If vaccines are working, how could vaccinated people make up such a large proportion of an outbreak?
The answer is simple: They can if they make up a large proportion of a population. Even though vaccinated people have much lower odds of getting sick than unvaccinated people, they’ll make up a sizable fraction of infections, hospitalizations, and deaths if there are more of them around.
Let’s work through some numbers. Assume, first, that vaccines are 60 percent effective at preventing symptomatic infections. (There’s a lot of conflicting information about this, but the exact number doesn’t affect this exercise much.) Vaccinated people are still less likely to get infected, but as their proportion of the community rises, so does the percentage of infections occurring among them. If 20 percent of people are fully vaccinated, they’ll account for 9 percent of infections; meanwhile, the 80 percent of the population that’s unvaccinated will account for 91 percent. Now flip that. If only 20 percent of people are unvaccinated, there will be fewer infections overall. But vaccinated people, who are now in the majority, will account for most of those infections—62 percent.
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That is why this particular statistic—the proportion of vaccinated people in a given outbreak—is so deeply misleading. “The better the vaccine uptake, the scarier this number will seem,” wrote Lucy D’Agostino McGowan, a statistician at Wake Forest University. By extension, the safer communities become, the more it will seem like the sky is falling—if we continue focusing on the wrong statistics.
“If you’re trying to decide on getting vaccinated, you don’t want to look at the percentage of sick people who were vaccinated,” McGowan wrote. “You want to look at the percentage of people who were vaccinated and got sick.”
Note percentage. In July, an NBC News article stated that “At Least 125,000 Fully Vaccinated Americans Have Tested Positive” for the coronavirus. In isolation, that’s an alarming number. But it represented just 0.08 percent of the 165 million people who were fully vaccinated at the time. More recently, Duke University reported that 364 students had tested positive in a single week—a figure that represents just 1.6 percent of the more than 15,000 students who were tested. The denominator matters.
The denominators in these calculations also change, dragging the numerators higher along with them. As surges grow, so too will the number of infected people, which means the number of breakthrough infections will also grow. Even if the percentage of breakthroughs stays steady, though, vaccines will feel less effective if the pandemic is allowed to rage out of control, because …
- Candy Dogood - Tuesday, Sep 21, 21 @ 9:36 am:
Great article, but I was really hoping for something that would justify forgetting to invite one’s vaccinated family members to Thanksgiving.
- ZC - Tuesday, Sep 21, 21 @ 9:41 am:
If the whole country wears seat belts, 100% of the hospitalizations after car crashes will involve drivers who were wearing seat belts. This is not a reason to take them off.
- Homebody - Tuesday, Sep 21, 21 @ 9:46 am:
Say what you want about Americans being terrible at math, the major news outlets are egregiously bad about educating people about numbers. They just want to post the big scary number that gets eyes and clicks.
- truthteller - Tuesday, Sep 21, 21 @ 10:05 am:
my wife (immune compromised) andI are both fully vacinated and will get the booster next month. We cancelled the 2nd winter in a row in wintering in Florida in our RV (we came back 2 months early when COVID first burst out in March of 2020. We are taking all the same steps with masks, crowds and enclosed areas (avoid)for the next 3-6 months. I want to avoid being a statistic. We will let the “freedom” of others take that honor.
- Grandson of Man - Tuesday, Sep 21, 21 @ 10:17 am:
“If the whole country wears seat belts, 100% of the hospitalizations after car crashes will involve drivers who were wearing seat belts.”
Great analogy. If we can get to a lower number of hospitalizations with a higher percentage of patients vaccinated, it will be great.
But we have the extra burden of disinformation and distrust that may not have existed in the past for other vaccines, especially at the speed information travels today. This is in part because of years of promoting distrust and hatred of government. What kind of fruit would those trees produce, so to speak?
- Sir Reel - Tuesday, Sep 21, 21 @ 11:17 am:
Americans are too busy to think nowadays. They barely have time to read the headlines.
- Honeybear - Tuesday, Sep 21, 21 @ 11:38 am:
Thank you so much for posting Rich. Really got some education this morning. I so appreciate that.
- thisjustinagain - Tuesday, Sep 21, 21 @ 11:59 am:
A couple of much more important numbers: How many Covid cases hospitalized are unvaccinated (estimates between 90-99% from different in interview sources), and how many vaccinated wind up hospitalized, let alone dying (less than 5% from different sources). Those are two of the most important metrics to bear in mind going forward.
- RNUG - Tuesday, Sep 21, 21 @ 1:55 pm:
A bit of a lesson in how to use and misuse statistics. The article is good at explaining things clearly.
Related:
One much repeated / shared story yesterday had the headline about more US deaths than in 1918. That was true in absolute numbers. However, in about the 3rd or 4th paragraph in the original article they noted the population is 3 times bigger now, so the percentage of deaths is still only about 1/3 of back in 1918. To the author’s credit, they did include that fact even though the headline was a bit misleading.