Overlap Measures Against ROC Summary Indices

Several indices of accuracy have been proposed to summarize ROC curves. Based on these indices, statistical tests have been developed to compare the accuracy of diagnostic tests. We briefly review three of them, AUC, Youden index, and the length of the ROC curve. Besides, we explore overlap measures as alternative measures for assessing the effectiveness of a diagnostic marker. Both parametric and nonparametric estimators as well as different methods for constructing confidence intervals are proposed for these measures. We show that they are related to distances and divergences and provide some properties. We then identify situations in which the overlap measures outperform the ROC summary indices through a simulation study. Furthermore, we compare the methods for constructing confidence intervals in terms of coverage and width. Our approaches are illustrated using a real data set.