Individualized treatment rules (ITRs) have been widely applied in many fields such as precision medicine and personalized marketing. Beyond the extensive studies on ITR for binary or multiple treatments, there is considerable interest in applying combination treatments. This paper introduces a novel ITR estimation method for combination treatments incorporating interaction effects among treatments. Specifically, we propose the generalized $\psi$-loss as a non-convex surrogate in the residual weighted learning framework, offering desirable statistical and computational properties. Statistically, the minimizer of the proposed surrogate loss is Fisher-consistent with the optimal decision rules, incorporating interaction effects at any intensity level - a significant improvement over existing methods. Computationally, the proposed method applies the difference-of-convex algorithm for efficient computation. Through simulation studies and real-world data applications, we demonstrate the superior performance of the proposed method in recommending combination treatments.

翻译：个体化治疗规则（ITRs）已广泛应用于精准医疗和个性化营销等领域。除了针对二元或多重治疗的ITR广泛研究外，联合治疗应用也备受关注。本文提出了一种新的联合治疗ITR估计方法，纳入治疗间的交互效应。具体而言，我们在残差加权学习框架中提出了广义$\psi$-损失作为非凸替代函数，具有理想的统计和计算性质。统计上，所提替代函数的极小化器与最优决策规则在Fisher意义上保持一致，能够纳入任意强度水平的交互效应——这是对现有方法的显著改进。计算上，所提方法采用差异凸算法进行高效计算。通过仿真研究和实际数据应用，我们证明了所提方法在推荐联合治疗方面的优越性能。