Penalized variable selection procedure for Cox models with semiparametric relative risk

TL;DR

This paper introduces a penalized variable selection method for Cox models with semiparametric relative risk, combining smoothing splines and penalties like SCAD or adaptive LASSO to estimate parameters and select variables effectively.

Contribution

It proposes a novel penalized partial likelihood approach that simultaneously estimates and selects variables in both parametric and nonparametric components of Cox models with semiparametric relative risk.

Findings

Estimator of parametric part has oracle property

Nonparametric estimator achieves optimal convergence rate

Method performs well in simulations and real data analysis

Abstract

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts. Two penalties are applied sequentially. The first penalty, governing the smoothness of the multivariate nonlinear covariate effect function, provides a smoothing spline ANOVA framework that is exploited to derive an empirical model selection tool for the nonparametric part. The second penalty, either the smoothly-clipped-absolute-deviation (SCAD) penalty or the adaptive LASSO penalty, achieves variable selection in the parametric part. We show that the resulting estimator of the parametric part possesses the oracle property, and that the estimator of the nonparametric part achieves the optimal rate of convergence. The proposed procedures are shown to work well in simulation experiments, and then applied to a real data example on sexually transmitted diseases.