Why not test everyone for HIV infection? Because all screening tests have a property known as positive predictive value -- the probability that a positive test result is truly positive. Positive predictive value is greatly influenced by the prevalence of the disease or infection in the population being tested. Why this is so is shown by calculating the positive predictive value for the same test when applied to a population in which HIV infection is highly prevalent as compared to population in which the prevalence is low.

Consider the example of a high-prevalence population -- injection drug users in a major city in which half the drug users are infected (i.e., the prevalence of HIV in the population is 50%). For convenience, the size of the population is said to be 100,000. That means 50,000 people will be infected and 50,000 uninfected. The text used in the example will have a specificity of 99.9% -- it will yield 1 false positive per 1,000 people tested, or 50 false positives per 50,000 people tested. The positive predictive value is calculated as follows:

Positive predictive value

=

True positives       True positives + False positives 49,950 50,000

= 99.9%

This result means that a positive test result has a 99.9% chance of being a true positive. But the probability changes when the same calculation is applied to a population with a low prevalence of infection. Take, for example, self selected and previously tested blood donors from the general population. Here the prevalence of infection might be 1 case per 100,000 people.

Thus, for every 100,000 people, 1 person is infected and 99.999 are uninfected. If the test has a specificity of 99.9%, it means 0.1% -- about 100 of the test results will be false positives. Now calculate the positive predictive value:

Positive predictive value

=

True positives       True positives + False positives  1  101

= 1.0%

This means that a positive test result in this population has only a 1% chance of being a true positive!