In the ROC analysis, the area under the ROC curve (AUC) serves as an overall measure of a biomarker/diagnostic test’s accuracy. Another popular index is Youden index (J), which corresponds to the maximum sum of sensitivity and specificity thus can be used for diagnostic threshold optimization. Although researchers mainly evaluate the diagnostic accuracy using the AUC, for the purpose of making diagnosis, Youden index provides a direct measure of the diagnostic accuracy at the optimal threshold and hence should be taken into consideration in addition to the AUC. Our previous research proposed the joint confidence region of AUC and Youden index for a single test. Furthermore, it is very common to compare the diagnostic accuracy of two correlated tests and see if one bio-marker is more preferable in terms of both summary indices. This can be done by testing Ho: AUC1-AUC2=0 and J1-J2=0 versus Ha: AUC1-AUC2>0 and J1-J2>0. The existing approach for testing such order restrictive hypothesis is the intersection-union test (IUT), which marginally test the AUC and the Youden index independently. We propose an alternative test procedure in both parametric and non-parametric settings, which is shown by simulations to be much more powerful than IUT test under the alternative and maintain the type I error rate under the null.