The reassuring math explaining COVID hospitalization percentages for vaccinated people

As if dealing with an ever-changing understanding of the novel coronavirus over the past year and a half hasn't been enough, we've also had to try to understand the math behind the data analysis, which for some of us (hi, English major here) is a nightmare.
It's vitally important that we understand these numbers, though, because misinformation peddlers are using them to push misconceptions about vaccines. And even though the math isn't actually that complicated, those of us who aren't particularly mathematically inclined may read headlines like "50% of COVID patients in XX hospital are fully vaccinated" and find ourselves alarmed. Wasn't the vaccine supposed to prevent hospitalizations? If half of the people in the hospital are vaccinated, doesn't that mean the vaccine makes no difference?
Well, no. That's not at all what it means, and here's why. It's all about the denominators.
On a super basic level: 2 = 2, but 2 out of 20 is not the same as 2 out of 80. If 4 people are hospitalized, 2 vaccinated and 2 not vaccinated, in an area with an 80% vaccination rate, it's not a meaningful measurement to say that half of the hospitalizations are in vaccinated people. Your chances of hospitalization with the vaccination are significantly lower because of the denominator.
Biostatistician Lucy D'Agostino McGowan simplified why the percent vaccinated in hospitalizations numbers aren't as scary as they sound with some helpful visuals in a Twitter thread.
The director of the Maine CDC, Nirav D. Shah, gave an even more thorough explanation for those who actually want to wade a little deeper into the statistical waters.
He wrote:
"It's important to consider the full picture when interpreting data on things like the % of people fully vaccinated who are hospitalized with #COVID19, or the fact that 74% of the cases in the P-town outbreak were fully vaccinated.
I have seen folks express concern upon learning, for example, that 45% of people hospitalized w/COVID19 are vaccinated.
"But I thought the vaccine keeps you out of the hospital? Is this evidence that vaccines aren't working?" No, it is not. I'll walk through why here.
First, some basic assumptions. There are two Worlds, each with 1M people. And we'll consider the same infectious disease affecting each World, with the parameters below.
There is also a vaccine, with the effectiveness parameters noted below. These could all be changed.
In World 1, 50% of the population has been vaccinated against the disease. Out of the 1M people, there are 30,000 infections and 2525 hospitalizations.
Among vaccinated folks, 25 end up in the hospital. The other 2500 hospitalized are UNvaccinated.
World 2 is different: 90% of the population is vaccinated.
Here, there are only 14,000 cases. And only 545 people are hospitalized in total.
BUT, 45 of the hospitalized are vaccinated! Compare that with only 25 vaccinated folks in the hospital in World 1.
What is going on?
How could it be that, in a World with 90% of the population vaccinated, 20 *more* vaccinated people are hospitalized with the disease (45 vs. 25?)? Is the vaccine not working in World 2?
It's important to compare World 1 and World 2 side by side.
First, note that the case rate in World 2 (90% vaccinated) is far lower than in World 1 (50%). The vaccine is working.
Second, the hospitalization RATE is also far lower in World 2: 545/million vs. 2525/mil.
But because there are simply more vaccinated people in World 2, something that affects them at the same rate as others (hospitalization) will generate more cases, numerically.
Indeed, the % of all hospitalized who are fully vaccinated is HIGHER in World 2 than in World 1.
In World 2 (90%), 8.25% of all those in the hospital are vaccinated. But in World 1 (50%), it's only 1%!
This is NOT evidence that the vaccines are ineffective. It is a function of the fact that there are simply more vaccinated folks in World 2 relative to unvaccinated.
The question to ask yourself is this: which world would you rather be in?
For that, you would look to the hospitalization rate: 545 vs. 2525/million. World 2, with its higher vaccination rate, is preferable, given that it experiences 1980 fewer hospitalizations. In World 1, fewer people are vaccinated, so their rate of hospitalization is just lower.
Where else does this (common) phenomenon occur?
For a stark example, consider this: what % of skydiving accidents occur in people who were wearing a parachute? Probably 100%.
Are parachutes not effective? They are. But the baseline rate of parachute wearing among those who sky dive is 100%.
Another example: what percentage of fatal car accidents occur in people who were wearing a seat belt? It's about 52%.
