Study On Variable Selection Methods For The Cox Model

In the survival analysis,the Cox model is the most commonly used model for survival data.The two requirements are needed for this model.First,the number of observations must be larger than the number of covariates.Second,the covariates are independent or not highly correlated.So the Cox model is no longer applicable to deal with survival data in which the number of covariates is larger than the number of observations and the covariates are highly correlated.To overcome this drawback,several variable selection methods,such as the Lasso(Tibshirani),the Adaptive Lasso(Fan and Li)and the Elastic Net(A.Benner et al.),had proposed to apply to the Cox model.These variable selection methods improve the Cox model very well so that the Cox model has ability to deal with high-dimensional and high-correlated data,but they also have their shortcomings.In this paper,to further modify the Cox model,we propose the Adaptive Elastic Net method for the Cox model and prove the grouping effect property of the Adaptive Elastic Net estimation.Then we make simulations and fit the data by using R.The Adaptive Elastic Net is compared with the Lasso,the Adaptive Lasso and the Elastic Net from the three aspects of variable selection,estimation bias and goodness of fit.Moreover,we discuss the influence of different correlation and different censoring proportion for the four methods.At last,we apply the Cox model to analyze breast cancer expression profiling data based on the Adaptive Elastic Net method.The results of simulations indicate that: when dealing with high-dimensional and high-correlated data,the Adaptive Elastic Net method can select almost all signal group variables into the model,i.e.,it has the grouping effect property,while the Lasso and the Adaptive Lasso have not.Because of the high dimensionality,the data contains many noise variables,the Adaptive Elastic Net method is more accurate to deal with these noise variables than the Elastic Net method.The Adaptive Elastic Net method performs better than the other three methods in terms of estimation bias and goodness offit.As the correlation coefficient increases,the superiority of the Adaptive Elastic Net method is more obvious.Fitting efficiency of the four methods will be reduced along with the increasing censoring proportion of data.Combining the Adaptive Elastic Net and the Cox model is the good method to deal with breast cancer expression profiling data and can get the good result.