Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters

In regression models with a grouping structure among the explanatory variables, variable selection at the group and within group individual variable level is important to improve model accuracy and interpretability. In this article, we propose a hierarchical bi-level variable selection approach for censored survival data in the linear part of a partially linear additive hazards model where the covariates are naturally grouped. The proposed method is capable of conducting simultaneous group selection and individual variable selection within selected groups. Computational algorithms are developed, and the asymptotic rates and selection consistency of the proposed estimators are established. Simulation results indicate that our proposed method outperforms several existing penalties, for example, LASSO, SCAD, and adaptive LASSO. Application of the proposed method is illustrated with the Mayo Clinic primary biliary cirrhosis (PBC) data.