Some more covid vaccine math

[izard]

Some may think that I am beating a dead horse here, but the horse isn't dead until there are still active covid vaccine mandates in the USA.

According to CDC director's recent public announcement

at 1:01. "teen boys have been up to 5 times as likely to have heart inflammation after having covid infection than after getting vaccinated". There are several peer reviewed publications that estimate this difference in this age group, and she selected the one which resulted in estimate of 2x-5x, and took the highest number.


Here is a quote from another study (SARS-CoV-2 Vaccination and Myocarditis in a Nordic Cohort Study of 23 Million Residents, April 20, 2022): "Among males aged 16 to 24 years of age, the excess number of Myocarditis events within the 28-day risk period was 27.49(14.41 to 40.56) per 100 000 vaccinated. Excess events of myocarditis were 1.37 (−0.14 to 2.87) events per 100 000 individuals with a positive test result among males aged 16 to 24 years". So it is not 5x, but rather 20X other way around.

But let's just trust CDC and assume that 5x is the correct number.

Let the probability of heart inflammation after getting vaccinated is X, and probability of heart inflammation after having covid infection is then 5X.

CDC stops here and gives the recommendation which then translated to mandates, but why they don't continue calculation to estimate the final risk?

If I chose to vaccinate my teen son, the probability of heart inflammation from vaccine is X.
If I chose not to vaccinate my teen son, the probability of heart inflammation from covid is 5X multiplied by (probability of getting covid) multiplied by (vaccine effectiveness in preventing covid).

My son, like 96% of US children has already some immune memory of covid (from prior infection in his case). Like for 99.99%+ US children who had covid it was a mild cold for him, much milder than RSV or flu. He is not vaccinated and had covid once, while he lived through many covid peaks in Germany and USA. I estimate that in the current seasonal peak his odds of having covid again is 10%. But for the sake of argument let's assume it is much more, e.g. 25%, or 0.25.

I trust CDC that the vaccine is very effective in preventing severe decease and death. Not so much in preventing infection, but let's assume it is as effective as flu vaccine and prevents ~50% of cases.

So finally, the probability of heart damage for non-vaccinated teen boy is 5*0.25*0.5*X=0.63X.

0.63X < X, so not vaccinating a teen boy seems to be the right decision. But wait, there is more! If I chose to vaccinate my child, the probability of heart inflammation is not actually X, but X + 5X * (probability of getting covid) * (1 - vaccine effectiveness in preventing covid) * (1 - vaccine effectiveness in preventing severe covid that leads to heart damage).
I'll assume vaccine effectiveness in preventing severe covid leading to heart damage is 99%. It is likely less, but we all trust CDC that it is very effective.
So it is then X+5X*0.25*0.5*0.01=1.06X.

0.63X is still less than 1.06X.

Comments

[sab123]

Observations of complaints on parent forums in our school district show 5 complaints in a district of 25000 students, at an early time when probably only 10% of children were vaccinated. So the probability is at about 1/500 or at least 1/5000. An interesting addition is that probably everyone here experienced Covid before vaccination, so that might have made the vaccination effect worse. But that should be comparable with the effects of a booster shot (and besides, who hadn't had covid by now?)