Why we need to compare the rates of death between vaccinated and unvaccinated
During a pandemic, you might see headlines like “Half of those who died from the virus were vaccinated”.
It would be wrong to draw any conclusions about whether the vaccines are protecting people from the virus based on this headline. The headline is not providing enough information to draw any conclusions.
Let’s think through an example to see this.
Imagine we live in a place with a population of 60 people.
Then we learn that of the 10 who died from the virus, 50% were vaccinated.
The newspaper may run the headline “Half of those who died from the virus were vaccinated”. But this headline does not tell us anything about whether the vaccine is protecting people or not.
To be able to say anything, we also need to know about those who did not die: how many people in this population were vaccinated? And how many were not vaccinated?
Now we have all the information we need and can calculate the death rates:
- of 10 unvaccinated people, 5 died → the death rate among the unvaccinated is 50%
- of 50 vaccinated people, 5 died → the death rate among the vaccinated is 10%
We therefore see that the death rate among the vaccinated is 5-times lower than among the unvaccinated.
In the example, we invented numbers to make it simple to calculate the death rates. But the same logic applies also in the current COVID-19 pandemic. Comparisons of the absolute numbers, as some headlines do, is making a mistake that’s known in statistics as a ‘base rate fallacy’: it ignores the fact that one group is much larger than the other. It is important to avoid this mistake, especially now, as in more and more countries the number of people who are vaccinated against COVID-19 is much larger than the number of people who are unvaccinated (see our vaccination data).
This example was illustrating how to think about these statistics in a hypothetical case. Below, you can find the real data for the situation in the COVID-19 pandemic now.
