Estimation of the volume under the ROC surface with three ordinal diagnostic categories

With three ordinal diagnostic categories, the most commonly used measure for the overall diagnostic accuracy is the volume under the ROC surface (VUS), which is the extension of the area under the ROC curve (AUC) for binary diagnostic outcomes. This article proposes two kernel smoothing based approaches for estimation of the VUS. In an extensive simulation study, the proposed estimators are compared with the existing parametric and nonparametric estimators in terms of bias and root mean square error. A real data example of 203 participants from a cohort study for the detection of Glycan biomarkers for liver cancer is discussed.