Estimation of Youden Index and Its Associated Optimal Cut-point When the Parameters of Gamma Biomarkers Are Estimated by the Method of Moments

The ROC (Receiver Operating Characteristics) curves are frequently used to measure the effectiveness of diagnostic biomarkers. A global measure of the ROC curve is the Youden index, the maximum difference between sensitivity and 1-specificity. The cut-point is the value for which the maximum is attained. In this paper we obtain the asymptotic distribution of the optimal cut-point under the assumption that both the healthy and diseased populations are gamma distributed with a common shape parameter and when the gamma parameters are estimated by the method of moments. Based on the asymptotic distribution we construct confidence intervals for the cut-point. We also consider a nonparametric estimator of the Youden index and a measure of its precision based on the kernel estimator of a distribution function. We construct confidence intervals based on this methodology which we compare with those based on the delta method.