In the field of diagnostic studies, the area under the Receiver Operating Characteristic (ROC) curve (AUC) serves as an overall measure of a biomarker/diagnostic test’s accuracy. Youden index, defined as the maximum overall correct classification rate minus one at the optimal cut-off point, is another popular index. For continuous biomarkers of binary disease status, although researchers mainly evaluate the diagnostic accuracy using AUC, for the purpose of making diagnosis, Youden index provides an important and direct measure of the diagnostic accuracy at the optimal threshold and hence should be taken into consideration in addition to AUC. Furthermore, AUC and Youden index are generally correlated. We initiate the idea of evaluating diagnostic accuracy based on AUC and Youden index simultaneously. As the first step towards this direction, we only focus on the confidence region estimation of AUC and Youden index for a single marker. Both parametric and non-parametric approaches for estimating joint confidence region of AUC and Youden index are considered. Extensive simulation study is carried out to evaluate the performance of the proposed methods, and for illustration, a real data set is analyzed by the proposed methods.