Because many illnesses show heterogeneous response to treatment, there is
increasing interest in individualizing treatment to patients [Arch. Gen.
Psychiatry 66 (2009) 128--133]. An individualized treatment rule is a decision
rule that recommends treatment according to patient characteristics. We
consider the use of clinical trial data in the construction of an
individualized treatment rule leading to highest mean response. This is a
difficult computational problem because the objective function is the
expectation of a weighted indicator function that is nonconcave in the
parameters. Furthermore, there are frequently many pretreatment variables that
may or may not be useful in constructing an optimal individualized treatment
rule, yet cost and interpretability considerations imply that only a few
variables should be used by the individualized treatment rule. To address these
challenges, we consider estimation based on $l_1$-penalized least squares. This
approach is justified via a finite sample upper bound on the difference between
the mean response due to the estimated individualized treatment rule and the
mean response due to the optimal individualized treatment rule.

利用临床试验数据构建个体化治疗规则，采用基于 $l_{1}$- 惩罚最小二乘的估计方法，并找到最高的平均反应率。