AbstractCox’s proportional hazard models with time-varying coefficients have much flexibility for modeling the dynamic of covariate effects. Although many variable selection procedures have been developed for Coxs proportional hazard model, the study of such models with time-varying coefficients appears to be limited. The variable selection methods involving nonconvex penalty function, such as the minimax concave penalty (MCP), introduces numerical challenge, but they still have attractive theoretical properties and were indicated that they are worth to be alternatives of other competitive methods. We propose a group MCP method that uses B-spline basis to expand coefficients and maximizes the log partial likelihood with nonconvex penalties on regression coefficients in groups. A fast, iterative group shooting algorithm is carried out for model selection and estimation. Under some appropriate conditions, the simulated example shows that our method performs competitively with the group lasso method. By comparison, the group MCP method and group lasso select the same amount of important covariates, but group MCP method tends to outperform the group lasso method in selection of unimportant covariates.
Use of time-varying coefficients in a Cox regression model when the proportional hazard assumption is violated
