Abstract: In the presence of treatment heterogeneity due to unknown grouping information, standard methods that assume homogeneous treatment effects cannot capture the subgroup structure in the population. To accommodate such heterogeneity, we propose a concave fusion approach to identifying the subgroup structures and estimating the treatment effects for a semiparametric linear regression with censored data. In particular, the treatment effects are subject-dependent and subgroup-specific, and our concave fusion penalized method conducts the subgroup analysis without needing to know the individual subgroup memberships in advance. The proposed estimation procedure automatically identifies the subgroup structure and simultaneously estimates the subgroup-specific treatment effects. The proposed algorithm combines the Buckley-James iterative procedure and the alternating direction method of multipliers. The resulting estimators enjoy the oracle property, and simulation studies and a real-data application demonstrate the good performance of the proposed method.

Key words and phrases: Concave penalization, oracle property, subgroup analysis, survival data, treatment heterogeneity.