The Diagnostic Efficiency Ratio (DER): conceptual rationale, mathematical derivation, and hypothetical evaluation of a prevalence-sensitive benefit–harm metric

OBJECTIVES: Traditional diagnostic accuracy metrics - sensitivity, specificity, predictive values, likelihood ratios, and global indices such as Youden's J and the diagnostic odds ratio - describe important statistical properties of diagnostic tests but do not express benefit-harm balance in a single, prevalence-sensitive measure. The Diagnostic Efficiency Ratio (DER) is introduced as a composite metric designed to quantify diagnostic discriminative efficiency. METHODS: )]. Closed-form derivation was performed analytically and verified using independent algebraic tools. Hypothetical scenarios spanning plausible ranges of sensitivity, specificity, and prevalence were constructed to illustrate DER behavior, and an empirical illustration using published neonatal sepsis biomarker studies was conducted. RESULTS: Across hypothetical scenarios, DER demonstrated mathematically coherent and clinically intuitive behavior. High DER values occurred only when sensitivity and specificity were jointly strong and balanced. DER declined as specificity decreased or prevalence increased, with small values indicating contexts in which misdiagnoses consume a larger share of testing effort. In the empirical neonatal sepsis examples, DER differentiated biomarkers and settings in a manner consistent with its structural formulation, highlighting context-dependent diagnostic efficiency. CONCLUSIONS: DER provides a prevalence-sensitive, frequency-based representation of diagnostic benefit relative to harm, reframing diagnostic accuracy in efficiency-oriented terms by expressing how effectively testing effort is converted into discriminative gain beyond chance relative to misclassification burden. This conceptual and illustrative evaluation supports DER's coherence and potential stewardship utility as a complement to traditional diagnostic accuracy metrics. Ultimately, the DER helps to recast diagnostic performance as an efficiency problem, aligning it with modern value-based healthcare and stewardship priorities.