ABSTRACT
Notions of receiver operating characteristic (ROC) curve analysis have been extended to accommodate problems of three-class and multiple-class classification, that is, to the general case of a categorical reference standard with more than two categories. The ROC surface has been proposed as a natural generalisation of the ROC curve for the assessment of diagnostic markers in three-class classification problems. ROC surface analysis is a valuable tool for three-class classification problems as it naturally generalizes ROC curve analysis within the ROC theoretical framework. This chapter presents different approaches for parametric, nonparametric, and empirical ROC surface modeling. Parametric estimation of the ROC surface often makes use of the so-called trinormal model. ROC curves and surfaces can be compared in their entirety or on the basis of summary measures such as the area under the curve or the volume under the surface.
