The Homa Files

Not a surprise according to Bayes’ Theorem
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According to the NYT and many other sources…

As part of a screening by the White House, Mr. DeWine first received an antigen test, a newer type of test that provides faster results but is less accurate than traditional laboratory testing.

He tested positive for Covid-19

He was later twice-tested using a more standard procedure known as polymerase chain reaction, or P.C.R., an accurate but time-intensive method that requires samples to be processed at a laboratory.

That test result was negative for the Covid-19.

DeWine’s experience is a classic “false positive” … to be expected based on Bayes’ (Statistical) Theorem.

Let me explain…

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Med tests aren’t 100% accurate … Covid tests are no exception.

So, they are susceptible to false positives (indicating an infection when there isn’t one) … and false negatives (failing to detect an infection that is present).

The likelihood of a false reading is a function of a test’s accuracy and contextual factors.

Context

Bayes’ Theorem (or “Bayesian Inference)is a way to calculate probabilities by combining case-specific observations (think: testing results or witness testimony) with contextual information.

For a complete explanation, see “Confirmed cases” are skyrocketing … how many are false positives?

For Covid testing, the contextual factors include the prevalence of COVID where you live, your behavior (e.g. sheltering-in-place, out working with patient or customer contact, socializing) and your symptomology (i.e. no, mild or severe COVID-like symptoms).

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Gov. DeWine’s context

Gov. DeWine (age 73) had been doing business from his secluded farm (i.e. sheltering in place) … and wasn’t experiencing any Covid-like symptoms.

So, the swing factors for evaluating the likelihood of a false positive are Covid’s prevalence in his locale and the test’s accuracy.

In a prior post, we reported some estimates for Covid’s prevalence.

See How many people are walking around infected with Covid-19?

The IHME estimates that the current prevalence rate in Ohio is 1.05%.  That is, about 1 in 100 Ohioans are currently infected.

Note: The prevalence rate within Gov. DeWine’s specific “reference group” — given his lack of symptoms and sheltering-in-[lace behavior — is likely well below 1%.

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Test accuracy

Admiral Brett Giroir, in charge of testing for the Feds, says the current tests have a 90% accuracy rate, with errors evenly balanced between false positives and false negatives.  Source

Tech note: Rapid results antigen tests are generally less sensitive and less accurate than the traditional nasal swab, PCR laboratory test.

Antigen tests are more likely to produce false negatives — missing someone who has the virus — than false positives.

When testing known positive patients, the tests produce false negative results between 15 and 20 percent of the time.

While false positives are less likely than false positives, the odds of a false positive are still statistically significant — in the range of 5% to 10% when testing people known to be uninfected.

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Plugging those parameters — 90% accuracy and 1.05% prevalence — into a standard Bayesian matrix (the chart above) indicates  that Gov. DeWine’s positive test result had a 91.3% chance of being a false positive.

Despite that long odds of DeWine being infected, his meeting with Pres. Trump was cancelled. That was a prudent action.

Then, DeWine was retested using a standard Covid PCR lab test.  He tested negative. The probability of a false negative (given 90% accuracy and 1.05 prevalence) is less than 1%.

If DeWine had tested positive again, the positive diagnosis would be a near certainty.

Trust me on the stats: The probability of 2 consecutive false positives is very remote, especially when at least one of the tests is a PCR version.

A 2nd follow-up PCR test administered to DeWine on Saturday confirmed the negative diagnosis.

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Bottom line

It’s not surprising that DeWine’s retest was negative.  In fact, it should be expected given the test accuracy and Covid prevalence.

More generally, if you test positive but you’re asymptomatic and not living in a current Covid hot spot, don’t panic.  Get retested. There’s a high probability that the test was a false positive.

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Question: What does all of this imply for the skyrocketing number of “confirmed” cases being reported?

My bet: there are a lot of false positives in those numbers.

This entry was posted on August 11, 2020 at 10:00 am and is filed under Coronavirus - Covid 19, Covid-19 Testing. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.