Hello!

-1 out of 4 people on the intensive care unit are vaccinated, the rest isnt
-2/3 of the population of the country for which this ratio counts are vaccinated, 1/3 isn't

Is this enough information to tell how likely it is to get on the intensive care unit for people who have been vaccinated and for those who haven't?

Am I right that there is information missing in order to tell:
- How many people who are vaccinated get covid
- How many people who arent vaccinated get covid
- What percentage of those who get covid, get on the intesive care unit


OR could we tell given the information provided?

Are you only talking about people in the ICU because of covid?

yes all numbers are covid related. So 4 people in the ICU have a covid infection and one out of 4 is vaccinated. Am I right that this ratio doesnt tell us anything about how much less likely it is to end in the ICU with a covid infection despite being vaccinated?


Its just that I read in the newspaper that out of 4 people with covid in the ICU 1 had been vaccinated and I asked myself what exactly that would mean about how effective the vaccination is and how much less likely it makes it to get a severe covid infection. Can I tell with the rest of the infortion (2/3 of the country is vaccinated, 1/3 isnt) or is there still information missin in order to tell?

Assuming every person in ICU = COVID

Unvaccinated = 6x probability going to Covid hospital vs unvaccinated

Assume 200 vaccinated vs 100 not vaccine in population...And any 3 to 1 ratio in ICU gets you 6 to 1 probability ratio

You have enough information. Let x be the total population of the country and y be the number of ICU Covid patients. Then the number of vaccinated patients is 1/4 y. The number of vaccinated people overall is 2/3x. The probability of a vaccinated person requiring ICU admission is therefore (1/4 y)/(2/3 x) = 3/8 y/x.

Similarly the number of unvaccinated patients is 3/4y, while the total unvaccinated population is 1/3x. The probability of an unvaccinated person requiring ICU treatment is therefore (3/4y)/(1/3x) = 9/4 y/x.

When taking the ratio of these it is clear that the y/x common term cancels out and the ratio is just (9/4)/(3/8) = 6. Therefore the info you gave is sufficient to conclude that an unvaccinated person is 6 times more likely to require ICU treatment than a vaccinated person.

Care should be taken with something like this though. There is not enough information to calculate the actual probabilities involved, only their ratio. This ratio may or may not be meaningful in a practical sense. If the underlying probability, for instance is 1 in 6 billion for the vaccinated population, then it would be 1 in 1 billion for the unvaccinated. If it’s 5% for the vaccinated, it’s 30% for the unvaccinated. Certainly those would represent very different situations in terms of actual public health measures, such as vaccination mandates. (I’m not opining one way or the other on such things - just pointing out that a phrase such as “6x more likely” might not really mean much).