An individualized treatment rule (ITR) is a decision rule that recommends treatments for patients based on their individual feature variables. In many practices, the ideal ITR for the primary outcome is also expected to cause minimal harm to other secondary outcomes. Therefore, our objective is to learn an ITR that not only maximizes the value function for the primary outcome, but also approximates the optimal rule for the secondary outcomes as closely as possible. To achieve this goal, we introduce a fusion penalty to encourage the ITRs based on different outcomes to yield similar recommendations. Two algorithms are proposed to estimate the ITR using surrogate loss functions. We prove that the agreement rate between the estimated ITR of the primary outcome and the optimal ITRs of the secondary outcomes converges to the true agreement rate faster than if the secondary outcomes are not taken into consideration. Furthermore, we derive the non-asymptotic properties of the value function and misclassification rate for the proposed method. Finally, simulation studies and a real data example are used to demonstrate the finite-sample performance of the proposed method.

翻译：个体化治疗规则是一种根据患者个体特征变量推荐治疗方案的决策规则。在实际应用中，针对主要结局的理想治疗规则通常还需尽可能减少对次要结局的不良影响。因此，我们的目标是学习一种既能最大化主要结局的价值函数，又能尽可能逼近次要结局最优规则的治疗规则。为实现这一目标，我们引入融合惩罚项，促使基于不同结局的治疗规则产生相似推荐。本文提出两种算法，通过替代损失函数估计治疗规则。我们证明，相较于未考虑次要结局的情形，基于主要结局估计的治疗规则与次要结局最优治疗规则的一致率能够更快收敛至真实一致率。此外，我们推导了所提方法价值函数与误分类率的非渐近性质。最后通过模拟研究与真实数据实例验证所提方法在有限样本下的表现。