A Concave Pairwise Fusion Approach to Subgroup Analysis

Shujie Ma, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)


An important step in developing individualized treatment strategies is correct identification of subgroups of a heterogeneous population to allow specific treatment for each subgroup. This article considers the problem using samples drawn from a population consisting of subgroups with different mean values, along with certain covariates. We propose a penalized approach for subgroup analysis based on a regression model, in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject-specific intercepts. We apply concave penalty functions to pairwise differences of the intercepts. This procedure automatically divides the observations into subgroups. To implement the proposed approach, we develop an alternating direction method of multipliers algorithm with concave penalties and demonstrate its convergence. We also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between groups to recover them. These results provide a sound basis for making statistical inference in subgroup analysis. Our proposed method is further illustrated by simulation studies and analysis of a Cleveland heart disease dataset. Supplementary materials for this article are available online.

Original languageEnglish
Pages (from-to)410-423
Number of pages14
JournalJournal of the American Statistical Association
Issue number517
Publication statusPublished - 2 Jan 2017
Externally publishedYes


  • Asymptotic normality
  • Heterogeneity
  • Inference
  • Linear regression
  • Oracle property

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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