Exploration of Heterogeneous Treatment Effects via Concave Fusion

Ma Shujie (), Zhang Zhiwei (), Huang Jian () and Liu Mingming ()
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Zhang Zhiwei: Department of Statistics, University of California at Riverside, Riverside, California 92521, USA
Huang Jian: Department of Statistics and Actuarial Science, University of Iowa, Iowa City, USA
Liu Mingming: Department of Statistics, University of California at Riverside, Riverside, California, USA

The International Journal of Biostatistics, 2020, vol. 16, issue 1, 26

Abstract: Understanding treatment heterogeneity is essential to the development of precision medicine, which seeks to tailor medical treatments to subgroups of patients with similar characteristics. One of the challenges of achieving this goal is that we usually do not have a priori knowledge of the grouping information of patients with respect to treatment effect. To address this problem, we consider a heterogeneous regression model which allows the coefficients for treatment variables to be subject-dependent with unknown grouping information. We develop a concave fusion penalized method for estimating the grouping structure and the subgroup-specific treatment effects, and derive an alternating direction method of multipliers algorithm for its implementation. We also study the theoretical properties of the proposed method and show that under suitable conditions there exists a local minimizer that equals the oracle least squares estimator based on a priori knowledge of the true grouping information with high probability. This provides theoretical support for making statistical inference about the subgroup-specific treatment effects using the proposed method. The proposed method is illustrated in simulation studies and illustrated with real data from an AIDS Clinical Trials Group Study.

Keywords: fusiongram; oracle property; penalized least squares; subgroup analysis; treatment heterogeneity (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/ijb-2018-0026

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