The tremendous increase in testing for COVID-19 (C19) this summer was associated with an increase in cases. Most of these tests were so-called PCR tests with samples collected via deep nasal swabs. More testing did not fully explain the increased case load, but false positives (FPs) still accounted for a substantial share. That’s especially true in light of the decline in positivity rates, which reflected a decline in the actual prevalence of active infections. FPs also account for a substantial share of the deaths attributed to COVID, which are obviously cases of false attribution. If a test for C19 is positive, it will be listed on the death certificate.  

COVID Case Inflation

The exaggeration of confirmed cases due to FPs is more substantial as the prevalence of active infection declines. That’s because the share of true positives in the tested population declines, while the share of false positives must rise due to the greater share of uninfected individuals in the population.

Now, as the contagion is waning in former hot spots, there is a danger that FPs create the impression of persistence in the case counts. That’s costly not just for those incorrectly diagnosed, but also in terms of medical resources, for communities subject to excessive public intervention, such as inappropriate lockdowns, and in terms of the fear promoted by these inaccuracies.

FPs are extremely disruptive when testing is relied upon in critical situations such as health care staffing, or even among sports teams. For example, at the University of Arizona, out of 25 positive tests on September 3, only 10 were confirmed as positives in later tests. The NFL has also had its share of false positives. 

Lax Testing Standards

There is evidence that testing standards under CDC guidance are so broad that a large number of inactive, non-infectious cases are being flagged as positives (see the chart above for the intuition, as well as the graphic at the bottom of this post). The tests sometimes amount to a coin flip when it comes to evaluating positives; some of the positives might even come from non-novel coronaviruses such as the common cold! This paper by Andrew N. Cohen, Bruce Kessel, & Michael G. Milgroom – CKM) questions the guidance of public health authorities on testing more generally. From the abstract (my emphasis):

“Unlike previous epidemics, in addressing COVID-19 nearly all international health organizations and national health ministries have treated a single positive result from a PCR-based test as confirmation of infection, even in asymptomatic persons without any history of exposure. …  positive results in asymptomatic individuals that haven’t been confirmed by a second test should be considered suspect.”

False Positive Math

When I wrote about “The Scourge of False Positives” in July. I noted that a test specificity of 95% implies that 5% of uninfected individuals will falsely test positive. Unfortunately, that still produces a huge number of FPs when testing is broad. That’s NOT a good reason to avoid broad testing; it just means that positive tests should be confirmed by another test. (In this case, two tests with the same specificity reduce a 5% false positive rate to 0.25%. That’s why fast, cheap tests are necessary for confirmation.

Again, exaggerated case counts due to FP’s become more severe as a contagion wanes. That’s because FPs become an increasingly large share of positive test results and overstate the persistence of the virus. If active infections fall to 1% of 750,000 daily tests, or 7,500 true cases, the 5% specificity implies 37,125 FPs: true positives would be only 17% of positive cases. Much worse than a coin flip! And again, which cases are infectious?

How Bad Are FPs, Really?

This recent research, also authored by CKM, explains the reasons why FPs are usually an issue in the real world, despite the tests’ reportedly perfect reactivity to anything other than the virus’ genetic fragments. CKM find that the median FP rate in their sample of “tests of tests” was 2.3%. That means 23 out of every 1,000 uninfected people tested will test positive.

If that seems small to you, suppose the true prevalence of active infection in a population is 4%. If 1,000,000 people are tested and there are no false negatives (unlikely), then 40,000 infected people will be identified by the test. However, another 22,000 uninfected people will also test positive ((1,000,000 – 40,000 infected) x 0.023). That means the number of positive tests will be inflated by 55%. They’ll all receive some form of treatment or ordered into quarantine. Expanded Testing and FPs This summer, the volume of daily tests increased from about 150,000 a day in early April to more than 750,000 a day in July. That’s a 400% increase, but the true prevalence of active infection in the expanded test population during the summer was almost certainly lower than in the spring. Suppose active infections fell from 10% of the test population in the spring to 5% in the summer. That means the daily number of “true positives” would have risen from 15,000 to 35,000 in the expanded test population (and again I assume no false negatives for simplicity). The number of FPs, however, would have risen from 3,105 to 16,445. Therefore, FPs would have accounted for 40% of the increase in “confirmed” cases between spring and summer.

False COVID Deaths

FPs are also inflating COVID death counts. PCR tests are routinely given at hospital admission for any cause, and even after sudden death, especially as the availability of tests increased late in the spring. This subset of the tested population will certainly have its share of FPs. If such a patient dies, regardless of underlying cause, it might well be attributed to COVID-19 as it will still appear on the death certificate. The same has occurred in the case of traffic fatalities, suicides, and other sudden deaths.

Antibody Tests

The FP problem also plagues tests of seroprevalence, which determine whether an individual has had the virus or is cross-protected against the virus by antibodies acquired via non-novel coronavirus infections. The consequences of these antibody FPs can be serious as well, because it means a positive test might not ensure immunity. As the exposed share of the population increases, however, the FP share of antibody tests is diminished.

Conclusion

As long as testing is required, dealing with FPs (and false negatives, of course) requires repeated testing, as CKM state unequivocally. And the tests must be fast to be of any use. The current testing regime must be overhauled to prevent false positives from costly impositions on the lives of uninfected patients, consuming unnecessary medical resources, making unrealistic assessments of cases and deaths, and unnecessary suspensions of normal human social activity and liberty.