## HCSL Publications

# Diagnostic Accuracy

### 1. Hatjimihail AT. Resource review: Whiting P. Quality of diagnostic accuracy studies: The development, use,
and evaluation of QUADAS. Bristol: P E Whiting, 2006.Evidence-Based
Medicine 2006:11;189.

Full text in Evidence Based Medicine

### 2. Hatjimihail AT. Receiver Operating
Characteristic Plots and Uncertainty of Measurement. Wolfram Demonstrations
Project, 2007.

#### Abstract

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.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code (Revised on 09/04/2018)

### 3. Hatjimihail AT. Uncertainty of Measurement
and Areas Over and Under the ROC Curves. Wolfram Demonstrations Project,
2009.

#### Abstract

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.

#### Comment

Although the uncertainty of measurement correlates poorly with the ratio of the areas under the curves, correlates better with the areas over the curves. Therefore, although the uncertainty of measurement has little effect on the diagnostic accuracy of the test, it has a considerably greater effect on its diagnostic inaccuracy.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code (Revised on 06/04/2018)

### 4. Hatjimihail AT. Uncertainty of Measurement
and Diagnostic Accuracy Measures. Wolfram Demonstrations Project,
2009.

#### Abstract

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.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code (Revised on 06/04/2018)

### 5. Chatzimichail T. Analysis of Diagnostic
Accuracy Measures. Wolfram Demonstrations Project, 2015.

#### Abstract

This Demonstration shows various diagnostic accuracy measures of a
diagnostic test for normally distributed nondiseasdy 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.

Snapshot of the Demonstration

Demonstration at the
Wolfram Demonstrations Project

Mathematica source code (Revised on 30/03/2018)

### 6. Chatzimichail T. Correlation of Positive and
Negative Predictive Values. Wolfram Demonstrations Project, 2018.

#### Abstract

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.

Snapshot of the Demonstration

Demonstration at the Wolfram
Demonstrations Project

Mathematica source code

### 7. Chatzimichail T, Hatjimihail AT. Analysis
of Diagnostic Accuracy Measures for Two Combined Diagnostic Tests. Wolfram
Demonstrations Project, 2018.

#### Abstract

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. You can select the following measures of the combined tests using the "plot" popup menu: sensitivity, specificity, positive predictive value, negative predictive value, (diagnostic) odds ratio, likelihood ratio for a positive result, and likelihood ratio for a negative result. These measures are plotted against the sensitivities or the specificities of each single test. You can select them by clicking the respective "versus" button.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code (Revised on 10/04/2018)

### 8. Chatzimichail T, Hatjimihail AT. Relation of Diagnostic Accuracy Measures. Wolfram Demonstrations Project, 2018.

#### Abstract

This Demonstration examines the relation of pairs of accuracy measures of diagnostic tests applied on normally distributed nondiseased and diseased populations. This is done for differing prevalence of the disease, taking into account the means and standard deviations of the populations. The means and standard deviations are expressed in arbitrary units. The measures considered 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 can be selected by clicking the respective "plot" and "versus" buttons.

#### Comment

To the best of our knowledge, with the exception of the pair PPV and NPV, the relation of any other pair of the given diagnostic accuracy measures has not been discussed in the literature.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code

### 9. Chatzimichail T. Calculator for Diagnostic Accuracy Measures. Wolfram Demonstrations Project, 2018.

#### Abstract

This Demonstration calculates various accuracy measures of a diagnostic test for a disease. This is done for differing negative and positive test results of nondiseased and diseased populations. The measures calculated are the sensitivity, the specificity, the positive predictive value ("PPV"), the negative predictive value ("NPV"), the (diagnostic) odds ratio ("OR"), the likelihood ratio for a positive test result ("LR+"), and the likelihood ratio for a negative test result ("LR-"). The negative and positive test results of the nondiseased and diseased populations are selected using the sliders.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code (Revised on 12/06/2018)

### 10. Chatzimichail T, Hatjimihail AT. Calculation of Diagnostic Accuracy Measures. Wolfram Demonstrations Project, 2018.

#### Abstract

This Demonstration shows calculations of point estimations and confidence intervals for various accuracy measures of a diagnostic test for a disease. This is done for differing negative and positive test results of nondiseased and diseased populations and differing *p*-values for the estimations of the lower and upper bounds of the confidence intervals. The calculated measures are the sensitivity, the specificity, the positive predictive value ("PPV"), the negative predictive value ("NPV"), the (diagnostic) odds ratio ("OR"), the likelihood ratio for a positive test result ("LR+"), and the likelihood ratio for a negative test result ("LR-"). The measures can be selected using the menu. The negative and positive test results of the nondiseased and diseased populations, along with the *p*-value, are chosen using the sliders.

#### Comment

The Wilson score method with continuity correction is used for calculating the confidence intervals of the sensitivity, the specificity, the positive predictive value and the negative predictive value. For the calculation of the confidence intervals of the (diagnostic) odds ratio, the likelihood ratio for a positive test result and the likelihood ratio for a negative test result, it is assumed that their natural logarithms have asymptotically normal distributions.

Snapshot of the Demonstration

Demonstration at the Wolfram Demonstrations Project

Mathematica source code
(Revised on 26/07/2018)