title: Ordered multiple-class ROC analysis with continuous measurements.
abstract: Receiver operating characteristic (ROC) curves have been useful in two-group classification problems. In three- and multiple-class diagnostic problems, an ROC surface or hyper-surface can be constructed. The volume under these surfaces can be used for inference using bootstrap techniques or U-statistics theory. In this article, ROC surfaces and hyper-surfaces are defined and their behaviour and utility in multi-group classification problems is investigated. The formulation of the problem is equivalent to what has previously been proposed in the general multi-category classification problem but the definition of ROC surfaces here is less complex and addresses directly the narrower problem of ordered categories in the three-class and, by extension, the multi-class problem applied to continuous and ordinal data. Non-parametric manipulation of both continuous and discrete test data and comparison between two diagnostic tests applied to the same subjects are considered. A three-group classification example in the context of HIV neurological disease is presented and the results are discussed.
authors.affiliation: Division of Biostatistics, Indiana University School of Medicine, 1050 Wishard Boulevard, RG 4101, Indianapolis, IN 46202-2872, USA.
authors.forename: Christos T
authors.initials: CT
authors.lastname: Nakas
authors.forename: Constantin T
authors.initials: CT
authors.lastname: Yiannoutsos
mesh_terms: D015526:AIDS Dementia Complex / Q000473:pathology; D002986:Clinical Trials as Topic / Q000379:methods; D003198:Computer Simulation; D003955:Diagnostic Tests, Routine / Q000379:methods*; D006678:HIV / Q000254:growth & development; D015658:HIV Infections / Q000188:drug therapy / Q000473:pathology; D006801:Humans; D009483:Neuropsychological Tests; D012372:ROC Curve