The condition of “We will use testing” to decide to relax restrictions is a security blanket of thin cloth. Basically, we’re screwed by mathematics. What you are about to receive is a proven fact, i.e., a truth. If you wish to know more, it’s called Bayes Theorem on Conditional Probabilities. After you read this, you will know what Trump’s and Northam’s advisors have ALREADY told them.
Because the panacea bonfire of the new “Abbott Labs Antibody Test” is being stoked, I have been forced to revive some brain cells that have been comfortably soaking up rum for the past 8 years just to answer one question:
“How much help is random testing for CoV2 going to be in deciding to ‘Open Up’ Virginia?”
Let’s use Abbott’s EUA application for our Gold Standard for answering this question.
From the test results that Abbott submitted to get the FDA Emergency Use Authorization (EUA), Abbott declares that the 95% confidence interval for the Probability of Detection, Pd, of the virus is (94.0, 100), greater than 94% but less than 100%. In addition, they tell us that the 95% confidence interval for the Probability of a False Alarm, Pfa, is (0, 11). See the last or next to last page (alpah =0.05, CI) table.
Pretty impressive, well, impressive enough to secure a EUA so to soak up $Billions of taxpayer money, but is really going to help Northam with decisions to end the quarantine measures for Virginia or the USA? Remember, we’re making an executive decision that could cost Granny her life.
We need to know that, if I select someone from the population and his test returns a positive result then the person really is sick (immune). Errata: sick would be determined by the presence of the virus, which is the device covered in the EUA application. The question of immunity, as yet unanswered, would be suggested by a device that detects antibodies. The manufacturer applied for an EUA for just such a device on 4-15-2020. The exact confidence intervals for that device are as yet unpublished, but for the sake of this document, we assume they are the same.
We need what is known as the “conditional probability, P(A|B)”, read Probability of event A given event B has occurred. In our case, P(sick person | +test), or shortened to P(s|+). Mathematically, this written as
P(s|+) = P(+|s)P(s) / P(+)
where the RHS of the equation is P(+|s), the probability of getting a positive test (+) from a sick person (that’s just Pd from Abbott) times P(s), the probability the guy REALLY is sick/immune from CoV2, divided by P(+), the probability of getting a positive result at all, either through a good detection or a false alarm, or
P(+) = P(+|s)P(s) +P(+|not s)P(not s).
We’re all set to go except we don’t know P(s), and P(not s) = 1.0-P(s). But we can estimate them.
The US has 600,000+ reported cases, and estimates for total sickened is 10x that, or 6M, out of a population of 360M so,
P(s) =approx 0.1666… Meh, let’s call it 2%
Let’s grab some values from the CI in Abbott’s application, Pd = 97%, Pfa = 5%, P(not s) = 98% and this gives us
P(s|+) = (0.97×0.02)/(0.97×0.02 + 0.05×0.98) = 0.0194/(0.0194 + 0.049) = 0.2836
P(not sick|+) = 1.0-0.2836 = 0.7164
Do you see the problem? The test sucks since nearly ¾ of the time a non-immune person will be declared to be immune, given that immunity exists at all. For Virginia, it’s much, much worse because P(s) <0.01 — the results will driven entirely by the False Alarms, aka “False Positives”
 This article is a co-publication appearing on Bacon’s Rebellion authored by me under the pseudonym Dean Wortmier and I attest to its authenticity, Nancy Naive.
 this one is better and contains corrections