In this study, we compared two groups, in which subjects were assigned to either the treatment or the control group. In such trials, if the efficacy of the treatment cannot be demonstrated in a population that meets the eligibility criteria, identifying the subgroups for which the treatment is effective is desirable. Such subgroups can be identified by estimating heterogeneous treatment effects (HTE). In recent years, methods for estimating HTE have increasingly relied on complex models. Although these models improve the estimation accuracy, they often sacrifice interpretability. Despite significant advancements in the methods for continuous or univariate binary outcomes, methods for multiple binary outcomes are less prevalent, and existing interpretable methods, such as the W-method and A-learner, while capable of estimating HTE for a single binary outcome, still fail to capture the correlation structure when applied to multiple binary outcomes. We thus propose two methods for estimating HTE for multiple binary outcomes: one based on the W-method and the other based on the A-learner. We also demonstrate that the conventional A-learner introduces bias in the estimation of the treatment effect. The proposed method employs a framework based on reduced-rank regression to capture the correlation structure among multiple binary outcomes. We correct for the bias inherent in the A-learner estimates and investigate the impact of this bias through numerical simulations. Finally, we demonstrate the effectiveness of the proposed method using a real data application.

翻译：在本研究中，我们比较了两组受试者，其中受试者被分配至治疗组或对照组。在此类试验中，若治疗在符合资格标准的总体中无法证明其有效性，则识别治疗对其有效的亚组是必要的。此类亚组可通过估计异质性处理效应（HTE）来识别。近年来，HTE估计方法日益依赖于复杂模型。尽管这些模型提高了估计精度，但往往牺牲了可解释性。尽管针对连续或单变量二元结局的方法已取得显著进展，但针对多重二元结局的方法仍较为少见，且现有的可解释方法（如W-方法与A-学习器）虽能估计单一二元结局的HTE，但在应用于多重二元结局时仍无法捕捉其相关性结构。因此，我们提出了两种估计多重二元结局HTE的方法：一种基于W-方法，另一种基于A-学习器。我们还证明了传统A-学习器在处理效应估计中会引入偏差。所提出的方法采用基于降秩回归的框架来捕捉多重二元结局间的相关性结构。我们校正了A-学习器估计中固有的偏差，并通过数值模拟研究了该偏差的影响。最后，我们通过实际数据应用证明了所提出方法的有效性。