Confidence regions for optimal sensitivity and specificity of a diagnostic test

We propose new methods that provide approximate joint confidence regions for the optimal sensitivity and specificity of a diagnostic test, fixed by the Youden index criterion. Such methods are semiparametric and overcome limitations of alternative approaches available in the literature. Our proposal is based on empirical likelihood pivots and covers two situations: binormal model and binormal model after the use of Box-Cox transformations. In the last case, we show how to use two different transformations, for the healthy and the diseased subjects.