ROC Surface: a Generalization of ROC Curve Analysis

Receiver operating characteristic (ROC) curve analysis is widely used in biomedical research to assess the performance of diagnostic tests. Much of the work has been directed at developing accurate indices to describe ROC curves and appropriate statistics to test differences between them. The analysis, however, is largely built on the assumption that the test results are dichotomous. We generalize the ROC curve analysis to allow for tests to have more than two outcomes. The generalized ROC curve constitutes a surface. We propose to use the volume under the surface to measure the accuracy of a diagnostic test.