F-score for medical diagnostics tests under tree or umbrella ordering: proposing new measures of accuracy and optimal cut-off point selection

Accurately distinguishing between diseased and non-diseased states in clinical diagnostics is fundamental, particularly in complex cases with multiple disease stages or subtypes. This paper introduces a novel diagnostic metric, the Harmonic Mean of F-score and inverse (negative) F-score, developed to provide a more comprehensive assessment of diagnostic accuracy under tree or umbrella ordering for multi-subtype diseases (HTF). HTF integrates Specificity (TSp) and Negative Predictive Value (TNPV) into the Negative F-score (TNFγ), allowing for a robust evaluation of true negatives and negative test reliability. Also, the HTF metric was applied to estimate optimal cut-off points in tree ordering models, where subtypes categorize diseases. Through simulations, HTF measures demonstrated superior performance in certain situations compared to traditional methods. Applied to real-world multi-class (tree ordering) data using Lung Cancer data, the proposed measure consistently provided a more balanced evaluation of diagnostic accuracy. It frequently outperformed conventional metrics and delivered comparable results to the extended Youden index in tree-ordering settings. The versatility of HTF measure enables customization, allowing researchers and clinicians to adjust its parameters to prioritize specific elements of diagnostic performance based on the clinical context.