Semiparametric inference of the Youden index and the optimal cut‐off point under density ratio models

Abstract

AbstractThe Youden index is a popular summary statistic for receiver operating characteristic curves. It gives the optimal cut‐off point of a biomarker to distinguish the diseased and healthy individuals. In this article, we model the distributions of a biomarker for individuals in the healthy and diseased groups via a semiparametric density ratio model. Based on this model, we propose using the maximum empirical likelihood method to estimate the Youden index and the optimal cut‐off point. We further establish the asymptotic normality of the proposed estimators and construct valid confidence intervals for the Youden index and the corresponding optimal cut‐off point. The proposed method automatically covers both cases when there is no lower limit of detection (LLOD) and when there is a fixed and finite LLOD for the biomarker. Extensive simulation studies and a real data example are used to illustrate the effectiveness of the proposed method and its advantages over the existing methods.