Estimation of Multi-Category Youden Index Based on the Lehmann Assumption

The Youden index is a widely used metric for assessing diagnostic accuracy in two-class classification problems, particularly for determining the optimal decision cutoff point. In this article, we extend this concept to a multiple-category classification framework by introducing semi-parametric estimators for the generalized Youden index and its associated optimal threshold, under the Lehmann assumption. Our proposed estimators are much easier to implement than the traditional nonparametric estimators. We further establish the theoretical properties of these estimators, ensuring their consistency and asymptotic normality. To evaluate the effectiveness of the proposed methods, we conduct extensive simulation studies and apply them to a real-world liver cancer dataset, demonstrating their practical applicability in medical diagnostics.