A treatment regime is a rule that assigns a treatment, among a set of possible treatment options, to a patient as a function of his/her
individual characteristics, hence “personalizing” treatment to the patient. A goal is to identify the optimal treatment regime; that is,
the regime that, if followed by the entire population of patients, would lead to the best outcome on average. Given data from a clinical
trial or observational study, for a single treatment decision, the optimal regime can be found by assuming a regression model for the
expected outcome conditional on observed treatment and covariates, where, for a given set of covariates, the optimal treatment is the one
that yields the most favorable expected outcome. However, clearly, treatment assignment via such a regime is suspect if this regression
model is incorrectly specified.  Even if misspecified, such a regression model defines a class of regimes; moreover, for reasons of
cost, interpretability, or feasibility of implementation, investigators may wish to focus on a class of regimes having a certain
form.  Accordingly, rather than focusing on the optimal regime, we consider finding the optimal regime within a specified class by finding the
regime that optimizes an estimator of overall population mean outcome. To take into account possible confounding in an observational study
and to increase precision, we use a doubly robust augmented inverse probability weighted estimator for this purpose. Simulations and
application to data from a breast cancer clinical trial demonstrate the performance of the method.