A concave pairwise fusion approach to subgroup analysis

TL;DR

This paper introduces a penalized regression approach using concave pairwise fusion to automatically identify subgroups with different means in heterogeneous populations, facilitating personalized treatment strategies.

Contribution

It proposes a novel concave penalty-based method for subgroup detection that automatically partitions data and provides theoretical guarantees for subgroup recovery.

Findings

Method effectively identifies subgroups in simulations.

Algorithm converges reliably with theoretical support.

Applied successfully to Cleveland heart disease data.

Abstract

An important step in developing individualized treatment strategies is to correctly identify subgroups of a heterogeneous population, so that specific treatment can be given to each subgroup. In this paper, we consider the situation with samples drawn from a population consisting of subgroups with different means, 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. We develop an alternating direction method of multipliers algorithm with concave penalties to implement the proposed approach 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 in order 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 the Cleveland heart disease dataset.