Several Variable Selection Methods For Cox Model

In the survival analysis, Cox model is a classical model for survival data. With the prevalence of large data, the chance of facing the survival data which are low-dimensional and uncorrelated is more and more frequent. How to overcome the defects that the traditional Cox model can not deal with these survival data above, has become a hot topic in the statistical circles. In order to solve this problem, we study Cox model by using the two important variable selection methods, i.e., the Elastic Net method and the Adaptive Elastic Net method. The main research and results are as follows:On the one hand, since the Elastic Net method can deal with the data which are high-dimensional and correlated, we propose the Elastic Net method for Cox model, and study the group effect property. It is proved that the Elastic Net method can select the all strong correlation variables into model, i.e., it has the group effect property. The numerical simulation proves that the Elastic Net method has the group effect property while the Lasso method has not. The instantiation affirms that the Elastic Net method is well applied to Cox model and it is better than the stepwise method of the fitting and forecasting ability, and then indicates that Cox model is better than the traditional Cox model after combining with the Elastic Net method.On the other hand, since the Adaptive Elastic Net method performs better than the Elastic Net method when estimating zero variables, we propose the Adaptive Elastic Net method for Cox model, and study the group effect property and the Oracle property. The numerical simulation proves that the Adaptive Elastic Net method has the group effect property, and is more accurate when dealing with zero variables, and then indicates that for Cox model, the Adaptive Elastic Net method performs better than the Lasso method, Adaptive Lasso method and Elastic Net method in the aspect of the fitting effect and accuracy.