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(ITR)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ITR通常还要求对次要结局的损害最小化。因此，我们的目标是学习一种ITR，既能最大化主要结局的价值函数，又能尽可能接近次要结局的最优规则。为实现该目标，我们引入融合惩罚项，促使基于不同结局的ITR生成相似推荐。我们提出两种使用替代损失函数估计ITR的算法。理论证明，相比未考虑次要结局的情况，基于主要结局估计的ITR与次要结局最优ITR之间的一致率能更快收敛至真实一致率。进一步，我们推导了所提方法的价值函数和误分类率的非渐近性质。最后，通过模拟研究和真实数据实例验证所提方法的有限样本性能。