# Uh, Oh… by Dean Wortmier

Because the panacea bonfire of the “New Abbott Labs 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.

How much help is testing for CoV2 going to be in deciding to ‘Open Up’ Virginia?

Let’s use Abbott’s Emergency Use Authorization (EUA) application for our Gold Standard.

From the tests that Abbott submitted to get the EUA, the 95% confidence interval for the Probability of Detection, Pd, of the virus is (94.0, 100), greater than 94 but less than 100.  Moreover, the document tells us that the 95% confidence interval for the Probability of a False Alarm, Pfa, is (0, 11).

Pretty impressive, well, impressive enough to secure a EUA to soak up \$Billions of taxpayer money, but is really going to help with decisions to end the quarantine measures for Virginia? (Did you see how I kept it relevant to Bacon’s Rebllion’s blog?) 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 is really sick (immune).

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 P(s|+).  Mathematically, this written as

P(s|+) = P(+|s)P(s) / P(+)

where P(+|s) is probability of getting a + from a sick person (that’s just Pd), P(s) is the probability the guy REALLY is sick/immune from CoV2, and P(+) is the probability of getting a positive result at all, either through a good detection or a false alarm, or 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-P(s). But we can estimate. The U.S. has 600,000 reported cases, and estimates for total sickened is 10x that, 6M, out of a population of 360M so,

P(s) =approx 0.1666… Meh, let’s call it 2%

Let’s grab some values, Pd = 97%, Pfa = 5%, P(not s) = 98% and this

P(s|+) = 0.97×0.02/(0.97×0.02 + 0.05×0.98) = 0.0194/(0.0194 + 0.049) = 0.0194/0.0684 = 0.2836

P(not sick|+) = 1.0-0.2836

Do you see the problem? The test sucks for any decisions to ‘Open Up’ since nearly ¾ of the time a non-immune person will be declared to be immune.

Dean Wortmier is the pen name of a retiree living in Hampton Roads. A former employee of government-contracting businesses, he spent 23 years as an adjunct professor in mathematics, physics and computer science, and published more than a dozen degrees in information theory.

 https://www.molecular.abbott/sal/9N77-095_SARS-CoV-2_US_EUA_Amp_PI.pdf