Open Access
2022 Estimating individualized treatment rules for treatments with hierarchical structure
Yiwei Fan, Xiaoling Lu, Junlong Zhao, Haoda Fu, Yufeng Liu
Author Affiliations +
Electron. J. Statist. 16(1): 737-784 (2022). DOI: 10.1214/21-EJS1948


Precision medicine is an increasingly important area of research. Due to the heterogeneity of individual characteristics, patients may respond differently to treatments. One of the most important goals for precision medicine is to develop individualized treatment rules (ITRs) involving patients’ characteristics directly. As an interesting topic in clinical research, many statistical methods have been developed in recent years to find optimal ITRs. For binary treatments, outcome weighted learning (OWL) was proposed to find a decision function of patient characteristics maximizing the expected clinical outcome. Treatments with hierarchical structure are commonly seen in practice. In hierarchical scenarios, how to estimate ITRs is still unclear. We propose a new framework named hierarchical outcome-weighted angle-based learning (HOAL) to estimate ITRs for treatments with hierarchical structure. Statistical properties including Fisher consistency and convergence rates of the proposed method are presented. Simulations and an application to a type 2 diabetes study under linear and nonlinear learning show the highly competitive performance of our proposed procedure in both numerical accuracy and computational efficiency.

Funding Statement

Xiaoling Lu’s research was supported in part by the National Natural Science Foundation of China (No. 72171229) and fund for building world-class universities (disciplines) of Renmin University of China. Junlong Zhao’s research was supported in part by National Science Foundation of China, No. 11871104 and No. 12131006. Yufeng Liu’s research was supported in part by NSF grants DMS-1821231 and DMS-2100729, and NIH grant R01GM126550.


The authors would like to thank the Editor, the Associate Editor, and reviewers, whose helpful comments and suggestions led to a much improved presentation.


Download Citation

Yiwei Fan. Xiaoling Lu. Junlong Zhao. Haoda Fu. Yufeng Liu. "Estimating individualized treatment rules for treatments with hierarchical structure." Electron. J. Statist. 16 (1) 737 - 784, 2022.


Received: 1 October 2020; Published: 2022
First available in Project Euclid: 19 January 2022

MathSciNet: MR4366820
zbMATH: 07524940
Digital Object Identifier: 10.1214/21-EJS1948

Keywords: Heterogeneity , hierarchical angle-based classification , Precision medicine , Support Vector Machine

Vol.16 • No. 1 • 2022
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