On F _β -score for medical diagnostics tests of binary diseases: proposing new measures of accuracy

Accurate differentiation between health states - diseased or non-diseased - is essential in clinical diagnostics. Optimal cut-off points, or thresholds used to classify test results, are crucial for precise diagnoses. This work introduces the Harmonic Mean of F-score and inverse F-score (<i>HF</i>), a novel metric for a balanced assessment of diagnostic accuracy. <i>HF</i> integrates Specificity (<i>Sp</i>) and Negative Predictive Value (NPV) into the Negative F-score (<i>NF</i>_<i>γ</i>), ensuring a comprehensive evaluation of true negatives and negative test reliability. Prioritizing both true positives and true negatives, <i>HF</i> was used in optimal cut-off point estimation under binary disease classification. Simulation results revealed that the <i>HF</i> measure performed well, often surpassing established methods in specific settings. The <i>HF</i> measure and cut-off point selection criterion were applied to real-life data, showcasing its ability to provide a balanced evaluation of diagnostic accuracy. The <i>HF</i> measure frequently outperformed traditional metrics. The <i>HF</i> metric's flexibility, allowing parameter adjustments to accommodate diverse scenarios, enables researchers and clinicians to tailor its emphasis on specific aspects of diagnostic performance depending on the context.