  The Youden index is a popular summary statistic for receiver operating
characteristic curve. It gives the optimal cutoff point of a biomarker to
distinguish the diseased and healthy individuals. In this paper, we propose to
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 use the maximum empirical likelihood method to estimate the Youden index and
the optimal cutoff point. We further establish the asymptotic normality 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. 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.
