Inference in receiver operating characteristic surface analysis via a trinormal model-based testing approach

Receiver operating characteristic (ROC) analysis is the methodological framework of choice for the assessment of diagnostic markers and classification procedures in general, in both two-class and multiple-class classification problems. We focus on the three-class problem for which inference usually involves formal hypothesis testing using a proxy metric such as the volume under the ROC surface (VUS). In this article, we develop an existing approach from the two-class ROC framework. We define a hypothesis-testing procedure that directly compares two ROC surfaces under the assumption of the trinormal model. In the case of the assessment of a single marker, the corresponding ROC surface is compared with the chance plane, that is, to an uninformative marker. A simulation study investigating the proposed tests with existing ones on the basis of the VUS metric follows. Finally, the proposed methodology is applied to a dataset of a panel of pancreatic cancer diagnostic markers. The described testing procedures along with related graphical tools are supported in the corresponding R-package trinROC, which we have developed for this purpose.