Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 112, Issue 517, Pages 410-423Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2016.1148039
Keywords
Asymptotic normality; Heterogeneity; Inference; Linear regression; Oracle property
Categories
Funding
- U.S. NSF [DMS-13-06972, DMS-12-08225]
- Hellman Fellowship
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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.
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