Exploration of Heterogeneous Treatment Effects via Concave Fusion

• Published in: The international journal of biostatistics Vol. 16; no. 1
• Main Authors: Ma, Shujie, Huang, Jian, Zhang, Zhiwei, Liu, Mingming
• Format: Journal Article
• Language: English
• Published: Germany De Gruyter 20.09.2019; Walter de Gruyter GmbH
• Subjects: Anti-HIV Agents - pharmacology; Biostatistics; Computer Simulation; fusiongram; HIV Infections - drug therapy; Humans; Models, Statistical; oracle property; penalized least squares; Precision Medicine; Randomized Controlled Trials as Topic; subgroup analysis; treatment heterogeneity; penalized least squares; fusiongram; treatment heterogeneity; subgroup analysis; oracle property
• ISSN: 2194-573X; 1557-4679; 1557-4679
• DOI: 10.1515/ijb-2018-0026

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 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 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.