This Week in the Pandemic, January 29, 2021
…In which we try to anticipate some anti-vaxxer messaging. For centuries people have fought against vaccines. Despite being one of the most effective (if not the single most effective) public health interventions in history and saving God-knows-how-many lives, vaccines are seen by some as a method of “The Man” to control The Masses. Obvious flaws in most conspiracy theories notwithstanding, here we’ll try to head off one probable anti-vaccination talking point using very simple math.
Probable Anti-Vaccination Talking Point: If the vaccine works, why are so many vaccinated people getting infected?
The logic here is pretty simple and reasonable. The shots for COVID-19 (both Moderna and Pfizer/BioNTech) have been shown to reduce symptomatic infections by more than 90%. That means if 100 people received the vaccine and 100 similar people didn’t receive the vaccine, then all of them were exposed to COVID-19, we’d expect 100 of those without the vaccine to get sick and only 10 or fewer of those with the vaccine to get sick.
Anti-vaxxers latch on to the 10 people who got the vaccine and then got sick and say “See?!?! The vaccine didn’t work!” But in the real world, as vaccination rates increase, this argument gets stickier.
“Look at all of the sick people who got the vaccine!” they’ll say. “There are more vaccinated sick people than unvaccinated sick people!” you’ll hear. “More than half of the sick people were vaccinated!” will come the cry.
Alas. Some will take this as proof that vaccines don’t work.
But they do.
Here’s how we poke holes in that logic
Imagine 100 people in a town called Shotsville. 90 of those people get vaccinated. 10 of them do not. We don’t need to know why those 10 didn’t get shots. Maybe they have a preexisting condition. It doesn’t matter. It’s moo.
Below is one of the best tools in epidemiology. The table. It shows the people who were vaccinated and not vaccinated and we’ll use math to fill in the blanks.
Now suppose half of the people in Shotsville get exposed to enough virus to get them sick and the other half do not. It’s a random half of the people, so we see the unexposed counts below.
Since all of the exposed people were exposed to enough virus to get them sick, all of the not vaccinated people get sick. But since we know the vaccine is at least 90% effective, only 10% of the vaccinated people get sick. And, of course, the rest of the vaccinated people are exposed, but not sick.
Look at the “Sick” column. Anti-vaxxers will point to that and say, “Look! Half of the sick people were vaccinated. Obviously, the vaccine doesn’t work.”
But that’s incomplete. You have to also look at the number of people who were exposed and not sick, and compare the vaccinated people to the unvaccinated people. Among the unvaccinated people, 100% got sick after they were exposed. Among the vaccinated people, only 11% got sick after they were exposed. That’s how we know if something is effective.
