Smoothed empirical likelihood for the Youden index

For a continuous scale biomarker of binary disease status, the Youden index is a frequently used measurement of diagnostic accuracy in the context of the receiver operating characteristic curve and provides an optimal threshold for making diagnosis. The majority of existing inference methods for the Youden index are either parametric or bootstrap based. In the current paper, the empirical likelihood method for the Youden index is derived via defining novel smoothed estimating equations, and Wilks' theorem for the empirical likelihood ratio statistic is established. Extensive simulation studies suggest that the chi-square calibrated empirical likelihood interval estimators are robust to model assumptions, enjoy computational efficiency and perform better than the bootstrap procedure almost uniformly across a variety of scenarios in terms of coverage probabilities.