Inference of the Youden index and associated threshold using empirical likelihood for quantiles

The Youden index is a widely used measure in the framework of medical diagnostics, where the effectiveness of a biomarker (screening marker or predictor) for classifying a disease status is studied. When the biomarker is continuous, it is important to determine the threshold or cut-off point to be used in practice for the discrimination between diseased and healthy populations. We introduce two methods aimed at estimating the Youden index and its associated threshold. The first one is a modified version of a recent approach based on the delta method, and the second one is based on the adjusted empirical likelihood for quantiles in the setting of a two-sample problem. We also include CIs for both of them. In the simulation study, we compare both methods under different scenarios. Finally, a real example of prostatic cancer, well known in the literature, is analysed to provide the reader with a better understanding of the new methodology.