Today’s lesson plan included teaching my students about Bayes’ Rule and its application to disease and drug testing. Coincidentally, the first news article on MSN.com this morning (which I found about an hour before class) was on the CDC’s recent recommendation to routinely test everyone between 13 and 64 for HIV.
Hoping for a concrete and topical application, I tried to get estimates of the relevant numbers. Finding HIV prevalence was easy enough; according to the latest estimates, about 1 million Americans have HIV, of whom about a quarter don’t know it. If we assume all infected persons are in the 10-64 age range (a group of 215 million people), the prevalence rate for that group is about 0.47%. But what about false positive rates? Those turned out to be harder to find.
The good news is that HIV tests are usually administered sequentially: if the first test comes up positive, a second (presumably more accurate) test is performed, and only if both tests come up positive is the subject presumed to be infected.
The bad news is that the first round tests (like ELISA/EIA and OraQuick) have a false positive rate of about 0.2%. That doesn’t sound bad, until you realize (based on the prevalence numbers above) that if we tested everyone aged 10-64, nearly 30% of those who tested positive on the first round would actually be uninfected. That’s about 430,000 people. (I’m assuming a zero false negative rate for simplicity.)
Fortunately, many of those people would eventually be ruled out by the subsequent test. But how many false positives would remain? This is the part that came as something of a surprise to me: we just don’t know. To calculate the answer, we’d need the false positive rate of the Western Blot test, which is the test used in the second round. But the Western Blot is widely used as the definition of what it means to be infected. When they calculate the false positive rates of other tests – like those used in the first round – they use the Western Blot as the standard of truth. Yet apparently there are good reasons to question the infallibility of the Western Blot; see this 1993 paper, for example. I couldn’t find anything more recent on the reliability of this test. Does anyone know where I can find an estimate of the Western Blot’s false positive rate, or better yet, the rate at which uninfected persons test positive for both the initial test (usually ELISA) and Western Blot? (Don’t point me to the Burke study, because that’s the one sharply criticized in the article cited above.)