Correlation of Positive and Negative Predictive Values of Diagnostic Tests

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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.

Contributed by: Theodora Chatzimichail (April 2018)
(Hellenic Complex Systems Laboratory)
Open content licensed under CC BY-NC-SA


The PPV and NPV that are used in the evaluation of the clinical accuracy of a diagnostic test applied to a diseased or nondiseased population can be calculated given the sensitivity and specificity of the test. Sensitivity is the fraction of the diseased population with a positive test, while specificity is the fraction of the nondiseased population with a negative test. If we denote by the sensitivity, the specificity and the prevalence, then:



Given a diseased and a nondiseased population, the specificity can be defined as a function of sensitivity; therefore, we can plot PPV versus NPV (a parametric plot).

The population data in the snapshots describes a bimodal distribution of serum glucose measurements in nondiabetic and diabetic populations [1].

This Demonstration is based on [2].


[1] T.-O. Lim, R. Bakri, Z. Morad and M. A. Hamid, "Bimodality in Blood Glucose Distribution: Is It Universal?," Diabetes Care, 25(12), 2002 pp. 2212–2217. doi:10.2337/diacare.25.12.2212.

[2] A. T. Hatjimihail. "Uncertainty of Measurement and Diagnostic Accuracy Measures," from the Wolfram Demonstrations Project—A Wolfram Web Resource.


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