Assessing the prediction accuracy of a cure model for censored survival data with long-term survivors: Application to breast cancer data.
The Cox proportional hazards cure model is a survival model incorporating a cure rate with the assumption that the population contains both uncured and cured individuals. It contains a logistic regression for the cure rate, and a Cox regression to estimate the hazard for uncured patients. A single predictive model for both the cure and hazard can be developed by using a cure model that simultaneously predicts the cure rate and hazards for uncured patients; however, model selection is a challenge because of the lack of a measure for quantifying the predictive accuracy of a cure model. Recently, we developed an area under the receiver operating characteristic curve (AUC) for determining the cure rate in a cure model (Asano et al., 2014), but the hazards measure for uncured patients was not resolved. In this article, we propose novel C-statistics that are weighted by the patients' cure status (i.e., cured, uncured, or censored cases) for the cure model. The operating characteristics of the proposed C-statistics and their confidence interval were examined by simulation analyses. We also illustrate methods for predictive model selection and for further interpretation of variables using the proposed AUCs and C-statistics via application to breast cancer data.
a Biostatistics Group, Center for Product Evaluation , Pharmaceuticals and Medical Devices Agency , Tokyo , Japan.
Junichi
http://orcid.org/0000-0002-0803-8738
J
Asano
b Biostatistics Section, Center for Advanced Medicine and Clinical Research , Nagoya University Graduate School of Medicine , Nagoya , Japan.
Akihiro
A
Hirakawa
D000328:Adult; D001943:Breast Neoplasms / Q000175:diagnosis / Q000453:epidemiology*; D016208:Databases, Factual / Q000706:statistics & numerical data* / Q000639:trends; D005260:Female; D006801:Humans; D008954:Models, Biological; D011237:Predictive Value of Tests; D016019:Survival Analysis; D017741:Survivors / Q000706:statistics & numerical data*
Area under the receiver operating characteristic curve; C-statistic: cure model; Cox proportional hazards model; discrimination index; prognostic study