1.1.3. Positive and negative predictive values
While sensitivity and specificity primarily measure a test’s accuracy, epidemiologists use two other measures, positive and negative predictive values, to help describe the certainty of a specific test result. A Positive Predictive Value (PPV) is the probability that a person/animal with a positive test result truly has a disease P(D+/T+). PPV is typically expressed as a proportion (Equation 1.1.3.a).
A Negative Predictive Value (NPV) is the probability that a person/ animal with a negative test result truly does not have disease P (D-/T-). NPV is typically expressed as a proportion (Equation 1.1.3.b).
If sensitivity and specificity remain constant, as the prevalence of a disease increases so does the PPV while the NPV decreases.
Over the inspection season of 2004 and 2005, Pennsylvania state bee inspectors preformed 107 Holst’s milk tests on suspect cases of clinical American foulbrood disease (for more information about this test, see the BEEBOOK paper on American foulbrood (de Graaf et al., 2013)). Ninety samples tested positive with the Holst’s milk test (Holst, 1945), of which 89 were confirmed in the laboratory to be AFB infection. Confirmation of diagnosis was performed by culturing a smear of diseased larvae sampled from the same colony. The Holst’s milk test resulted in 14 negative and three inconclusive results. The latter were discarded. Six of the negative samples were later diagnosed to have had AFB when companion samples were cultured (vanEngelsdorp, unpublished data). The sensitivity and specificity as well as the positive and negative predictive value of this test can be calculated as follows:
Because the denominator is less than 30, the normal approximation of the binomial distribution cannot be assumed and for the calculation of the 95% CI we used the binomial tables. Thus, the
Thus, when a Holst’s milk test is performed and comes back positive we are 99% certain the sample does contain American Foulbrood spores, while if the Holst’s milk test comes back negative we are 53% sure that the sample does not have American foulbrood spores.