Adjusted empirical likelihood estimation of the youden index and associated threshold for the bigamia model

The Youden index is a widely used measure in the framework of medical diagnostic, 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 a new method based on adjusted empirical likelihood for quantiles aimed to estimate the Youden index and its associated threshold. We also include bootstrap based confidence intervals for both of them. In the simulation study, we compare this method with a recent approach based on the delta method under the bigamma scenario. Finally, a real example of prostatic cancer, well known in the literature, is analyzed to provide the reader with a better understanding of the new method