Positive and negative predictive values

To fully describe the accuracy of HIV tests, one further set of numbers is needed. The positive predictive value is defined as the proportion of persons with positive test results who are correctly diagnosed. While at first glance this may seem the same as 'sensitivity', it is in fact a distinct value that also depends on the prevalence of HIV infection in the population being tested.

The positive predictive value is the number of persons correctly diagnosed as HIV-positive, divided by the total number of HIV-positive findings. In our example, we had 9900 'true positive' test results – infected persons who tested positive – and 9000 false positive results. The positive predictive value in this case is (9900)/(9900 + 9000), or 52.4%. In other words, when our hypothetical test was used in a population with 10% prevalence of HIV, nearly half of its positive results were false. In a subpopulation with higher HIV prevalence, the positive predictive value would be higher, as there would be more truly HIV-positive findings compared to the constant rate of false positive results.

Because most tests have relatively low positive predictive value in a population where HIV infection is quite uncommon, an HIV diagnosis is never made on the basis of a single test result, but extra confirmatory tests are used. The positive predictive value of two or three different tests, used in combination, is extremely high.

Conversely, the negative predictive value is defined as the proportion of persons with negative test results who are correctly diagnosed. This value, too, depends on HIV prevalence. The negative predictive value is the number of persons correctly diagnosed as HIV-negative, divided by the total number of HIV-negative findings. The 81,000 'true negative' and 100 false negative results in our example yield a negative predictive value of (81,000/81,100), or over 99.9% – a very high likelihood that a negative result indicates a truly HIV-uninfected person.¹

The HPA provides an online calculator for positive and negative predictive values at: www.hpa-midas.org.uk/online_apps/ppv_npv_calculator.asp