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Yuan, M., Li, P. and Wu, C. (2021), Semiparametric inference of the Youden index and the optimal cut‐off point under density ratio models. Can J Statistics. https://doi.org/10.1002/cjs.11600
Receiver operating characteristic (ROC) curve is a widely used statistical tool in medical research to evaluate the discriminatory effectiveness of a biomarker for distinguishing diseased individuals from healthy ones. It plots the proportion of true positive (sensitivity) versus proportion of false positive (one minus specificity) across all possible choices of threshold values, called cutoff points, of the biomarker. The Youden index is a popular summary statistic for the ROC curve. It gives the optimal cutoff point of a biomarker to distinguish the diseased and healthy individuals. How to efficiently estimate the Youden index and the corresponding optimal cutoff point is an important research problem. This paper models 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 cutoff point. We further establish the limiting distribution of the proposed estimators and construct valid confidence intervals for the Youden index and the corresponding optimal cutoff 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. We confirm the proposed method is effective by both simulation experiments and application examples.