Ordered multiple-class ROC analysis with continuous measurements

Authors

  • Christos T. Nakas,

    1. Division of Biostatistics, Indiana University School of Medicine, 1050 Wishard Boulevard, RG 4101, Indianapolis, IN 46202-2872, U.S.A.
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  • Constantin T. Yiannoutsos

    Corresponding author
    1. Division of Biostatistics, Indiana University School of Medicine, 1050 Wishard Boulevard, RG 4101, Indianapolis, IN 46202-2872, U.S.A.
    • Division of Biostatistics, Indiana University School of Medicine, 1050 Wishard Boulevard, RG 4101, Indianapolis, IN 46202-2872, U.S.A.
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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. Copyright © 2004 John Wiley & Sons, Ltd.

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