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：个体化治疗方案（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。在许多实践中，针对主要结果的理想ITR还需对次要结果造成最小损害。因此，我们的目标是学习一种ITR，该方案不仅能最大化主要结果的价值函数，还能尽可能接近次要结果的最优规则。为实现此目标，我们引入融合惩罚项，以促使基于不同结果生成的ITR产生相似的治疗建议。通过代理损失函数，我们提出了两种算法来估计ITR。我们证明，与未考虑次要结果的情况相比，主要结果估计ITR与次要结果最优ITR的一致性率收敛到真实一致性率的速度更快。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，通过模拟研究和真实数据示例验证了所提方法的有限样本性能。