Positively Perplexed

Why are antibody tests inaccurate? The biostats, explained.

It seems complicated, but let's break it down.

Covid-19 antibody tests are tools scientists use to understand the epidemic.

But how useful they actually are right now, and if you should take one, is confusing.

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In some cases, a positive antibody test may only be right about half the time, reports the CDC.

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This may seem perplexing but it's easy to understand with pictures.

Every antibody test must do two things:

- Accurately identify people who have antibodies. Epidemiologists call this sensitivity.

- Accurately identify people without antibodies. This is called specificity.

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Now, imagine you have a test with:

1. 90 percent specificity. 9/10 people with antibodies correctly test positive.

2. 90 percent sensitivity. 9/10 people without antibodies correctly test negative.

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Imagine you use that test on two Earths, each with 100 people...

On Earth 1, let's say 10 percent of people have antibodies (red).

*This is theoretical, but you can get a good rundown of antibody prevalence in major world cities here.

On Earth 1, there are 10 people with antibodies (red). Nine of them get back correct, positive test results. One person receives a false negative (pale red).

Image: Zachary Binney. Altered for publication by Emma Betuel.

There are also 90 people without antibodies. Eighty-one (90 percent) of them get back correct, negative test results. But 9 people get false positives (pale blue).

Image: Zachary Binney. Altered for publication by Emma Betuel.

Let's zoom in on all the people who get positive antibody tests back.

9 people correctly test positive (red +).

9 people receive false positives (pale blue +).

That means there is only a 50 percent chance your positive test is one of the real positives. (9/18)

Image: Zachary Binney. Altered for publication by Emma Betuel.

Now, imagine that 40 percent of people have antibodies

Watch how the numbers change.

Here, 40 people have antibodies (red). Thirty-six people receive correct, positive test results. But four people receive false negatives (pale red).

Image: Zachary Binney. Altered for publication by Emma Betuel.

There are 60 people without antibodies. Fifty-four people receive correct, negative test results. But six people receive false positives (pale blue).

Image: Zachary Binney. Altered for publication by Emma Betuel.

36 people have correct positives (red +)

6 people have false positives (pale blue +)

Image: Zachary Binney. Altered for publication by Emma Betuel.

86%

There is about an 86 percent chance (36/42) that your positive antibody test is correct in this case.

The chance that your positive antibody test means you truly have coronavirus antibodies is called positive predictive value.

High sensitivity and specificity are important metrics for any test. But positive predictive value, even more so, is what helps gauge the accuracy of one's test results.

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The FDA estimates the positive predictive value of antibody tests by assuming that 5 percent of the population has antibodies.

Positive predictive values from some tests range from as low as 55 percent to as high as 100 percent (but it's still just an estimate).

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The WHO estimates only about 2 to 3 percent of the population has been exposed.

That number is higher in certain places, like New York City, where an estimated 20 percent of residents were infected by early May.

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With prevalence relatively low, there's a chance that your test may not be perfectly accurate.

However, you can read about the most useful way to get antibody tested here.

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