Variable selection in Cox regression models with varying coefficients

•We have established the sparsity and the oracle property of the group SCAD estimator for high-dimensional time-varying Cox regression models.•We have also established the sparsity and the improved convergence rate of the adaptive group Lasso estimator.•We have incorporated time-dependent covariates explicitly under simple and interpretable assumptions.•We have carried out some simulation studies and one real data analysis.

We deal with Cox regression models with varying coefficients. In this paper we concentrate on time-varying coefficient models and just give a brief comment on another kind of varying coefficient model. When we have p-dimensional covariates and p increases with the sample size, it is often the case that only a small part of the covariates are relevant. Therefore we consider variable selection and estimation of the coefficient functions by using the group SCAD-type estimator and the adaptive group Lasso estimator. We examine the theoretical properties of the estimators, especially the L2 convergence rate, the sparsity, and the oracle property. Simulation studies and a real data analysis show the performance of these procedures.