Hellenic Complex Systems Laboratory

22/09/2025

HCSL Technical Reports:
Chatzimichail RA, Chatzimichail T, Hatjimihail AT. Uncertainty Estimation of Diagnostic Accuracy Measures under Parametric Distributions. Technical Report XXIX. Hellenic Complex Systems Laboratory; 2025. Available at:https://www.hcsl.com/TR/hcsltr29/hcsltr29.pdf
Background:
Diagnostic accuracy measures (DAMs) are widely used in evaluating diagnostic tests, yet their uncertainty is often underreported or inconsistently quantified, which can bias threshold-based decisions in clinical practice.
Methods:
We developed a computational framework to estimate the measurement, sampling, and combined uncertainty of sixteen DAMs for threshold-based screening or diagnostic tests under three measurand distributional models: normal, lognormal, and gamma. Measurement uncertainty is modelled with linear and nonlinear heteroscedastic functions. Uncertainty is propagated using a first-order Taylor-series expansion. Optimality conditions are derived numerically where applicable. The framework has been implemented in the freely available program DiagAccU, in Wolfram Language, allowing parameter specification and estimation and plotting of the DAMs, their uncertainties and confidence intervals (CIs).
Results:
We used fasting plasma glucose for diabetes diagnosis as an illustrative case study. At extreme thresholds, ratio-type measures showed widened CIs. Agreement, association, and concordance based indices exhibited comparatively stable behaviour and typically attained interior optima. Confirmatory objectives favoured higher thresholds emphasising specificity, whereas exclusionary objectives favoured lower thresholds emphasising sensitivity. These findings support reporting threshold-wise confidence intervals and aligning cut-off point selection with the intended clinical objective.
Conclusions:
This framework offers a novel integrated, diagnostic threshold based approach for estimating uncertainty across a broad spectrum of DAMs, promoting reproducibility and uptake in laboratory medicine and diagnostic research, and directly supporting clinical decision-making for confirmatory diagnosis, diagnosis for exclusion, and triage.

The figure below, shows the 95% confidence intervals for sensitivity (Se), specificity (Sp), positive predictive value (PPV), and negative predictive value (NPV) of fasting plasma glucose (FPG) in the diagnosis of diabetes mellitus as a function of threshold 𝑡 (in mg/dl), in individuals aged 65–68 years.

21/12/2024

HCSL Publications:
Chatzimichail T, Hatjimihail AT. A Software Tool for Applying Bayes Theorem in Medical Diagnostics. BMC Med Inform Decis Mak. 2024;24:399. DOI: https://doi.org/10.1186/s12911-024-02721-x
Abstract
Background: In medical diagnostics, estimating post-test or posterior probabilities for disease, positive and negative predictive values, and their associated uncertainty is essential for patient care.
Objective: The aim of this work is to introduce a software tool developed in the Wolfram Language for the parametric estimation, visualization, and comparison of Bayesian diagnostic measures and their uncertainty.
Methods: This tool employs Bayes' theorem to estimate positive and negative predictive values and posterior probabilities for the presence and absence of a disease. It estimates their standard sampling, measurement, and combined uncertainty, as well as their confidence intervals, applying uncertainty propagation methods based on first-order Taylor series approximations. It employs normal, lognormal, and gamma distributions.
Results: The software generates plots and tables of the estimates to support clinical decision-making. An illustrative case study using fasting plasma glucose data from the National Health and Nutrition Examination Survey (NHANES) demonstrates its application in diagnosing diabetes mellitus. The results highlight the significant impact of measurement uncertainty on Bayesian diagnostic measures, particularly on positive predictive value and posterior probabilities.
Conclusion: The software tool enhances the estimation and facilitates the comparison of Bayesian diagnostic measures, which are critical for medical practice. It provides a framework for their uncertainty quantification and assists in understanding and applying Bayes' theorem in medical diagnostics.

Available at: https://rdcu.be/d4rV7

23/11/2024

01/11/2024

HCSL Publications:
Hatjimihail AT. Tool for Quality Control Design and Evaluation. Wolfram Demonstrations Project, 2010.

This Demonstration can be used to estimate various parameters of a measurement process and to design the quality control rule to be applied. You define the parameters of the control measurements that are the assigned mean, the observed mean, and the standard deviation, in arbitrary measurement units. In addition, you define the quality specifications of the measurement process, that is, the total allowable analytical error (as a percentage of the assigned mean), the maximum acceptable fraction of measurements nonconforming to the specifications, and the minimum acceptable probabilities for random and systematic error detection. Finally, you choose the number n of control measurements.

Available at:
https://demonstrations.wolfram.com/ToolForQualityControlDesignAndEvaluation/

01/11/2024

HCSL Publications:
Hatjimihail AT. Uncertainty of Measurement and Areas Over and Under the ROC Curves. Wolfram Demonstrations Project, 2009.

