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March 2022 Subgroup-effects models for the analysis of personal treatment effects
Ling Zhou, Shiquan Sun, Haoda Fu, Peter X.-K. Song
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Ann. Appl. Stat. 16(1): 80-103 (March 2022). DOI: 10.1214/21-AOAS1503


The emerging field of precision medicine is transforming statistical analysis from the classical paradigm of population-average treatment effects into that of personal treatment effects. This new scientific mission has called for adequate statistical methods to assess heterogeneous covariate effects in regression analysis. This paper focuses on a subgroup analysis that consists of two primary analytic tasks: identification of treatment effect subgroups and individual group memberships, and statistical inference on treatment effects by subgroup. We propose an approach to synergizing supervised clustering analysis via alternating direction method of multipliers (ADMM) algorithm and statistical inference on subgroup effects via expectation-maximization (EM) algorithm. Our proposed procedure, termed as hybrid operation for subgroup analysis (HOSA), enjoys computational speed and numerical stability with interpretability and reproducibility. We establish key theoretical properties for both proposed clustering and inference procedures. Numerical illustration includes extensive simulation studies and analyses of motivating data from two randomized clinical trials to learn subgroup treatment effects.

Funding Statement

Zhou’s research was partially supported by Fund of National Natural Science (Nos. 11901470, 11931014, 11571282, 11829101) and by Fundamental Research Funds for the Central Universities (Nos. JBK190904 and JBK1806002). Sun’s research was partially supported by the National Natural Science Foundation of China (No. 61902319 and No.82122061). Song’s research was partially supported by a National Institutes of Health grant R01ES024732 and National Science Foundation grants DMS1811734 and DMS2113564.


Part of the research was done when Zhou and Sun were postdoctoral research fellows at the Department of Biostatistics, University of Michigan. They appreciate the computing and other logistic support provided by the University of Michigan.


Download Citation

Ling Zhou. Shiquan Sun. Haoda Fu. Peter X.-K. Song. "Subgroup-effects models for the analysis of personal treatment effects." Ann. Appl. Stat. 16 (1) 80 - 103, March 2022.


Received: 1 February 2021; Published: March 2022
First available in Project Euclid: 28 March 2022

Digital Object Identifier: 10.1214/21-AOAS1503

Keywords: ADMM algorithm , EM algorithm , maximum likelihood , Precision medicine , supervised clustering

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 1 • March 2022
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