# Am I understanding COVID hospitalization rates for vaxxed vs unvaxxed?

January 13, 2022 5:00 AM Subscribe

I am trying to organize my thoughts around hospitalization rates as anti-vaxxers seem to be using them as big ol' GOTCHA! talking points.
This has been confusing for me so I thought I'd try to sort it out. I think I have it but I'd like to know if I am way off in my math & thought process.

It is my understanding that as vaccinations rates increase in a population the ratio of hospitalized vaxxed to unvaxxed will increase.

Say you have a population of 10000

- 20% are

- 80% are

If efficacy is 75% for the vaccine you'd have a group of 2000 vaxxed who have the same

So your PSI ratio (vaxxed to unvaxxed) would be 1:1. Therefore it makes sense that hospitalizations would be about equal from both groups.

So if that same population goes to 90% vaccinated you'd now have a PSI ratio of 2.25:1. You would expect to have

Do I have this right? I want to be prepared for the inevitable conversations with my antivax, covid-denying loved one.

It is my understanding that as vaccinations rates increase in a population the ratio of hospitalized vaxxed to unvaxxed will increase.

Say you have a population of 10000

- 20% are

**unvaccinated**(2000)

- 80% are

**vaccinated**(8000)

If efficacy is 75% for the vaccine you'd have a group of 2000 vaxxed who have the same

**potential for serious infection**(PSI) as the 2000 unvaxxed.

So your PSI ratio (vaxxed to unvaxxed) would be 1:1. Therefore it makes sense that hospitalizations would be about equal from both groups.

So if that same population goes to 90% vaccinated you'd now have a PSI ratio of 2.25:1. You would expect to have

**twice**as many vaxxed hospitalized as unvaxxed.

Do I have this right? I want to be prepared for the inevitable conversations with my antivax, covid-denying loved one.

Best answer: You may find this visualization helpful, which was posted to Reddit's Data is Beautiful subreddit yesterday.

posted by NotMyselfRightNow at 5:19 AM on January 13 [6 favorites]

posted by NotMyselfRightNow at 5:19 AM on January 13 [6 favorites]

Trying to infer things from a blended (vaxed + unvaxed) population in the hospital is fraught with trouble. Unless you know the demographics of the surrounding population and the demographics of the population in the hospital or the ICU, it's hard to draw meaningful conclusions.

If possible, it's better to find out the risks to each population separately - i.e. "for a vaccinated person, the chances of being hospitalized with covid are 1 in M; for a vaccinated person, the chances of being hospitalized with covid are 1 in N." This enables a proper comparison between the two different groups on the same baseline. (It's even better if you have age and comorbidity data, of course.)

In contrast, a summary report like "there are 40 people in the hospital who are vaccinated and 32 who are unvaccinated; there are 5 people in the ICU who are vaccinated and 3 who are unvaccinated" is largely useless. You don't know the populations that are feeding those separate counts; you don't know the demographics of the people involved. As such, it's hard to draw any conclusions from something like that.

posted by theorique at 5:24 AM on January 13 [5 favorites]

If possible, it's better to find out the risks to each population separately - i.e. "for a vaccinated person, the chances of being hospitalized with covid are 1 in M; for a vaccinated person, the chances of being hospitalized with covid are 1 in N." This enables a proper comparison between the two different groups on the same baseline. (It's even better if you have age and comorbidity data, of course.)

In contrast, a summary report like "there are 40 people in the hospital who are vaccinated and 32 who are unvaccinated; there are 5 people in the ICU who are vaccinated and 3 who are unvaccinated" is largely useless. You don't know the populations that are feeding those separate counts; you don't know the demographics of the people involved. As such, it's hard to draw any conclusions from something like that.

posted by theorique at 5:24 AM on January 13 [5 favorites]

The efficacy needs to be defined. Is it against infection, hospitalization or death? There 5x as many unvaccinated infected, and >10x as many hospitalized or dying according to the cdc. So there won’t be more vaccinated than unvaccinated any of those groups if the model is tested in similar populations.

posted by waving at 6:19 AM on January 13

posted by waving at 6:19 AM on January 13

If they are focussing on the numbers going to hospital then they simply trying to muddy the waters and are missing the real point. What is the outcome of that hospital stay? What percentage of each are leaving the hospital and the length of stay in the hospital? If you go to the hospital and the treatment works, that's a good thing, that's what hospitals are for, going to hospital and getting better is the point. It's the fact that an unvaccinated adult is are 11 times more likely to die of covid and never leave the hospital alive that is the issue. Not the percentage of them in hospital.

posted by wwax at 7:05 AM on January 13

posted by wwax at 7:05 AM on January 13

Best answer: You're correct but we're making a TON of assumptions, like the vaccine is 75% effective across the board (prevention, preventing serious symptoms / hospitalization, etc.)

