The Overlapping Coefficient: A Complementary Measure to ROC-AUC in Biomedical Statistics

The Weitzman overlapping coefficient (OVL) is a probabilistic measure of similarity between two distributions defined as the common probability mass shared by their density functions. In biomedical statistics, OVL has become increasingly attractive because of its direct interpretability and its ability to quantify distributional similarity between healthy and diseased populations. Although substantial progress has been made in parametric, nonparametric, and numerical estimation methods, the relationship between OVL and the Receiver Operating Characteristic Area Under the Curve (ROC-AUC) has received comparatively little attention. This paper presents a unified overview of OVL estimation methods and investigates its theoretical and empirical relationship with ROC?AUC. A probabilistic representation of OVL is developed and compared with the classical probabilistic representation of ROC-AUC. Under the equal-variance normal model, explicit analytical expressions for both measures are reviewed, revealing a monotonic inverse relationship between them. A simulation study demonstrates how increasing distributional separation leads to decreasing overlap and increasing classification performance. The results indicate that OVL and ROC-AUC provide complementary information and should be interpreted jointly in biomedical applications.