  Individualized treatment rules aim to identify if, when, which, and to whom
treatment should be applied. A globally aging population, rising healthcare
costs, and increased access to patient-level data have created an urgent need
for high-quality estimators of individualized treatment rules that can be
applied to observational data. A recent and promising line of research for
estimating individualized treatment rules recasts the problem of estimating an
optimal treatment rule as a weighted classification problem. We consider a
class of estimators for optimal treatment rules that are analogous to convex
large-margin classifiers. The proposed class applies to observational data and
is doubly-robust in the sense that correct specification of either a propensity
or outcome model leads to consistent estimation of the optimal individualized
treatment rule. Using techniques from semiparametric efficiency theory, we
derive rates of convergence for the proposed estimators and use these rates to
characterize the bias-variance trade-off for estimating individualized
treatment rules with classification-based methods. Simulation experiments
informed by these results demonstrate that it is possible to construct new
estimators within the proposed framework that significantly outperform existing
ones. We illustrate the proposed methods using data from a labor training
program and a study of inflammatory bowel syndrome.
