method for estimating the optimal ITR using data from a 2x2 crossover study with or without carryover effects. The proposed method is similar to policy search methods such as outcome weighted learning; however, we take advantage of the crossover design by using the difference in responses under each treatment as the observed reward. We establish Fisher and global consistency, present numerical experiments, and analyze data from a feeding trial to demonstrate the improved performance of the proposed method compared to standard methods for a parallel study design.
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