Ordered multiple‐class ROC analysis with continuous measurements

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. Copyright © 2004 John Wiley & Sons, Ltd.