Gao Daiqi, Wang Yuanjia, Zeng Donglin
Harvard University.
Columbia University.
Proc Mach Learn Res. 2024 May;238:712-720.
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.
个性化治疗规则（ITR）是一种基于患者个体特征变量为患者推荐治疗方案的决策规则。在许多实践中，对于主要结局的理想ITR还应尽量减少对其他次要结局的损害。因此，我们的目标是学习一种ITR，它不仅能使主要结局的价值函数最大化，还能尽可能接近次要结局的最优规则。为实现这一目标，我们引入了一种融合惩罚，以鼓励基于不同结局的ITR产生相似的推荐。提出了两种使用替代损失函数估计ITR的算法。我们证明，与不考虑次要结局的情况相比，主要结局的估计ITR与次要结局的最优ITR之间的一致率更快地收敛到真实一致率。此外，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，通过模拟研究和一个实际数据示例来展示所提方法的有限样本性能。
