In the field of diagnostic test studies, the accuracy of a diagnostic test is essential in evaluating the performance of the test. The receiver operating characteristic (ROC) curve and the area under the curve (AUC) are widely used in such evaluation procedures. Meanwhile, the Youden index is also introduced into practice to measure the accuracy of the diagnostic test from another aspect. The Youden index maximizes the sum of sensitivity and specificity, assuring decent true positive and negative rates. It draws one's attention due to its merit of finding the optimal cut-off points of biomarkers. Similar to Partial ROC, a new index, called "Partial Youden index" can be defined as an extension of Youden's Index. It is more meaningful than regular Youden index since the regular one is just a special case of the Partial Youden Index. In this thesis, we focus on construction of generalized confidence intervals for the Partial Youden Index and its corresponding optimal cut-off points. Extensive simulation studies are conducted to evaluate the finite sample performances of the new intervals.