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    Area of Science:

    • Biostatistics
    • Medical Screening
    • Diagnostic Test Evaluation

    Background:

    • Conditional statistics like true positive fraction (TPF) can equal unconditional statistics (e.g., disease detection rates).
    • This equality allows ratio calculation between two screening tests, even without full patient follow-up or known negative rates.

    Purpose of the Study:

    • To demonstrate that the property of equal conditional and unconditional statistic ratios extends to expected utility metrics.
    • To show how relative specificities and Area Under the ROC Curve (AUC) can be estimated despite unknown negative rates.

    Main Methods:

    • Mathematical derivation to extend the property of statistic ratios to expected utility.
    • Expressing ratios of relative specificity and AUC in terms of disease prevalence.
    • Analyzing the dependence of these ratios on posited prevalence values.

    Main Results:

    • The property enabling ratio calculation for TPF extends to expected utility metrics.
    • Relative specificity and AUC estimates depend on unknown negative rates but can be expressed using disease prevalence.
    • This dependence is often weak, especially with low prevalence or similar test performance.

    Conclusions:

    • Ratios of screening test performance, including expected utility, can be reliably calculated without complete data.
    • Relative specificity and AUC can be accurately estimated using approximate disease prevalence, minimizing loss of accuracy.