## On the Accuracy of Covid-19 Testing

As someone who suspects I may have had a mild case of Covid-19 a couple of months ago, I've been thinking about getting tested for antibodies. But as this video from ProPublica shows, even really accurate tests may not actually tell you all that much.

And the thing is, the "do I have Covid-19 right now" tests are plagued by the same issue.

For patients getting tested, the main concern is how to interpret the outcome: If I test negative with an RT-PCR genetic test, what are the chances I actually have the virus? Or if I test positive with an antibody test, does it actually mean I have the antibodies?

It turns out that the answers to these questions don't just hinge on the accuracy of the test. "Mathematically, the way that works out, that actually depends on how many people in your area have Covid," Eleanor Murray, an assistant professor of epidemiology at the Boston University School of Public Health, said.

The rarer the disease in the population, the less you'll learn by testing.

Let's say we have a hypothetical Covid-19 test for antibodies that is both 99 percent sensitive — meaning almost all people with antibodies will test positive — and 99 percent specific, meaning almost all people who were never infected will yield a negative result.

If you test a group of 100 uninfected people, odds are one of them will still test positive even though they don't have the virus. Conversely, if you test 100 people who were infected, it's likely one of them will still test negative.

Now let's presume the virus has a prevalence rate of 1 percent, so one person in 100 carries antibodies to it. If you test 100 random people and get a positive result, what is the chance that this person was truly infected?

Deborah Birx, the White House Covid-19 response coordinator, explained the answer at a press conference on April 20: "So if you have 1 percent of your population infected and you have a test that's only 99 percent specific, that means that when you find a positive, 50 percent of the time will be a real positive and 50 percent of the time it won't be."

So even if I test positive for antibodies and I assume that confers immunity, given that the number of confirmed infections in Vermont is so low (~900 statewide), it doesn't seem like I would be justified in changing my behavior at all. I would still have to act as though I've never had the virus, both for my own health and the health of those around me. Maybe if I had two or three corroborating tests could I be more certain...