A Stepwise Variable Selection for a Cox Proportional Hazards Cure Model with Application to Breast Cancer Data

Abstract

A cure rate model is a survival model incorporating the cure rate on the assumption that a population contains both uncured and cured individuals. It is a powerful statistical tool for cancer prognostic studies. In order to accurately predict long-term outcome the proportional hazards (PH) cure model requires variable selection methods. However, no specific variable selection method for the PH cure model has been established in practice. In this study, we present a stepwise variable selection method for the PH cure model with a logistic regression for the cure rate and a Cox regression for the hazard for uncured patients. We conducted simulation studies to evaluate the operating characteristics of the stepwise method in comparison to those of the best subset selection method based on Akaike information criterion and of the convenience variable selection method that puts all variables in the PH cure model and selects the significant ones. The results demonstrated that in many cases the stepwise method outperformed other methods with respect to false positive determinations and estimation bias for the survival curve. In addition, we demonstrated the usefulness of the stepwise method for the PH cure model by applying it to analyze clinical data on breast cancer patients.