Sensitivity and specificity evaluated at an optimal diagnostic cut-off are fundamental measures of classification accuracy when continuous biomarkers are used for disease diagnosis. Joint inference for these quantities is challenging because their estimators are evaluated at a common, data-driven threshold estimated from both diseased and healthy samples, inducing statistical dependence. Existing approaches are largely based on parametric assumptions or fully nonparametric procedures, which may be sensitive to model misspecification or lack efficiency in moderate samples. We propose a semiparametric framework for joint inference on sensitivity and specificity at the Youden-optimal cut-off under the density ratio model. Using maximum empirical likelihood, we derive estimators of the optimal threshold and the corresponding sensitivity and specificity, and establish their joint asymptotic normality. This leads to Wald-type and range-preserving logit-transformed confidence regions. Simulation studies show that the proposed method achieves accurate coverage with improved efficiency relative to existing parametric and nonparametric alternatives across a variety of distributional settings. An analysis of COVID-19 antibody data demonstrates the practical advantages of the proposed approach for diagnostic decision-making.

翻译：当连续生物标志物用于疾病诊断时，在最优诊断截断点处评估的灵敏度与特异度是分类准确性的基本度量指标。对这些量进行联合推断具有挑战性，因为其估计量是在一个共同的、数据驱动的阈值处进行评估的，该阈值由患病和健康样本共同估计得到，从而引入了统计依赖性。现有方法主要基于参数假设或完全非参数程序，这些方法可能对模型设定错误敏感，或在中等样本量下缺乏效率。我们提出了一种在半参数密度比模型下对尤登最优截断点处的灵敏度与特异度进行联合推断的框架。利用最大经验似然，我们推导了最优阈值及相应灵敏度与特异度的估计量，并建立了它们的联合渐近正态性。由此导出了Wald型和保持取值范围的logit变换置信域。模拟研究表明，在各种分布设定下，与现有的参数和非参数方法相比，所提方法在达到准确覆盖概率的同时具有更高的效率。一项针对COVID-19抗体数据的分析展示了所提方法在诊断决策中的实际优势。