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 ( HUM K $$ {\mathrm{HUM}}_K $$ ) and the generalized Youden index ( J K $$ {J}_K $$ ) are the most popular measures for assessing classification accuracy under multiple classes. While HUM K $$ {\mathrm{HUM}}_K $$ is frequently used to evaluate the overall accuracy, J K $$ {J}_K $$ provides direct measure of accuracy at the optimal cut-points. Simultaneous evaluation of HUM K $$ {\mathrm{HUM}}_K $$ and J K $$ {J}_K $$ 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 HUM K $$ {\mathrm{HUM}}_K $$ and J K $$ {J}_K $$ 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.