Simulation Study of Feature Selection on Survival Least Square Support Vector Machines with Application to Health Data

Abstract

One of semi parametric survival model commonly used is Cox Proportional Hazard Model (Cox PHM) that has some conditions must be satisfied, one of them is proportional hazard assumption among the category at each predictor. Unfortunately, the real case cannot always satisfy this assumption. One alternative model that can be employed is non-parametric approach using Survival Least Square-Support Vector Machine (SURLS-SVM). Meanwhile, the SURLS-SVM cannot inform which predictors are significant like the Cox PHM can do. To overcome this issue, the feature selection using backward elimination is employed by means of c-index increment. This paper compares two approaches, i.e. Cox PHM and SURLS-SVM, using c-index criterion applied on simulated and clinical data. The empirical results inform that the c-index of SURLS-SVM is higher than Cox PHM on both datasets. Furthermore, the simulation study is repeated 100 times. The simulation results show that the non-relevant predictors are often included in the model because the effect of confounding. For the application on clinical data (cervical cancer), the feature selection yields nine relevant predictors out of twelve predictors. The three predictors among the nine relevant predictors in SURLS-SVM are the significant predictors in Cox PHM.