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.