The 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.

中文翻译：

---

约登指数的半参数推断和密度比模型下的最佳截止点

Youden 指数是接收者操作特征曲线的流行汇总统计量。它给出了生物标志物的最佳截止点，以区分患病和健康个体。在本文中，我们通过半参数密度比模型对健康组和患病组中个体的生物标志物分布进行建模。基于该模型，我们提出使用最大经验似然法来估计约登指数和最优分界点。我们进一步建立了建议估计量的渐近正态性，并为约登指数和相应的最佳截止点构建了有效的置信区间。当没有检测下限 (LLOD) 和生物标志物有固定和有限的 LLOD 时，所提出的方法自动涵盖两种情况。