Wednesday, June 30, 2021

Published June 30, 2021 by with 0 comment

If 10 Vaccinated and 10 Unvaccinated People Die, Can We Still Say Vaccines Work?

You will almost certainly be seeing headlines about vaccinated people dying and  might even see that more vaccinated than unvaccinated die. Here's one from the week that I wrote this post. Why do we still say vaccines work if this is happening?
Imagine as an example that you see '10 vaccinated and 10 unvaccinated doctors died from COVID-19 today'. Your brain probably thinks 'well...the vaccine didn't work I guess.' We see those numbers, then just assume that the populations were similar. They're all doctors right?

Digging more, say that it turns out that 90% of the doctors were vaccinated. To make it easy, assume that there are 1,000 total doctors. 90% vaccinated means there were 900 vaccinated and 100 unvaccinated. If 10 died from each group, that means:

  • 10 / 100, or 10% of unvaccinated doctors died
  • 10 / 900, or 1.1% of vaccinated doctors died
Unvaccinated doctors were 9 times as likely to die as vaccinated ones. Another way of phrasing that is that the vaccine's efficacy was:

vaccine efficacy = 1 - (vaccinated risk/unvaccinated risk) = 1 - (0.011/0.1) = 89%

This is how you have to think about things like this. Vaccines, masks, seat belts, helmets, etc. aren't 100% effective. Use the calculation above whenever you see headlines like this and want to know the actual story. 

You can even have more vaccinated deaths than unvaccinated. Imagine for the 89% efficacy vaccine above, you have 99% of the population vaccinated. For 10,000 doctors in that example, you'd expect to have 10% of the 100 unvaccinated die and 1.1% of the vaccinated 9900 die, so that's 10 unvaccinated deaths and 120 vaccinated deaths. A highly effective vaccine can still have more vaccinated people die than unvaccinated ones.

In case a visual helps, here is the initial example's distribution as a colored grid (red = dead and green = alive):



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