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 …