Evaluating joint confidence region of hypervolume under ROC manifold and generalized Youden index

In biomarker evaluation/diagnostic studies, the hypervolume under the receiver operating characteristic manifold (HUMK) and the generalized Youden index (J(K)) are the most popular measures for assessing classification accuracy under multiple classes. While HUMK is frequently used to evaluate the overall accuracy, J(K) provides direct measure of accuracy at the optimal cut-points. Simultaneous evaluation of HUMK and J(K) provides a comprehensive picture about the classification accuracy of the biomarker/diagnostic test under consideration. This article studies both parametric and non-parametric approaches for estimating the confidence region of HUMK and J(K) for a single biomarker. The performances of the proposed methods are investigated by an extensive simulation study and are applied to a real data set from the Alzheimer's Disease Neuroimaging Initiative.