This Demonstration compares the ratios of the areas under the curve (AUC) and the ratios of the areas over the curve (AOC) of the receiver operating characteristic (ROC) plots of two diagnostic tests (ratio of the AUC of the first test to the AUC of the second test: blue plot, ratio of the AOC of the first test to the AOC of the second test: orange plot). The two tests measure the same measurand, for normally distributed nondiseased and diseased populations, for various values of the mean and standard deviation of the populations, and of the uncertainty of measurement of the tests. A normal distribution of the uncertainty is assumed. The uncertainty of the first test is defined. It is assumed that the uncertainty of the second test is greater than the uncertainty of the first test and varies up to a user defined upper bound. The six parameters that you can vary using the sliders are measured in arbitrary units.

Available at:
https://demonstrations.wolfram.com/UncertaintyOfMeasurementAndAreasOverAndUnderTheROCCurves/

01/11/2024

HCSL Publications:
Hatjimihail AT. Receiver Operating Characteristic Plots and Uncertainty of Measurement. Wolfram Demonstrations Project, 2007.

This Demonstration compares two receiver operating characteristic (ROC) plots of two diagnostic tests (first test: blue plot, second test: orange plot) measuring the same measurand, for normally distributed nondiseased and diseased populations, for various values of the mean and standard deviation of the populations, and of the uncertainty of measurement of the tests. A normal distribution of the uncertainty is assumed. The ratio of the areas under the ROC curves of the two diagnostic tests is calculated. The six parameters that you can vary using the sliders are measured in arbitrary units.

Available at:
https://demonstrations.wolfram.com/ReceiverOperatingCharacteristicCurvesAndUncertaintyOfMeasure/

01/11/2024

HCSL Publications:
Hatjimihail AT. Uncertainty of Measurement and Diagnostic Accuracy Measures. Wolfram Demonstrations Project, 2009.

This Demonstration compares various diagnostic accuracy measures of two diagnostic tests. The two tests measure the same measurand, for normally distributed nondiseased and diseased populations, for various values of the prevalence of the disease, of the mean and standard deviation of the populations, and of the uncertainty of measurement of the tests. A normal distribution of the uncertainty is assumed. The mean and the standard deviation of each population and the uncertainty of each test are measured in arbitrary units. The measures compared are the positive predictive value (PPV), the negative predictive value (NPV), the (diagnostic) odds ratio (OR), the likelihood ratio for a positive result (LR+), and the likelihood ratio for a negative result (LR-). The measures are calculated versus the sensitivity or the specificity of each test. That can be selected by pressing the respective button. The types of plot are: both measures (first test: blue plot, second test: orange plot), partial derivatives of both measures with respect to uncertainty (first test: blue plot, second test: orange plot), difference, and ratio of the two measures. The types of plot can be selected by pressing the respective buttons, while the seven parameters can vary using the sliders.

Available at:
https://demonstrations.wolfram.com/UncertaintyOfMeasurementAndDiagnosticAccuracyMeasures/

01/11/2024

HCSL Publications:
Chatzimichail T. Analysis of Diagnostic Accuracy Measures. Wolfram Demonstrations Project, 2015.

This Demonstration shows various diagnostic accuracy measures of a diagnostic test for normally distributed nondiseased and diseased populations, for various values of the prevalence of the disease, and of the mean and standard deviation of the populations. The mean and the standard deviation of each population are measured in arbitrary units. The measures shown are the positive predictive value (PPV), the negative predictive value (NPV), the (diagnostic) odds ratio (OR), the likelihood ratio for a positive result (LR+), and the likelihood ratio for a negative result (LR-). The measures are calculated versus the sensitivity or the specificity of each test. That can be selected by clicking the respective button.

Available at:
https://demonstrations.wolfram.com/AnalysisOfDiagnosticAccuracyMeasures/

01/11/2024

HCSL Publications:
Chatzimichail T. Correlation of Positive and Negative Predictive Values. Wolfram Demonstrations Project, 2018.

This Demonstration examines the correlation of the negative predictive value (NPV) and the positive predictive value (PPV) of a diagnostic test for normally distributed nondiseased and diseased populations. Differing levels of prevalence of the disease are considered. The mean and standard deviation of the populations, measured in arbitrary units, are used.

Available at:
https://demonstrations.wolfram.com/CorrelationOfPositiveAndNegativePredictiveValuesOfDiagnostic/

01/11/2024

HCSL Publications:
Chatzimichail T, Hatjimihail AT. Analysis of Diagnostic Accuracy Measures for Two Combined Diagnostic Tests. Wolfram Demonstrations Project, 2018.

This Demonstration shows plots of various accuracy measures for two combined diagnostic tests applied at a single point in time on nondiseased and diseased populations. This is done for differing prevalence of the disease, taking into account the means and standard deviations of the populations and the respective correlation coefficients. The means and standard deviations are expressed in arbitrary units.

Available at:
https://demonstrations.wolfram.com/AnalysisOfDiagnosticAccuracyMeasuresForTwoCombinedDiagnostic/