  Precision medicine is of considerable interest in clinical, academic and
regulatory parties. The key to precision medicine is the optimal treatment
regime. Recently, Zhou et al. (2017) developed residual weighted learning (RWL)
to construct the optimal regime that directly optimize the clinical outcome.
However, this method involves computationally intensive non-convex
optimization, which cannot guarantee a global solution. Furthermore, this
method does not possess fully semiparametrical efficiency. In this article, we
propose augmented outcome-weighted learning (AOL). The method is built on a
doubly robust augmented inverse probability weighted estimator, and hence
constructs semiparametrically efficient regimes. Our proposed AOL is closely
related to RWL. The weights are obtained from counterfactual residuals, where
negative residuals are reflected to positive and accordingly their treatment
assignments are switched to opposites. Convex loss functions are thus applied
to guarantee a global solution and to reduce computations. We show that AOL is
universally consistent, i.e., the estimated regime of AOL converges the Bayes
regime when the sample size approaches infinity, without knowing any specifics
of the distribution of the data. We also propose variable selection methods for
linear and nonlinear regimes, respectively, to further improve performance. The
performance of the proposed AOL methods is illustrated in simulation studies
and in an analysis of the Nefazodone-CBASP clinical trial data.