Does that mean the effectiveness of seat belts is a coin flip? No, the baseline rate matters. Seat belt usage is around 85%. As with so many things, where you end up depends on the baseline rate of where you started.
Lots of vaccinated folks are being hospitalized with COVID because there are a growing number of vaccinated folks. But the RATE of total hospitalizations is going down. That's good. Similarly, in P-town, 74% (346) of the cases were among vaccinated folks.
But there, what percentage of folks were vaccinated vs. unvaccinated? If the baseline rate of vaccinated was sky high, then this finding is entirely predictable. This is a common theme in epidemiology and statistics. Once you know to look for it, it jumps out all over the place. But without the context around background rates, denominators, etc., it's easy to scare yourself and make incorrect decisions.
Another example: imagine World 3, also with 1M people. 999,999 are vaccinated.
Two cases of COVID occur. One in the unvaccinated person. The other in a vaccinated person.
So 50% of new COVID cases are in the vaccinated. Really? Yes, but deceiving. Denominators matter."
Denominators matter. Even those of us who aren't mathematicians or statisticians can understand that, but we do need media reports to be clear about it; otherwise, we end up with people believing that the vaccines don't do much.
We also need to remember that data is always being gathered and that our understanding of this virus, the vaccines, and how best to balance safety measures and other needs will continue to evolve. The constant shifts are hard, but such is the nature of a novel viral pandemic, and it looks like we're still going to be in it for a while.
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An Irish woman went to the doctor for a routine eye exam. She left with bright neon green eyes.
It's not easy seeing green.
Did she get superpowers?
Going to the eye doctor can be a hassle and a pain. It's not just the routine issues and inconveniences that come along when making a doctor appointment, but sometimes the various devices being used to check your eyes' health feel invasive and uncomfortable. But at least at the end of the appointment, most of us don't look like we're turning into The Incredible Hulk. That wasn't the case for one Irish woman.
Photographer Margerita B. Wargola was just going in for a routine eye exam at the hospital but ended up leaving with her eyes a shocking, bright neon green.
At the doctor's office, the nurse practitioner was prepping Wargola for a test with a machine that Wargola had experienced before. Before the test started, Wargola presumed the nurse had dropped some saline into her eyes, as they were feeling dry. After she blinked, everything went yellow.
Wargola and the nurse initially panicked. Neither knew what was going on as Wargola suddenly had yellow vision and radioactive-looking green eyes. After the initial shock, both realized the issue: the nurse forgot to ask Wargola to remove her contact lenses before putting contrast drops in her eyes for the exam. Wargola and the nurse quickly removed the lenses from her eyes and washed them thoroughly with saline. Fortunately, Wargola's eyes were unharmed. Unfortunately, her contacts were permanently stained and she didn't bring a spare pair.
- YouTube youtube.com
Since she has poor vision, Wargola was forced to drive herself home after the eye exam wearing the neon-green contact lenses that make her look like a member of the Green Lantern Corps. She couldn't help but laugh at her predicament and recorded a video explaining it all on social media. Since then, her video has sparked a couple Reddit threads and collected a bunch of comments on Instagram:
“But the REAL question is: do you now have X-Ray vision?”
“You can just say you're a superhero.”
“I would make a few stops on the way home just to freak some people out!”
“I would have lived it up! Grab a coffee, do grocery shopping, walk around a shopping center.”
“This one would pair well with that girl who ate something with turmeric with her invisalign on and walked around Paris smiling at people with seemingly BRIGHT YELLOW TEETH.”
“I would save those for fancy special occasions! WOW!”
“Every time I'd stop I'd turn slowly and stare at the person in the car next to me.”
“Keep them. Tell people what to do. They’ll do your bidding.”
In a follow-up Instagram video, Wargola showed her followers that she was safe at home with normal eyes, showing that the damaged contact lenses were so stained that they turned the saline solution in her contacts case into a bright Gatorade yellow. She wasn't mad at the nurse and, in fact, plans on keeping the lenses to wear on St. Patrick's Day or some other special occasion.
While no harm was done and a good laugh was had, it's still best for doctors, nurses, and patients alike to double-check and ask or tell if contact lenses are being worn before each eye test. If not, there might be more than ultra-green eyes to worry about.