Assessing the prediction accuracy of a cure model for censored survival data with long-term survivors: Application to breast cancer data |
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Authors: | Junichi Asano Akihiro Hirakawa |
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Affiliation: | 1. Biostatistics Group, Center for Product Evaluation, Pharmaceuticals and Medical Devices Agency, Tokyo, Japan;2. Biostatistics Section, Center for Advanced Medicine and Clinical Research, Nagoya University Graduate School of Medicine, Nagoya, Japan |
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Abstract: | 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. |
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Keywords: | Area under the receiver operating characteristic curve discrimination index Cox proportional hazards model C-statistic: cure model prognostic study |
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