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.

在解释变量之间具有分组结构的回归模型中，组内和组内单个变量级别的变量选择对​​于提高模型的准确性和可解释性很重要。在本文中，我们提出了一种针对部分线性累加危害模型的线性部分中被审查的生存数据的分级双层变量选择方法，在该线性部分中，协变量已自然分组。所提出的方法能够在选择的组内同时进行组选择和个体变量选择。开发了计算算法，并建立了估计量的渐近率和选择一致性。仿真结果表明，我们提出的方法优于现有的几种惩罚，例如LASSO，SCAD和自适应LASSO。