A more intuitive interpretation of the area under the ROC curve

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. Most of the criticism is traced back to the fact that the ROC curve was introduced as the discriminative ability of a binary classifier across all its possible thresholds. Yet, this is not the curve’s only 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 the ROC plot is another way of presenting these risk distributions. This alternative perspective on the ROC plot invalidates most limitations of the AUC and attributes others to the underlying risk distributions. The separation of these distributions, represented by the area between the curves (AUC), is a more straightforward and intuitive measure of the inference of the discriminative ability of prediction models.