Personalized medicine, a paradigm of medicine tailored to a patient's characteristics, is an increasingly attractive field in health care. An important goal of personalized medicine is to identify a subgroup of patients, based on baseline covariates, that benefits more from the targeted treatment than other comparative treatments. Most of the current subgroup identification methods only focus on obtaining a subgroup with an enhanced treatment effect without paying attention to subgroup size. Yet, a clinically meaningful subgroup learning approach should identify the maximum number of patients who can benefit from the better treatment. In this paper, we present an optimal subgroup selection rule (SSR) that maximizes the number of selected patients, and in the meantime, achieves the pre-specified clinically meaningful mean outcome, such as the average treatment effect. We derive two equivalent theoretical forms of the optimal SSR based on the contrast function that describes the treatment-covariates interaction in the outcome. We further propose a ConstrAined PolIcy Tree seArch aLgorithm (CAPITAL) to find the optimal SSR within the interpretable decision tree class. The proposed method is flexible to handle multiple constraints that penalize the inclusion of patients with negative treatment effects, and to address time to event data using the restricted mean survival time as the clinically interesting mean outcome. Extensive simulations, comparison studies, and real data applications are conducted to demonstrate the validity and utility of our method.

翻译：个性化医疗是一种根据患者特征量身定制的医疗范式，在医疗保健领域日益受到关注。个性化医疗的重要目标之一是，基于基线协变量，识别出相较于其他对照治疗更能从靶向治疗中获益的患者亚组。当前大多数亚组识别方法仅关注获取具有增强治疗效果的亚组，而未考虑亚组规模。然而，具有临床意义的亚组学习方法应能识别出可从更优治疗中获益的最大患者数量。本文提出了一种最优亚组选择规则（SSR），该规则在最大化所选患者数量的同时，能够实现预先指定的具有临床意义的平均结局（如平均治疗效果）。我们基于描述结局中治疗-协变量交互作用的对比函数，推导出了最优SSR的两种等价理论形式。进一步地，我们提出了一种约束策略树搜索算法（CAPITAL），用于在可解释的决策树类别中寻找最优SSR。该方法具有灵活性，可处理多个约束条件（用于惩罚纳入具有负治疗效应的患者），并可通过将限制平均生存时间作为具有临床意义的平均结局来处理时间至事件数据。通过大量模拟研究、对比分析及真实数据应用，验证了我们方法的有效性与实用性。