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Prognostic ROC Curves: A Method for Representing the Overall Discriminative Capacity of Binary Markers with Right-Censored Time-to-Event Endpoints

Combescure, Christophea; Perneger, Thomas V.b; Weber, Damien C.c; Daurès, Jean-Pierred; Foucher, Yohanne,f

Epidemiology:
doi: 10.1097/EDE.0000000000000004
Methods
Abstract

Survival curves are a popular tool for representing the association between a binary marker and the risk of an event. The separation between the survival curves in patients with a positive marker (high-risk group) and a negative marker (low-risk group) reflects the prognostic ability of the marker. In this article, we propose an alternative graphical approach to represent the discriminative capacity of the marker—a receiver operating characteristic (ROC) curve, tentatively named prognostic ROC curve—obtained by plotting 1 minus the survival in the high-risk group against 1 minus the survival in the low-risk group. The area under the curve corresponds to the probability that a patient in the low-risk group has a longer lifetime than a patient in the high-risk group. The prognostic ROC curve provides complementary information compared with survival curves. However, when the survival functions do not reach 0, the prognostic ROC curve is incomplete. We show how a range of possible values for the area under the curve can be derived in this situation. A simulation study is performed to analyze the accuracy of this methodology, which is also illustrated by applications to the survival of patients with brain metastases and survival of kidney transplant recipients.

Author Information

From the aCRC and Division of Clinical Epidemiology, Department of Health and Community Medicine, University of Geneva, University Hospitals of Geneva, Geneva, Switzerland; bDivision of Clinical Epidemiology, Department of Health and Community Medicine, University of Geneva, University Hospitals of Geneva, Geneva, Switzerland; cDepartment of Radiation-Oncology, University Hospitals of Geneva, Geneva, Switzerland; dLaboratoire de Biostatistique, Institut Universitaire de Recherche Clinique, Université Montpellier I, Montpellier, France; eLaboratoire de Biostatistique, Recherche Clinique et Mesures Subjective en Santé, Université de Nantes, Nantes, France; and fITUN, Inserm, Nantes, France.

The authors report no conflicts of interest.

This work was partially supported by a grant from the French National Agency of Research (ANR-11-JSV1-0008-01). The data collection in the cohort DIVAT is supported by Roche laboratory.

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (www.epidem.com). This content is not peer-reviewed or copy-edited; it is the sole responsibility of the author.

Correspondence: Christophe Combescure, Division of clinical epidemiology, University Hospital of Geneva, Rue Gabrielle Perret-Gentil 6, 1211 Geneva, Switzerland. E-mail: christophe.combescure@hcuge.ch.

© 2014 by Lippincott Williams & Wilkins, Inc