Assessing the prediction accuracy of cure in the Cox proportional hazards cure model: an application to breast cancer data.

A cure rate model is a survival model incorporating the cure rate with the assumption that the population contains both uncured and cured individuals. It is a powerful statistical tool for prognostic studies, especially in cancer. The cure rate is important for making treatment decisions in clinical practice. The proportional hazards (PH) cure model can predict the cure rate for each patient. This contains a logistic regression component for the cure rate and a Cox regression component to estimate the hazard for uncured patients. A measure for quantifying the predictive accuracy of the cure rate estimated by the Cox PH cure model is required, as there has been a lack of previous research in this area. We used the Cox PH cure model for the breast cancer data; however, the area under the receiver operating characteristic curve (AUC) could not be estimated because many patients were censored. In this study, we used imputation-based AUCs to assess the predictive accuracy of the cure rate from the PH cure model. We examined the precision of these AUCs using simulation studies. The results demonstrated that the imputation-based AUCs were estimable and their biases were negligibly small in many cases, although ordinary AUC could not be estimated. Additionally, we introduced the bias-correction method of imputation-based AUCs and found that the bias-corrected estimate successfully compensated the overestimation in the simulation studies. We also illustrated the estimation of the imputation-based AUCs using breast cancer data.