Partial Youden index and its inferences

In medical diagnostic research, medical tests with continuous values are widely employed to distinguish between diseased and non-diseased subjects. The diagnostic accuracy of a medical test can be assessed by using the receiver operating characteristic (ROC) curve of the test. To summarize the ROC curve and determine an optimal cut-off point for test results, the Youden index is commonly used. In particular, the Youden index is optimized over the entire range of values for sensitivity and specificity, which determine the ROC space. However in clinical practice, one may only be interested in the regions of the ROC curve that correspond to low false-positive rates or/and high sensitivities. In this paper, a new summary index for the ROC curve, called the "partial Youden index", is defined on regions of the ROC space in which sensitivity/specificity values are of practical interest. The traditional Youden index is a special case of the partial Youden index. Various parametric and non-parametric interval estimation methods are proposed for the partial Youden index. Extensive simulation studies are conducted to evaluate the finite sample performances of the proposed methods. A real example is used to illustrate the application of the new methods.