Half-AUC for the evaluation of sensitive or specific classifiers

This paper describes a simple, non-parametric variant of area under the receiver operating characteristic (ROC) curve (AUC), which we call half-AUC (HAUC). By measuring AUC in two halves: first when the true positive rate (TPR) is greater than the true negative rate (TNR) and then when TPR is less than TNR, we obtain a measure of a classifier's overall sensitivity (HAUC(Se)) and specificity (HAUC(Sp)) respectively. We show that these HAUC measures can be interpreted as the probability of correct ranking under the constraint that one class must have a higher detection rate than the other. We then go on to describe application domains where this constraint is appropriate and hence where HAUC may be superior to AUC. We show examples where HAUC discriminates ROC curves both when one curve dominates another and when the curves cross, but have an equivalent AUC. (C) 2013 Elsevier B.V. All rights reserved.