Comparing the performance of two observers using a novel utility-based performance metric for ROC analysis

Abstract

We previously introduced a utility-based ROC performance metric, the surface-averaged expected cost (SAEC), to address difficulties which arise in generalizing the well-known area under the ROC curve (AUC) to classification tasks with more than two classes. In a two-class classification task, the SAEC can be shown explicitly to be twice the area above the conventional ROC curve (1-AUC) divided by the arclength along the ROC curve. In the present work, we show that in tasks comparing the performance of two observers whose behavior is described by the proper binormal model, our proposed performance metric is consistent with AUC in the qualitative sense of deciding which of the two observers is better, and by how wide a margin.