Hierarchically penalized additive hazards model with diverging number of parameters

In many applications, covariates can be naturally grouped. For example, for gene expression data analysis, genes belonging to the same pathway might be viewed as a group. This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped. A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level. For the situations in which the number of parameters tends to ∞ as the sample size increases, we establish an oracle property and asymptotic normality property of the proposed estimators. Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso, smoothly clipped absolute deviation (SCAD) and adaptive lasso.