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Math Is Hard—but Vital for Understanding Vaccine Risks Neil deMause ([link removed])


Readers of CNN’s website (4/15/21 ([link removed]) ) saw an alarming headline: “So Far, 5,800 Fully Vaccinated People Have Caught Covid Anyway in US, CDC Says.” Nearly 6,000 so-called “breakthrough” infections—cases of Covid-19 contracted by people after they had been vaccinated against the coronavirus that causes Covid — had been identified in the US by the Centers for Disease Control and Prevention, and “some became seriously ill and 74 people died.”
Ars Technica: 99.992% of fully vaccinated people have dodged COVID, CDC data shows

Ars Technica (4/15/21 ([link removed]) ) and CNN (4/15/21 ([link removed]) ) wrote about the same report—but only Ars Technica understood the point of the report.

Three hours later, the tech news site Ars Technica (4/15/21 ([link removed]) ) reported: “99.992% of Fully Vaccinated People Have Dodged Covid, CDC Data Shows.” Breakthrough infections, Ars Technica wrote, “occur at the teeny rate of less than 0.008% of fully vaccinated people.”

The two stories were, in fact, the same story. Both CNN and Ars Technica had read the same CDC analysis of its vaccination database and come to opposite conclusions: one that breakthrough infections were alarmingly high, the other that they were hearteningly low.

Scientists, when they appeared in news reports, tended toward reassurance. "This is a really good scenario, even with almost 6,000 breakthrough infections," Kent State epidemiologist Tara Smith told NBC News (4/15/21 ([link removed]) ). "Most of those have been mildly symptomatic or asymptomatic. That's exactly what we were hoping for." Yet NBC went with the headline “CDC: About 5,800 'Breakthrough Infections' Reported in Fully Vaccinated People.”

The Hill (4/15/21 ([link removed]) ) reported the breakthrough infection rate of just 0.008% in its story, but for a headline went with “CDC Finds Less Than 1% of Fully Vaccinated People Got Covid-19”—which, while true, still overstates the breakthrough infection rate by a factor of 100, making its headline equivalent to saying “less than 25% of the US House of Representatives is under investigation for child sex trafficking ([link removed]) .”

A similar math problem reared its head in the other big vaccine-related story of the week: the news that the CDC and FDA were calling for a “pause” in the use of Johnson & Johnson’s Covid vaccine as a result of some recipients having developed potentially life-threatening blood clots. In typical reporting, CBS News’ website (4/14/21 ([link removed]) ) ran the headline “US Recommends ‘Pause’ for Johnson & Johnson Covid Vaccine to Review Blood Clot Cases,” referring to “adverse side effects” but noting they were “extremely rare.”

How rare, exactly? Six people out of more than 6.8 million vaccinated had developed blood clots that, if treated improperly, could lead to severe complications or even death — enough for the government agencies to call a temporary halt to use of the vaccine. (Only one vaccine recipient, a woman from Virginia ([link removed]) , was reported to have actually died from blood clots after getting vaccinated.)

Math is hard, for journalists as well as readers ([link removed]') , and there’s an understandable reflex for news sites to try to keep the numbers in their stories simple, to avoid making people’s eyes glaze over. Yet a number, whether 5,800 or six, doesn’t tell you much unless you know not just the numerator of a fraction—how many people are affected—but also the denominator, how many people are in the total pool being studied. If six people out of every thousand suffer side effects, that’s alarming; if six people out of every 6 million do, that’s assuredly bad for those six people, but not necessarily a significantly bigger concern than that one out of every 2.4 million Florida residents will get eaten by an alligator (National Geographic, 6/15/16 ([link removed]) ).

Unfortunately, too much vaccine coverage has left readers and viewers with no way to tell whether news about infections and side effects should be cause for alarm, or just what’s to be expected in a world so large that even unlikely circumstances are likely to happen to someone, somewhere. Even attempts at reassurance sometimes missed the mark, as when Yahoo! (4/15/21 ([link removed]) ) warned in a headline, “CDC Reports 5,800 Breakthrough Covid-19 Infections in People Who Were Vaccinated,” but added the conciliatory note: “Doctors Say, ‘Don’t Panic.’” (Um, if you say so?)

NPR’s All Things Considered segment (4/13/21 ([link removed]) ) on the J&J story was headlined on the web “Blood Clot Concerns Put Johnson & Johnson Vaccine on Pause.” NPR science correspondent Joe Palca reported that seeing six of such cases among the 6.8 million people who received the J&J vaccine was “not very common, but more common than you would expect from people who never got the vaccine.” But even this, it turned out, wasn’t necessarily true: NYU Vaccine Center investigator and immunologist Purvi Parikh told CNBC (4/13/21 ([link removed]) ) the same day that a Canadian study had found people who contract Covid are “much more likely” to develop blood clots than those who get the vaccine.
New York Post: Australian woman dies after receiving COVID-19 vaccine, officials say

Contrary to the New York Post (4/7/21 ([link removed]) ), it's not news if one of the half a billion people who have gotten a Covid vaccines dies after the shot—not even if it happens in Australia.

Sometimes all it took was a numerator of one person to spark a story warning of potential vaccine failures. The New York Post (4/7/21 ([link removed]) ) ran an entire article on an 82-year-old Australian woman who died shortly after receiving a Pfizer vaccine shot, though it noted it was “unclear whether the jab played any role in her death.” (With millions of people being vaccinated every day, it would be more shocking news, statistically speaking, if no one ever died the same day they got a vaccine.)

Both the New York Times (1/12/21 ([link removed]) ) and the South Florida Sun-Sentinel (4/8/21 ([link removed]) ) ran long articles on a Miami Beach doctor who died of a brain hemorrhage 16 days after getting a Pfizer shot, though the only evidence linking the death to the vaccine was his wife’s Facebook post wondering about a connection.

Providing all the numbers is vital, because in a world where both policymakers and individuals are trying to decide whether vaccines are effective and safe, the only way to do so is with math. Does the benefit of having a fully vaccinated population outweigh the risk of possible side effects? But as medical experts have tried to point out in the wake of the J&J pause, people all too seldom consider numbers in context (STAT, 4/13/21 ([link removed]) ):

“You have a greater chance of being in a car accident on the way to getting this vaccine than you have of having a problem from this vaccine. But that’s not how people view risk,” said Paul Offit, a vaccine expert at Philadelphia Children’s Hospital.

It’s certainly important to investigate the potential side effects of vaccines, and to warn people that getting vaccinated isn’t a license to blithely ignore the virus as if you’re 100% immune. But as the Covid endgame increasingly turns into a political battle over whether to get vaccinated, it’s also not enough to run an alarmist headline and consign the scientific consensus to the latter half of a story—especially as more and more readers, especially on social media, never read past the headlines ([link removed]) .

Journalists’ job is to do the math for the rest of us, so we can better understand what are acceptable and unacceptable risks; just throwing the grabbiest numbers on a screen may be good for traffic, but it’s not likely to be good for public health.
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