How Good Are Vaccines? Try 99.9999% Effective

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I have a friend who works in the New York City Department of Education’s Covid-19 “situation room” — tracing cases, informing contacts and so on. She’s really good at her job, which is why I was surprised to hear her make a strange statistical assertion: Since the Pfizer and Moderna vaccines are 95% effective, one in 20 vaccinated people are going to get Covid.

That’s wrong, dangerously so. And given that an expert who works in the area every day can make such a mistake, I figure it’s worth some explaining.

The intuition is pretty straightforward. You can get Covid only if you’re exposed. At the current low level of cases in New York, and given reasonable precautions, you would expect only a small fraction of the population to be exposed. Hence, if those people are also protected by a vaccine, the actual infection rate should be much lower than one in 20.

How much lower? Let’s consider the clinical trial that measured the Pfizer vaccine’s efficacy. There were two groups of about 22,000 people each. They were similar in all ways — age, health, location, activities — except that one group received a real vaccine and the other received a fake one. Over time, 162 unvaccinated participants developed at least one symptom and tested positive, while only 8 people in the vaccinated group did. That’s 95% fewer infections, suggesting 95% efficacy. But less than 1 in 2,700 of the vaccinated participants fell ill.

In real life, the threat to the vaccinated will depend on the overall prevalence of Covid. In early January, when an estimated one in 34 people in the U.S. were infected, one could have expected inoculated people to have about a one in 700 chance of contracting Covid. Now that cases are down to less than one in 100, vaccinated people are even safer.

Keep in mind, too, that so far we’ve been talking only about infections. Vaccinated people are even less likely to actually die of Covid. And that’s where the evidence is extremely good. According to the government website tracking “breakthrough cases” in the general population, only 88 out of 87 million fully vaccinated people in the U.S. had been reported dead as of April 20, and 11 of those were unrelated to Covid. That’s a death rate of less than one in a million.

Of course, there are caveats. In the wild, the vaccinated aren’t necessarily comparable to the unvaccinated. They might be more careful types generally, which would contribute to their lower infection rates. Or they might take greater risks on the assumption that they’re protected. Deaths might be undercounted, and in any case will increase over time as more fully vaccinated people get exposed. And even an excellent vaccine can’t prevent cases like the one in Kentucky, where a nursing home worker refused inoculation and caused a deadly outbreak.

Still, the Covid-19 vaccines are a miracle of science. It’s enough to make me want to require vaccines next school year for all eligible students and staff, even if it puts my good friend out of a job.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

Cathy O’Neil is a Bloomberg Opinion columnist. She is a mathematician who has worked as a professor, hedge-fund analyst and data scientist. She founded ORCAA, an algorithmic auditing company, and is the author of “Weapons of Math Destruction.”

©2021 Bloomberg L.P.

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