Harmonic Fowlkes-Mallows Index for Medical Diagnostics Tests and Optimal Cut-Off Point Selection of Binary Diseases

Accurately distinguishing between healthy and diseased states is fundamental to clinical diagnostics. This paper introduces the Harmonic Fowlkes-Mallows (HFM) index, a novel and robust metric for assessing diagnostic accuracy and identifying optimal cut-off points. The proposed HFM index integrates performance across both positive and negative classes by combining the traditional Fowlkes-Mallows Index (FM) with the proposed Negative Fowlkes-Mallows Index (NFM), using a weighted harmonic mean. Unlike conventional measures such as the F1-score or Youden Index, HFM provides a more comprehensive evaluation of classification performance by simultaneously addressing sensitivity and specificity. Additionally, it incorporates a tunable β parameter to adjust for asymmetries in class importance. Through simulation studies, the HFM index demonstrates strong performance in binary classification tasks and proves effective in selecting optimal decision thresholds. To further demonstrate its practical utility, we apply the HFM index to real-world breast cancer data and compare its performance with other diagnostic accuracy measures.