Do you know minister Bayes? He is no longer with us, but he’s still offering a solution. Because after his death in 1761, an authoritative scientific article was found among his papers. It contains the answer to a current question. If a “have-I-had-COVID-19?” antibody blood test is positive, how likely are you to have actually gone through COVID-19?
The subject is point of discussion in every talk show. In the Netherlands there is a test on tour. The try-out visits parking places with a drive-through blood sampling point. And in late-night talk show Jinek, doctor-microbiologist Jean-Luc Murk, an entrepreneur and an antibody test, came along with 99.3% reliability. The latter is good news!, do you think? No. Nothing is what it seems with this type of probability calculation.
Dr. Murk’s team went to work. 60 blood samples from a year or so back on one of those test kits. That should give 0 positive results. But how many were there? Certainly 10. And that is not possible. Because blood from before the outbreak of a novel virus cannot contain the antibody of the virus. At least 10 errors from the test, rounded up: 1/6th incorrect.
Murk indicated that the test also showed positive results from the same parts in other similar antibodies. And so you get false positives. And you will be misdiagnosed. Hairsplitting, the entrepreneur thought. He wanted to start the one and a half meter economy. No time to lose! Massive blood tests! Because he had gone through corona and his blood test agreed. What’s up with that?
Back to the math minister. Three data are needed for the answer.
- the chance that the test will show that you have had it on the condition that you have actually gone through COVID-19 (that is called the sensitivity).
- the chance that the test is negative under the condition that you did not have COVID-19 (this is called the specificity).
- the chance of COVID-19 (this is called background prevalence).
Fill it out. At Jinek the first two data came by: 99.3% and 5/6th. After all, there is (at least) 1/6 the chance that the test will mistake clean blood for that of an ex-corona patient. For the third data we had to wait until after the examination of the Sanquin blood bank and the RIVM. What did they determine via a representative sample? Currently, 3% of blood donors have developed antibodies against the coronavirus.
And now the answer can be calculated with the Bayes formula. Is the COVID-19 blood test positive? Then the chances that you actually went through the coronavirus are ... only 15.6%. Oh. Judging from that result is downright dangerous. There’s a very good chance that you’ll be susceptible, or worse, infected but without symptoms. That’s a far cry from starting an economy.
Even if 14% of the Dutch people have had COVID-19, the test is still as reliable as throwing heads or tails: 50% chance that you have had it if the test is positive. The more people have had it, the more reliable the result becomes (see graph). But then the test is no longer necessary: group immunity is achieved.
In short, using such tests just like that is dangerous or unnecessary. RIVM is quite right to question a test with 99.3% reliability. And they insist that thorough research is needed. Deo gratias. Thanks to minister Bayes!
X
Prof. Dr Chris Verhoef is professor of computer science at the VU University in Amsterdam and scientific advisor to government and business.