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