Ran into one such antivaxxer two days ago, in fact. He was blabbing the following trying to Counter United Airline's Vaccine mandate have reduced 1 death a week to zero deaths a week.

posted by kschang at 7:06 AM on January 13

Ran into one such antivaxxer two days ago, in fact. He was blabbing the following trying to Counter United Airline's Vaccine mandate have reduced 1 death a week to zero deaths a week.

55% of COVID deaths from late August 2021 into early Jan 2022 in Vermont, are among the vaccinated. Worse, 44% of the state’s COVID deaths since the start of the outbreak happened in those 4+ months.My reply to him:

Given that 80% of all Vermonters 5+ have both doses, and 60% have #booster shot, it's no surprise "more deaths" in raw numbers came from the #vaccinated. That means #vaccines are WORKING to minimize the impact of #COVID.You'll notice that people will always quote the numbers that looks favorable to their side, and your job basically is to point out that they are evaluating it from the wrong context. This guy tried to claim "the raw numbers says more vaccinated die" and your job is to point out "well, when vaccinated outnumber the unvaxxed 4:1, that means the vaccines are working GREAT, because you are not measuring them in proportion! "

posted by kschang at 7:06 AM on January 13

Response by poster: Hi all! I just wanted to clarify. My friend will come to me and gleefully tell me that there as many (or more) vaxxed folk as there are unvaxxed (in ABC hospital).

I have to keep it very broad because he mistrusts any stat that doesn't confirm his bias. So all my numbers are pulled out of the ether & simplified so he can follow the math.

My question is: Is it accurate (in an ELI5 way) to tell him "as vaccinations rates increase in a population the ratio of hospitalized vaxxed to unvaxxed will increase and here's a very basic example showing that"?

posted by i_mean_come_on_now at 7:23 AM on January 13

I have to keep it very broad because he mistrusts any stat that doesn't confirm his bias. So all my numbers are pulled out of the ether & simplified so he can follow the math.

My question is: Is it accurate (in an ELI5 way) to tell him "as vaccinations rates increase in a population the ratio of hospitalized vaxxed to unvaxxed will increase and here's a very basic example showing that"?

posted by i_mean_come_on_now at 7:23 AM on January 13

Best answer: When I ran across this, I found that "COVID base rate fallacy" was a search that turned up some explanations that might be useful. E.g. first result is a pdf with a nice visual.

"My question is: Is it accurate (in an ELI5 way) to tell him "as vaccinations rates increase in a population the ratio of hospitalized vaxxed to unvaxxed will increase and here's a very basic example showing that"?"

Roughly, I think so, though there are complications because hospitalization and vaccination status may correlate with other factors. E.g. vaccination rates are higher among the elderly, so compared to the general population, a vaccinated person is more likely to be elderly, making them more likely to be hospitalized. That effect has probably diminished as vaccination has become more widespread?

Probably not worth going into until you've gotten the basic simple point across, though....

posted by bfields at 7:35 AM on January 13

"My question is: Is it accurate (in an ELI5 way) to tell him "as vaccinations rates increase in a population the ratio of hospitalized vaxxed to unvaxxed will increase and here's a very basic example showing that"?"

Roughly, I think so, though there are complications because hospitalization and vaccination status may correlate with other factors. E.g. vaccination rates are higher among the elderly, so compared to the general population, a vaccinated person is more likely to be elderly, making them more likely to be hospitalized. That effect has probably diminished as vaccination has become more widespread?

Probably not worth going into until you've gotten the basic simple point across, though....

posted by bfields at 7:35 AM on January 13

Best answer: I'd say something like this:

Let's say there are 100 people.

