Screening for HIV

Yesterday's news that the CDC is recommending HIV screening for people aged between 13-64 tended to overlook one key factor: the false positive rate.

No test is perfect, and the more people you test, the more false positives it will generate. A false positive is when the test indicates you have an infection, when really you don't.

Yesterday's recommendation will exacerbate this because it recommends testing for low-risk groups, where true positives are presumably rare. The rate of false positives to true positives will therefore be higher in this group. This means many healthy people will be told they have HIV.

Where the base rate of infection is low (say 0.01% as it is for women), it could be the case that for every truly identified person with infection, there will be 50 times as many identified who don't have HIV:

Interestingly enough, this situation is analogous to warrantless wiretaps. These wiretaps are a form of "data mining" which listen to our phone calls to find terrorists. They too will turn up thousands if not millions of false positives, that is, false leads that have to be traced down and dealt with--perhaps by forcibly conducting people to other countries to be tortured, perhaps just by using time and resources to check each lead.

To see why, let's do the numbers (this is based on an example developed by John Allen Paulos, and the New England Journal of Medicine article from which the graph above was taken. I'm not a mathematician so I hope I've interpreted things correctly).

Let's say that the HIV test is 99.5% accurate. So people with HIV will be found 99.5% of the time. That's great, it's pretty sensitive. Let's say out of every 200 people tested 1 person without HIV will also show positive (false positive rate of 0.005).

We also need to know the prevalence of a disease. Well, HIV varies by risk group. The CDC is proposing to test the entire adult population. I don't know the prevalence of HIV (although it is low).

Let's see. There are an estimated 1 million people with HIV/AIDS in this country. There are about 200 million people aged 14-65. If we test this age group, we will find 995,000 of the people with HIV if it is 99.5% accurate. But for every million tested it will indicate 5,000 people have HIV who don't. In a population of 200 million that's 1 million false positives. Too many.

An article in the New England Journal of Medicine raised the issue of false positives as long ago as 1987:

Plans to test low-risk populations for HIV antibody generally ignore the possibility of false positive results. ... But before we establish a public policy of widespread screening, we should consider whether testing that is justified in the blood bank is also justified in other settings. If the false positive rate is not virtually zero, screening a population in which the prevalence of HIV is low will unavoidably stigmatize and frighten many healthy people.
Is a test rate of 99.5% realistic? If a positive result is obtained it is usual to carry out a second test. This can lower the false positive rate. But obviously even if it is cut to 100,000 or 10,000, we're still talking about huge numbers of people who will go through the worry and anxiety of being told they have HIV.

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