Interval estimation for three-class Youden index with verification bias

Youden index is one of the broadly used measurements to assess the accuracy of the diagnostic test under consideration. In real medical diagnostic studies, verification of the true disease status might only be partially available due to ethical and cost considerations, and the drawbacks of gold-standard tests. Therefore, statistical evaluation of the diagnostic accuracy of a test based only on data from subjects with verified disease status is typically biased. Youden indices for the assessment of accuracy and optimal cutoff point(s) selection in diagnostic tests classifying two disease stages and three disease stages have been proposed without considering this verification bias. In this article, we develop novel confidence intervals for three-class Youden index to correct verification bias under the assumption that the true disease status, if missing, is missing at random (MAR). The proposed methods provide a comprehensive guide to dealing with the verification bias in diagnostic test accuracy studies and lead to a better choice of diagnostic tests.