Reflection on modern methods: Revisiting the area under the ROC Curve

Abstract

The area under the receiver operating characteristic (ROC) curve (AUC) is commonly used for assessing the discriminative ability of prediction models even though the measure is criticized for being clinically irrelevant and lacking an intuitive interpretation. Every tutorial explains how the coordinates of the ROC curve are obtained from the risk distributions of diseased and non-diseased individuals, but it has not become common sense that therewith the ROC plot is just another way of presenting these risk distributions. We show how the ROC curve is an alternative way to present risk distributions of diseased and non-diseased individuals and how the shape of the ROC curve informs about the overlap of the risk distributions. For example, ROC curves are rounded when the prediction model included variables with similar effect on disease risk and have an angle when, for example, one binary risk factor has a stronger effect; and ROC curves are stepped rather than smooth when the sample size or incidence is low, when the prediction model is based on a relatively small set of categorical predictors. This alternative perspective on the ROC plot invalidates most purported limitations of the AUC and attributes others to the underlying risk distributions. AUC is a measure of the discriminative ability of prediction models. The assessment of prediction models should be supplemented with other metrics to assess their clinical utility.

Keywords: Area under the curve; discriminative ability; receiver operating characteristic curve; risk distributions; risk prediction.