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Just Because You Test Positive for Antibodies Doesn’t Mean You Have Them

In a population whose infection rate is 5 percent, a test that is 90 percent accurate could deliver a false positive nearly 70 percent of the time.

Testing for the coronavirus last month at a drive-through site in Syracuse, N.Y.Credit...Damon Winter/The New York Times

Todd Haugh and

Professors Haugh and Bedi are researchers who study judgment and decision-making.

Whether you think the country is reopening too fast or too slowly (or whether you think “it depends”), almost everyone agrees that testing should be critical to the next phase of our coronavirus existence. In particular, antibody tests that detect whether a person has developed immunity to the virus seem to offer a promising path forward.

But what does a positive antibody test mean? It means you should feel confident that you can work, shop and socialize without getting sick or infecting others, right?

Not so fast.

The confidence that we should have in antibody tests depends on a key factor that is often ignored: the base rate of the coronavirus. The base rate is the actual amount of infection in a known population. In the United States, that appears to be between 5 percent and 15 percent.

This simple fact is essential to understanding the accuracy of an antibody test. Yet overlooking this fact is also one of the most common decision-making errors made, so much so that it has its own name: the base rate fallacy.

Here’s an example. If you took an antibody test that was 90 percent accurate, and it determined that you had coronavirus antibodies, how confident should you be that you actually have those antibodies?

Most people say about 90 percent, with the average answer being above 50 percent. This makes sense. After all, 90 percent accuracy is pretty high.

But the predictive value of an antibody test with 90 percent accuracy could be as low as 32 percent if the base rate of infection in the population is 5 percent. Put another way, there is an almost 70 percent probability in that case that the test will falsely indicate a person has antibodies.

The reason for this is a simple matter of statistics. The lower prevalence there is of a trait in a studied population — here, coronavirus infection — the more likely that a test will return a false positive. While a more accurate test will help, it can’t change the statistical reality when the base rate of infection is very low.

If this shocks you, you’re not alone. The base rate fallacy is not only common, it’s also almost universal, even among those that should know better. Doctors themselves make these errors. In fact, one of the most referenced studies demonstrating the base rate fallacy took place among students at Harvard Medical School.

So what does this mean as the country begins to open?

Mostly it means we have to educate ourselves to safeguard our own health. And it means that we’re all at risk of getting infected and spreading the virus, even if we’ve had a positive antibody test.

So we have to be circumspect. Just because a test is highly accurate, that may not be as comforting as it first appears.

To be sure, antibody tests are important, and we should encourage greater access to these tests. But we should also view them with thoughtful reflection, informed predictions as to their accuracy and, at the very least, good decision-making.

Todd Haugh is an associate professor and Suneal Bedi is an assistant professor of business law and ethics at Indiana University’s Kelley School of Business.

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