Probabilities in the Lab

"Pick a test tube. Any test tube ..."

On March 8, 2020 the results of tests for COVID-19 done at KULeuven and associated labs in their network in Belgium, suggested that any incoming test had a probability of being positive of 6.696±3.898%. 


The value that calculated out for their 2,522 tests done to date on March 8, was 7.93% positive.


Using the above mean values: 
6.696% gives an Odds ratio of 13.934289127:1 
93,304% being negative, means Odds of 0.071765411:1 in favor of a positive test


Just to be complete, using the value of standard deviation obtained, 3.898%:
6.696-3.898 = 2.707
6.969-(2*3.898) = -0.827 which we'll call 0.
6.696+3.898 = 10,594
6.696+(2*3.898) = 14.492
6.696+(3*3.898) = 18,39

So between 0% positive and 18.39% positive, covers 3 std.deviations, or 99.9% of cases. That's 81.61% negative. That gives Odds of 0.225340031:1 in favor of a positive test out in the tail of the curve.

The Odds for the 0% chance or less, is easy: its 0:1.

18.39% is a probability of 0.1839, and calculates to Odds of 4.437737901:1. So if you were to bet that the next COVID-19 test coming into the lab was going to be positive, with Odds between 13.93 to 4.44 :1 against, you might lose your bet. 

To be complete, or phrase things in mirror-image speak: Odds between 0.072 and 0.225:1 of the next incoming test being positive.


Laboratory Medicine is used to such results.

They just keep running the tests that the receive each day. And they return lots of normal results.

That's why there are lots of results on that (or those) page(s) of labwork that your doctor ordered, most of which (unless you're really in bad shape), are normal. Instead of 'normal' you can say 'negative' if you prefer.


But it means that quality control becomes all the more important. If you are looking for needles in haystacks, better have the method and required reagents up to speed. Better confirm that at the start and end of each day in the lab.


Otherwise, the next incoming test that is actually positive for COVID-19, might be called negative.

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