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：个性化治疗规则（ITRs）已广泛应用于精准医疗、个性化营销等领域。除了针对二元或多重治疗的ITR研究外，联合治疗的应用也备受关注。本文提出了一种考虑治疗间交互效应的新型联合治疗ITR估计方法。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，兼具优良的统计与计算特性。统计上，所提替代函数的最小化器在任意交互强度下均与最优决策规则保持Fisher一致性——这一改进显著优于现有方法。计算上，该方法采用差分凸算法实现高效求解。通过模拟研究与实际数据应用，我们证明了所提方法在推荐联合治疗方案方面的优越性能。