80 of them are vaccinated (80%).

20 of them are not vaccinated (20%).

10 people out of the 100 are in the hospital with COVID - half (5) are vaccinated, and half (5) are not.

That means that if you are vaccinated, you have a 5 in 80 chance (6.25%) of catching COVID and ending up in the hospital.

But if you are unvaccinated, you have a 5 in 20 chance (25%) of catching COVID and ending up in the hospital.

(Adjust the numbers as you see fit.)

posted by NotMyselfRightNow at 7:36 AM on January 13 [15 favorites]

Let's say there are 100 people.

80 of them are vaccinated (80%).

20 of them are not vaccinated (20%).

10 people out of the 100 are in the hospital with COVID - half (5) are vaccinated, and half (5) are not.

That means that if you are vaccinated, you have a 5 in 80 chance (6.25%) of catching COVID and ending up in the hospital.

But if you are unvaccinated, you have a 5 in 20 chance (25%) of catching COVID and ending up in the hospital.

(Adjust the numbers as you see fit.)

posted by NotMyselfRightNow at 7:36 AM on January 13 [15 favorites]

Notmyselfrightnow's answer is a good one. I will add this, from the Washington State DoH, which lays out, in great detail, the difference between being vaxxed and not, in terms of hospitalizations and deaths.

posted by OHenryPacey at 8:26 AM on January 13 [1 favorite]

posted by OHenryPacey at 8:26 AM on January 13 [1 favorite]

Best answer: The way I’ve explained it before with modest success is: in my local community, people who are vaccinated are a huge piece of the pie. People who are unvaccinated are a small sliver. If vaccines weren’t helping, you would only see a small sliver of unvaccinated people in the hospital, because that would be representative of the whole. But we are seeing something nearer to 50/50 where I am. The unvaccinated people are coming from such a tiny slice of the pie that a ton of them need to be hospitalized to keep up with the vaccinated. If half the people going to the hospital had red hair, and you had red hair, you might get nervous. Good thing getting vaccinated is easier than changing your hair color.

posted by tchemgrrl at 8:39 AM on January 13

posted by tchemgrrl at 8:39 AM on January 13

This most simple example is this: When we get to 100% vaccination rate, what percentage of hospitalizations and deaths with be among the vaccinated?

Both will be 100%, of course.

So that number by itself tells you literally nothing about how effective vaccines are. It does tell you that vaccines are not 100% effective, but it does not give you the information you are looking for - are vaccinations 1% effective, 50%, 80%, 90%, 99%, 99.9%?

To put it another way, with 0% vaccinations you might have a 20% hospitalization rate and with 100% vaccination rate you might have a 0.2% hospitalization rate - meaning that vaccines are awesomely effective, reducing hospitalization by a factor of 100.

But even in that situation, if 100% of people are vaccinated you are still going to have

posted by flug at 11:00 AM on January 13 [2 favorites]

Both will be 100%, of course.

So that number by itself tells you literally nothing about how effective vaccines are. It does tell you that vaccines are not 100% effective, but it does not give you the information you are looking for - are vaccinations 1% effective, 50%, 80%, 90%, 99%, 99.9%?

To put it another way, with 0% vaccinations you might have a 20% hospitalization rate and with 100% vaccination rate you might have a 0.2% hospitalization rate - meaning that vaccines are awesomely effective, reducing hospitalization by a factor of 100.

But even in that situation, if 100% of people are vaccinated you are still going to have

*some*hospitalizations. And if 100% are vaccinated, then 100% of hospitalizations will be from the vaccinated.posted by flug at 11:00 AM on January 13 [2 favorites]

For me, the graphical forms of evidence are very compelling. Check out the first three graphs on this San Diego county Covid data. They compare infection, hospitalization and death rates (per capita) for vaccinated versus unvaccinated people and the differences are very stark, e.g 12x to 5x differences.

posted by soylent00FF00 at 1:00 PM on January 13

posted by soylent00FF00 at 1:00 PM on January 13

Slightly off-topic, but studies have shown that vaccination also reduces chances of "long COVID", even when breakthrough infections occur (i.e. caught COVID in spite of having been vaccinated)

posted by kschang at 8:41 PM on January 17

posted by kschang at 8:41 PM on January 17

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