  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.
