  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 to achieve this
goal is that we usually do not have a priori knowledge of the grouping
information of patients with respect to treatment. To address this problem, we
consider a heterogeneous regression model by assuming that the coefficient for
treatment variables are subject-dependent and belong to different subgroups
with unknown grouping information. We develop a concave fusion penalized method
for automatically 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 with 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 based on the proposed method. We evaluate
the performance of the proposed method by simulation studies and illustrate its
application by analyzing the data from the AIDS Clinical Trials Group Study.
