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：个体化治疗方案（ITRs）已广泛应用于精准医疗和个性化营销等领域。除针对二元或多重治疗的ITR广泛研究外，联合治疗方案的应用也备受关注。本文提出一种融合治疗间交互效应的联合治疗方案ITR估计新方法。具体而言，我们在残差加权学习框架中提出广义ψ-损失作为非凸替代函数，兼具理想的统计与计算特性。统计方面，该替代损失函数的极小化器与最优决策规则具有Fisher一致性，且能纳入任意强度的交互效应——这较现有方法有显著改进。计算方面，所提方法采用凸差算法实现高效计算。通过仿真研究与真实世界数据应用，我们验证了该方法在推荐联合治疗方案中的优越性能。