Subgroup Analysis in Censored Linear Regression

Abstract

In the presence of treatment heterogeneity due to unknown grouping information, standard methods assuming homogeneous treatment effects cannot capture the subgroup structure in the population. To accommodate heterogeneity, we propose a concave fusion approach to identifying the subgroup structures as well as estimating treatment effects for 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 the need to know the individual subgroup memberships in advance. The proposed estimation procedure can automatically identify the subgroup structure and simultaneously estimate the subgroup-specific treatment effects. Our new algorithm proceeds through combining the Buckley–James iterative procedure and the alternating direction method of multipliers. The resulting estimators enjoy the oracle property, and simulation studies and real data application demonstrate the good performance of the new method.