Covariate Selection For Semi-parametric Risk Model And Its Simulation Study In Survival Analysis

Objective To introduce Lin-Ying semi-parametric additive risk (Lin-Ying) model, an alternative of Cox model in survival analysis, and its covariate selection methods. To explore whether Cox model is suitable when proportional hazard (PH) assumption is violated or when it is hard to test PH assumption for lots of variables simultaneously, and in such situations the possibility of using its alternative method, Lin-Ying model.Methods Methods of covariate selection and their realization by standard software (SAS and R) are introduced systematically, which include classic methods of selecting the best set and a family of penalized methods, especially the penalized methods based on Cox model and Lin-Ying model. In the cases of n>>p and p>>n (n indicates sample size and p indicates number of covariates),(1) two survival data were simulated based on Cox model, the former meet PH assumption and the latter do not. Then each data were analyzed with Lasso, adaptive Lasso and SCAD based on Cox model. Performance of selection of the same method based on two different situations was compared, including capabilities of selection of correct non-zero-coefficient variables and selection of correct model, mean squared error of true non-zero-coefficient variable, and relative model error;(2) survival data were simulated based on Lin-Ying model, In the case of n>> p, data were split by test of PH assumption. In the case of p>> n, lasso estimates and estimates of each univariate regression were given as two different kinds of initial values. Then each data were analyzed with Lasso, adaptive Lasso and SCAD based on Lin-Ying model. Performance of selection of the same method based on two different situations was compared in the two cases, respectively.Results (1) Result of Cox model:in the case of PH assumptions violated, proportion of selection of true non-zero-coefficient variables and selection of correct model are lower than that in the case of PH assumptions meted, and median of mean squared error of true non-zero-coefficient variable and relative model error are higher than that in the case of PH assumptions met.(2) Result of Lin-Ying model:results of proportion of selection of correct non-zero-coefficient variables and selection of correct model, median of mean squared error of true non-zero-coefficient variable and relative model error are similar in the case of PH assumptions violated and met.(3) Proportion of selection of correct non-zero-coefficient variables and selection of correct model increase as simple size adds and decrease as correlation adds.(4) Whenw>>p, Lasso, adaptive Lasso and SCAD based on Cox model and Lin-Ying model can select true model and important variables with high probability. These capabilities are bad when p>> n.Conclusion (1) When PH assumption is violated, analysis based on Cox model will decrease the capability of selection of true non-zero-coefficient variables, selection of correct model and increase mean squared error of true non-zero-coefficient variable, relative model error.(2) When PH assumption is violated, Lin-Ying can be an alternative covariate selection method.(3) Lasso, adaptive Lasso and SCAD is suitable when true model is sparse and w> p.