Title : A Harmonic Jaccard Index (HJI) for enhanced diagnostic accuracy and optimal cut-off point selection
Abstract:
Accurate evaluation of diagnostic tests is a cornerstone of evidence-based medicine, yet common statistical metrics like the Youden Index (J) show limitations with imbalanced class distributions. This paper introduces the Harmonic Jaccard Index (HJI), a metric for assessing diagnostic performance. We compared the HJI against the Youden Index, the Maximum Area (A) method, and the Fβ-score through extensive Monte Carlo simulations. We illustrated the proposed methods using real data from the Wisconsin Breast Cancer Dataset (WBCD). The results indicate that the HJI demonstrates competitive statistical power, particularly with asymmetrically distributed data. By incorporating all four elements of the confusion matrix, the HJI provides a more comprehensive and balanced assessment of a test’s ability to correctly identify both diseased and non-diseased individuals. This inherent balance makes the HJI a useful tool for selecting stable and accurate cut-off points, especially in clinical settings where misclassification costs are significant and disease prevalence is low. Although the HJI shares algebraic similarities with existing indices such as the Youden Index, its harmonic formulation explicitly penalizes imbalanced sensitivity and specificity trade-offs, making it particularly suitable for settings with class imbalance.
