A simulation study and application of feature selection on survival least square support vector machines

The Cox Proportional Hazard Model (Cox PHM) is commonly employed in survival analysis. It has proportional hazard assumption which is not always satisfied in real application. In such a case, the survival data can be analyzed using non-parametric approaches, one of them is the Survival Least Square Support Vector Machines (SURLS-SVM) recently developed. This approach does not require the proportional hazard assumption and the distribution of survival time can be unknown. Some papers apply SURLS-SVM on both simulation study and real data without considering feature selection. The performance of statistical methods can be determined by choosing relevant features selected as input. Therefore, the feature selection method is necessary to be applied in SURLS-SVM. In this paper, the Cox PHM and the SURLS-SVM with feature selection are applied on simulated data and clinical data, i.e. survival of cervical cancer patients. These two approaches are compared using prognostic index so-called concordance index (c-index). For both data sets, the c-index obtained from SURLS-SVM, with or without feature selection, is much higher than the one obtained from Cox PHM. On the cervical cancer data, SURLS-SVM with feature selection selects 10 relevant features out of 12 features. This also works for Cox PHM with feature selection.