Open Access
2024 Multi-label residual weighted learning for individualized combination treatment rule
Qi Xu, Xiaoke Cao, Geping Chen, Hanqi Zeng, Haoda Fu, Annie Qu
Author Affiliations +
Electron. J. Statist. 18(1): 1517-1548 (2024). DOI: 10.1214/24-EJS2236


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 ψ-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.

Funding Statement

This work is supported by National Science Foundation Grants DMS 2210640 and DMS 1952406.


The authors would like to thank the anonymous referees, the Associate Editor and the Editor for their constructive comments that improved the quality of this paper.


Download Citation

Qi Xu. Xiaoke Cao. Geping Chen. Hanqi Zeng. Haoda Fu. Annie Qu. "Multi-label residual weighted learning for individualized combination treatment rule." Electron. J. Statist. 18 (1) 1517 - 1548, 2024.


Received: 1 May 2023; Published: 2024
First available in Project Euclid: 27 March 2024

arXiv: 2310.00864
Digital Object Identifier: 10.1214/24-EJS2236

Primary: 62C12 , 62H30

Keywords: Combination therapy , decision making , difference of convex , Fisher consistency , Precision medicine

Vol.18 • No. 1 • 2024
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