There’s a new test for HIV which has just received FDA approval for over the counter sales. This has been widely reported in the press. Not surprisingly the press is having a lot of trouble understanding what a positive test means. The NY Times tied itself into a knot on the subject. The closest to reality I have found is the report from Reuters: The test is about 92 per cent accurate in detecting people who do have the virus and 99.98 percent accurate in detecting those who don’t, according to company trials. This means the test would produce a false negative for about one person in 5,000 and a false positive for one person in 12. Naturally, positive tests would require further confirmation by medics, who attain a higher accuracy of diagnosis.
They’re on the right track, but only get halfway home. What you want to know is how likely a person who has a positive test is likely to really be HIV positive; this is called the positive predictive value (PPV). The test is said to be 92% sensitive. This does not provide enough information to calculate the PPV despite what Reuters thinks, ie “a false positive for 1 person in12.” To get this value you must know the prevalence of the disorder you are testing for. The chart below shows the relationship of prevalence to PPV for a test with a 95% sensitivity. The new test has a lower sensitivity – 92%.
The prevalence of undiagnosed subjects who are HIV positive is 232,700 out of a US population of around 310,000,000 or 0.08%. Thus if the entire US population population were subjected to this new test there would be more than 24 million false positive tests. The test is 92% sensitive which mean it has an 8% false positive rate. True positive tests would number 213,400 (92% of 232,700). This gives a PPV of a little less than 0.9% – (213,400)/24,213,400) x 100. If a smaller population with the same prevalence were tested the PPV would still be the same.
It’s hard to know what the prevalence of HIV positivity will be in people who elect to undergo the test. It will certainly be higher than that of the general population. Thus the PPV will be higher. So the real question about the usefulness of this test will be whether its users are sufficiently self selected (will they have a higher risk for HIV than the general population?) to raise the PPV to a high enough level (look at the above chart) that will not overrun our already overburdened medical system with a tsunami of patients running to the doctor with false positive tests.