{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,3]],"date-time":"2026-11-03T00:06:26Z","timestamp":1793664386168,"version":"4.5.1"},"reference-count":15,"publisher":"Wiley","issue":"22","license":[{"start":{"date-parts":[[2004,10,25]],"date-time":"2004-10-25T00:00:00Z","timestamp":1098662400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2004,11,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Receiver operating characteristic (ROC) curves have been useful in two\u2010group classification problems. In three\u2010 and multiple\u2010class diagnostic problems, an ROC surface or hyper\u2010surface can be constructed. The volume under these surfaces can be used for inference using bootstrap techniques or U\u2010statistics theory. In this article, ROC surfaces and hyper\u2010surfaces are defined and their behaviour and utility in multi\u2010group classification problems is investigated. The formulation of the problem is equivalent to what has previously been proposed in the general multi\u2010category classification problem but the definition of ROC surfaces here is less complex and addresses directly the narrower problem of ordered categories in the three\u2010class and, by extension, the multi\u2010class problem applied to continuous and ordinal data. Non\u2010parametric manipulation of both continuous and discrete test data and comparison between two diagnostic tests applied to the same subjects are considered. A three\u2010group classification example in the context of HIV neurological disease is presented and the results are discussed. 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