Developments in ROC surface analysis and assessment of diagnostic markers in three-class classification problems

This article reviews current state of the art of ROC surface analysis and illustrates its use through an application on a pancreatic cancer diagnostic marker. Receiver Operating Characteristic (ROC) surfaces have been studied in the literature essentially only during the last decade and are considered as a natural generalization of ROC curves in three-class diagnostic problems. This article presents the definition, construction, modelling, and utility of the ROC surface while trying to provide an extensive reference list in the topic. It describes methodology for inference based on the Volume Under the ROC surface (VUS) and methodology for decision making through the selection of optimal cut-off points using the notion of the generalized Youden index as the optimality criterion of choice. It ends with a discussion regarding future directions for research in this field of knowledge. Key-Words: generalized Youden index; receiver operating characteristic (ROC) surface; true class fraction (TCF); volume under the ROC surface (VUS). AMS Subject Classification: 62C99, 62P10.