ROC curve and area under the curve (AUC)

The ROC curve shows sensitivity and specificity for every possible cut-off of a score. The area under the curve (AUC) is the probability that a randomly drawn person with the feature has a score that points more strongly to the feature than that of a person without. .50 means chance, 1 means complete separation. The Youden index J = sensitivity + specificity − 1 names the cut-off at which both together are largest.

Example: A short test with AUC = .91: a score of 24 or less counts as positive (screen-positive), with 85% sensitivity and 88% specificity.

Caution: The cut-off is chosen on exactly these data and usually does worse in new data. The Youden index does not know which error weighs more.