Prognostic ROC Curves

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.