# Why Your Positive Coronavirus Antibody Test May Be Wrong

The CDC has released new guidance on antibody testing, which notes that a test with 90-95% accuracy can give false positives in more than half of the time. This sounds shocking, but it may be true – and it is important to understand why if you are about to get tested or have already tested positive.

In this post, I am talking specifically about testing for antibodies to coronavirus. While the caveats we will discuss apply to many types of testing, they are especially important as we are trying to figure out how many people have been exposed to the novel coronavirus.

### There are different ways to measure accuracy

How do we know how accurate a test is? We have to compare this with another test. For antibody tests, precision figures are derived from the following:

How many positive samples does the test correctly identify as positive? To do this, laboratories use blood samples from people known to be infected with COVID-19 and who have tested positive for a smear. If the test correctly identifies 90% of them as positive, we say that the test has a sensitivity of 90%.

How many negative samples are correctly identified as negative? To answer this question, laboratories are using samples collected before the pandemic, before anyone could contract the virus that causes COVID-19. If the test correctly identifies 95% of negative samples as negative, we say that it has 95% specificity .

These numbers seem to be pretty high – 90 and 95 percent in our example – but they don’t answer the question of what the test result means . (I chose these numbers because, by the way, they are what the CDC uses in its example.) To do this, we need to know how common this virus is. Yes, that’s a little gimmick-22, as the only way to find out is to test people. But with the accuracy rates calculated above, estimates can be made. We know that we are far from herd immunity, for example, and most likely somewhere around 5% in many places.

### What does a positive result mean?

Let’s say 5% of the people in your community have developed antibodies to the coronavirus. Nice representative 100 of you lined up at the proving ground. Five of you do have antibodies and 95 do not.

Of the five people with antibodies, 90% are correctly identified as having them. That’s 4.5 people, so let’s round up and say that all five tested positive. So far, so good.

But of 95 without antibodies, only 95% are correctly identified as negative. This means that 90.25 people (rounded up to 90) got negative results, and the remaining five people got positive results.

Who leaves the testing center that day? 90 people with negative results and 10 people who have just been told they are positive.

Of these 10, 5 are true positive and 5 are false.

The number we just calculated has a name: positive predictive value . This test only has a 50% predictive value because true positive results are very rare. (If, instead, 70% of people were actually exposed to the virus, there would be 63 true positives and one or two false positives.)

### What if the test is positive?

Here’s the problem: I’ve heard people tested positive for antibodies and then assumed they were immune to the disease. They visit friends, go without masks, believe that there is nothing wrong with getting a job that will put them in close contact with infected people.

But our tests are not good enough to be used as a basis for this kind of decision. In fact, the CDC says you should n’t do anything differently after you get a positive test result.

• Asymptomatic people with a positive serological test and no recent history of COVID-19 compatible disease have a low likelihood of active infection and should follow general guidelines for preventing SARS-CoV-2 infection and continue with normal activities, including work.
• Individuals who have had a COVID-19 compatible illness or a confirmed illness should follow previous guidelines for resuming normal activities, including work .
• There should be no change in clinical practice or the use of personal protective equipment (PPE) by healthcare workers and first aiders who test positive for SARS-CoV-2 antibodies.

In short: if you have not been sick, you should not assume that you have ever been sick. And if you were sick, you should still follow whatever guidance you were given before. The test doesn’t change anything for you personally.

Antibody tests are useful for large groups of people so that the mayor, governor, or epidemiologist can assess how common infections really are. Research on this matter is ongoing. They are not useful for making decisions on an individual level. Sorry.

### Okay, but that was an example. What are the real numbers?

Hey, I have good news for you! Some tests are better than the above example and you can find out which is which.

The FDA has a list of currently approved tests that indicate their sensitivity and specificity. They even calculate both the positive predictive value and its counterpart, the negative predictive value, for you. Here are some examples:

This Cellex test finds 93.8% positive and 96% negative results. Assuming that 5% of the population has contracted the virus, if you get a negative test result, the chance that you are indeed negative is roughly 99.7%. But if you get a positive result, the chance that you do have antibodies is only 55.2%.

However, not all tests have such a low positive predictive value. Here’s another one:

This is a different type of test and is more accurate. So accurate, in fact, that even if only 5% of the population contracted the virus, the positive predictive value is still around 92.9%. Thus, your positive result is more likely to be accurate than with the test we discussed in the example, but this is still not a guarantee. (Also note that the confidence interval is quite wide – 92.9% is an estimate over a wider range.)

Regardless of which test you take, the recommendations still apply: even if you passed one of the most accurate tests, a positive result does not mean that you will go to a party and then cough up your grandmother. To find out more about which antibody tests may and may not tell you about your COVID-19 status, check out our post about just that .

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