Title: The length of the ROC curve as a summary measure under the binormal model
Authors: Maria del Carmen Pardo - Complutense University of Madrid (Spain) [presenting]
Alba Franco-Pereira - Universidad Complutense de Madrid (Spain)
Christos T Nakas - University of Bern (Switzerland)
Abstract: To evaluate the discriminatory ability of a diagnostic marker, it is common to summarize the information of the ROC curve into a single global value or index. The AUC is the most widely used summary measure for the ROC curve in two-class classification problems. It evaluates the overall discriminative power of a diagnostic marker under study. In general, the larger the AUC (when the standard ROC curve is closer to the upper-left corner of the unit square), the higher the distinguishing power of the diagnostic marker. Another summary measure is the maximum of the Youden index defined as the maximum vertical distance between the ROC curve and the chance line (i.e. the main diagonal). We propose the length of the arc of the ROC curve as an alternative index for the evaluation of diagnostic markers in the ROC curve context. We compare the bias and the RMSE of the length index with that of the AUC and the Youden index under the binormal model for the ROC curve under several scenarios. We illustrate with an application on data arising from an applied study.