Variable Selection And Estimation For Semi-parametric Additive Hazard Model With High-dimensional Covariates

In this paper, we consider the problem of variable selection and estimation for constant-coefficient and varying-coefficient semi-parametric additive hazard model both in ordinary setting and “small n, large p” setting. In the variable selection and estimation for semi-parametric additive hazard model, simulations and real data analysis are present to demonstrate the performance of penalty functions of the least absolute shrinkage and selection operator(Lasso) penalty, the smoothly clipped absolute deviation(SCAD) penalty and the minimax concave penalty(MCP) based on coordinate descent algorithms(CCD). As for the variable selection and estimation for the varying-coefficient semi-parametric additive hazard model, we use B spline to approximate the varying-coefficient and penalty functions to select variables and estimate coefficients, simulations and real data analysis are illustrated to show the performance of the group Lasso, group SCAD and group MCP based on group coordinate descent algorithms(GCD). The numerical results suggest that:(1) in the constant-coefficient setting, MCP is the preferred approach among those three methods in prediction, accuracy and consistency in all settings and all the three methods have a better performance when the covariates are lower correlated and the dimension of the covariates is small;(2) in the varying-coefficient setting, group MCP is the preferred approach among those three group methods in prediction, accuracy and consistency in all settings and all the three group methods have a better performance when the covariates are lower correlated and the sample size is smaller.