  Personalized medicine has received increasing attention among statisticians,
computer scientists, and clinical practitioners. A major component of
personalized medicine is the estimation of individualized treatment rules
(ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL)
to construct ITRs that directly optimize the clinical outcome. Although OWL
opens the door to introducing machine learning techniques to optimal treatment
regimes, it still has some problems in performance. In this article, we propose
a general framework, called Residual Weighted Learning (RWL), to improve finite
sample performance. Unlike OWL which weights misclassification errors by
clinical outcomes, RWL weights these errors by residuals of the outcome from a
regression fit on clinical covariates excluding treatment assignment. We
utilize the smoothed ramp loss function in RWL, and provide a difference of
convex (d.c.) algorithm to solve the corresponding non-convex optimization
problem. By estimating residuals with linear models or generalized linear
models, RWL can effectively deal with different types of outcomes, such as
continuous, binary and count outcomes. We also propose variable selection
methods for linear and nonlinear rules, respectively, to further improve the
performance. We show that the resulting estimator of the treatment rule is
consistent. We further obtain a rate of convergence for the difference between
the expected outcome using the estimated ITR and that of the optimal treatment
rule. The performance of the proposed RWL methods is illustrated in simulation
studies and in an analysis of cystic fibrosis clinical trial data.
