Smoothed empirical likelihood for optimal cut point analysis

In diagnostic studies, a continuous biomarker is often dichotomized for the diagnosis of binary disease status. Various criteria have been studied for the cut point selection of the continuous biomarker in receiver operating characteristic (ROC) analysis, in particular, the Youden index, the closest-to-(0,1) index, and the concordance probability index. Recently, Wang, Tian, and Zhao (2017) established a Wilks theorem for a smoothed empirical likelihood ratio statistic of Youden index. However, it is not directly useful for statistical inference compared to the cut point. In addition, the optimal cut point may vary with different criteria. In this article, we study smoothed empirical likelihood for optimal cut point selection with Youden index, closest-to-(0,1) criterion, and concordance probability. We develop confidence estimation for the optimal cut points based on the smoothed empirical likelihood ratio statistics. We examine the empirical performance by extensive simulation studies. We also illustrate the method with a real dataset.