Multi-Label Residual Weighted Learning for Individualized Combination Treatment Rule.

Qi Xu, Xiaoke Cao, Geping Chen, Hanqi Zeng, Haoda Fu, Annie Qu

Abstract: Individualizedtreatmentrules(ITRs)havebeenwidelyapplied in many fields such as precision medicine and personalized marketing. Be- yond 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 in- corporating interaction effects among treatments. Specifically, we propose the generalized ψ-loss as a non-convex surrogate in the residual weighted learning framework, offering desirable statistical and computational prop- erties. 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 al- gorithm for efficient computation. Through simulation studies and real- world data applications, we demonstrate the superior performance of the proposed method in recommending combination treatments.