Testing for Covid-19
This is a notes page for covid19 testing
Suppose there's a 1% probability of a false positive on a covid test and I never do get infected, but I keep taking the test. Taking it twice, the probability of coming out negative both times is (.99)(.99) = .98. Five times, it is .99^5 = .95. Twenty times, it is .99^20= .82. Fifty times, it is .61. Sixty-nine times, it is .4998, the first time it dips below .5000. So if you take a covid test with a false positive rate of 1% every day for 69 days, and the errors are independent, you 'd come up with a false positive with 50% probability.
Fast, low-cost testing is essential for averting a second wave of Covid-19 by MENACHEM FROMER, PAUL VARGHESE, and ROBERT M. CALIFFSEPTEMBER 23, 2020 notes that Abbot Labs's 5-minute test has a 1.5% false positive rate (a 98.5% "specificity"). If universities use that test or one of similar quality, that just about matches the infection rates they're finding in students. No wonder it seems none them are actually sick (we can't tell for sure because universities are secretive about actual sickness rates and won't say whether any of the students testing positive have any symptoms).
This could backfire disastrously. Universities are acting as if students testing positive are deadly dangerous. They are obviously not. Students figure this out. Students might well conclude, as I have been thinking, that covid is harmless, not even producting symptoms in 99% of cases. They would then abandon all safeguards. But they would be wrong--- covid could still be a big danger; it's just that the supposed high incidence is a false product of university publicity.
This is crucial information for the public. If a university is using that test, with its 1.5% false positive rate, or a similar one (and that is a reputable test from a big old respectable company), and is putting 1.5% of its students in quarantine as a result, telling them they have covid, but don't explain test error, students conclude that covid-19 is a harmless infection with no symptoms and no harm, that even precautions such as not coughing on your grandmother are unimportant, and that they will be immune since they had covid already.
Widespread testing is good, but it needs to be done intelligently, with full knowledge, understanding, and explanation that testing positive is not the same as (a) really being infected, (b) being infectious, or (c) being sick. It should be used for monitoring population levels, for tracing, and for mild precautions, not for quarantine.
The draconian quarantine policies backfire in another way. Their harshness means that if a student testis positive, he doesn't want to reveal his contacts because he doesn't want to ruin their lives. He knows the university will go to them, force them to be tested, and imprison them. He also knows that practically nobody he knows who tested positive actually is sick, so the quarantine is useless.
CDC Influenza SARS-CoV-2 (Flu SC2) Multiplex Assay|Instructions for Use does not, shamefully, say in any clear way what its false positive and false negative rates are in its 11-page "Performance Characteristics" section. How shameful! I looked around to see if they admit the false positive rate anywhere else. The FDA doesn't on its [FACT SHEET FOR HEALTHCARE PROVIDERS https://www.fda.gov/media/139742/download]. I find that incredible. I should think one of the very most important facts would to be to tell testers to tell subjects the probability that a positive test result indicates you have a possibly deadly disease. They should tell them the false-positive rate, and then also explain Bayes's Rule and gives examples of the posterior probability that someone in a given population with a positive test has covid. For example, they should explain that if the false positive rate is 1%, and only .5% of the population has covid at the time the test is administered, a positive result is wrong with probability 67%; and that if 2% of the population has covid, a positive test wrong with probability 33%. What they do say is this:
What does it mean if the specimen tests positive for SARS-CoV-2, the virus that causes COVID-19? A positive test result for SARS-CoV-2 indicates that RNA from this virus was detected, and therefore the patient is infected with the virus and is presumed to be contagious. Laboratory test results should always be considered in the context of clinical findings and observations and epidemiological data in making a final diagnosis. Patient management decisions should be made by a healthcare provider and follow current CDC guidelines. The Flu SC2 Multiplex Assay has been designed to minimize the likelihood of false-positive test results. However, in the event of a false-positive result, risks to individuals could include the following:
- a recommendation for isolation of the patient, monitoring
of household or other close contacts for symptoms, patient isolation that might limit contact with family or friends and might increase contact with other individuals with COVID-19, limits in the ability to work, delayed diagnosis and treatment for the actual infection causing the symptoms, and unnecessary prescription of a treatment or therapy.
All laboratories using this test must follow the standard confirmatory testing and reporting guidelines according to their appropriate public health authorities.
