Structure Identification in Varying-Coefficient Partially Linear Accelerated Failure Time Models via the Group MCP

Abstract

The accelerated failure time (AFT) model is commonly used for the analysis of survival data in the presence of right censored due to the interpretability. In some practical cases, especially when some covariates are time-related, it is not realistic to assume the linear predictors in the AFT model. We propose a varying-coefficient partially linear AFT model for right censored data, allowing the nonlinear effects of covariates. To tackle challenges in estimation, we propose a penalized profile likelihood approach which utilizes a group minimax concave penalty to determine the nonlinear effects of covariates. Under the suitable conditions, we show that the proposed method can correctly select linear components and nonlinear components with high probability. Simulation results demonstrate the satisfactory performance of the proposed method in finite sample cases.