Technical Report XXIX
Uncertainty Estimation of Diagnostic Accuracy Measures Under Parametric Distributions
RA Chatzimichail, T Chatzimichail, AT Hatjimihail
Abstract
Background: Diagnostic tests are evaluated by their ability to discriminate between diseased and nondiseased individuals; however, estimates of diagnostic accuracy alone do not quantify their associated uncertainty. Uncertainty assessment is therefore essential for interpreting accuracy estimates and comparing diagnostic thresholds.
Methods: We develop a parametric framework for propagating uncertainty to diagnostic accuracy measures formulated as functions of sensitivity, specificity, and prevalence. Normal, lognormal, or gamma models are specified separately for the diseased and nondiseased populations. At a diagnostic threshold, first-order uncertainty propagation retains covariance between estimated population means and standard deviations, incorporates prevalence sampling uncertainty when applicable, and adds the propagated measurement variance to the sampling variance while retaining measurement covariance between sensitivity and specificity. The Wolfram Language implementation provides uncertainty components by source, joint output covariance, and approximate expanded-uncertainty intervals calculated using effective degrees of freedom derived from the source-specific variance contributions. At estimated optimal thresholds, measurement variance is evaluated by Gauss–Hermite quadrature, conditional on the selected threshold; optimal threshold uncertainty is excluded.
Results: Illustrative analyses indicate that the contribution of each uncertainty source varies with the diagnostic accuracy measure, distributional assumptions, and threshold. Retaining measurement covariance can reduce the propagated measurement variance of a derived measure. In the cases examined, joint propagation reproduces the corresponding marginal variances and enables evaluation of uncertainty across diagnostic thresholds.
Conclusions: The framework provides a reproducible basis for assessing diagnostic accuracy and uncertainty while preserving relevant input and output dependencies. Decomposition by source helps identify the assumptions and uncertainty components underlying each estimate. The intervals remain local approximations; nominal coverage and optimal threshold uncertainty require separate assessment.
First Published
2025-09-21
Revised
2026-10-01
DOI
Citation
Chatzimichail RA, Chatzimichail T, Hatjimihail AT. Uncertainty Estimation of Diagnostic Accuracy Measures Under Parametric Distributions. Technical Report XXIX. Hellenic Complex Systems Laboratory; 2025. https://doi.org/10.5281/zenodo.23085657.
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