This is an old question in the public health world—whether all these numbers help people or overwhelm them. But increasingly it looks like more information about vaccines alleviates hesitancy rather than exacerbating it. That comes down to how people see their risk profiles. “If you got Covid, you got Covid 100%, and if you don’t, it’s 0% Covid,” Olliaro says. “You have to consider the individual’s perspective within the community.”

One of the hallmarks of the pandemic has been that it affects different groups of people in different ways. In the US, poor people and people of color have been much more likely to get sick and die of Covid-19 than white people and rich people. Old people are at more risk than young people.

And like every other medical intervention ever, vaccines themselves have risks as well as benefits. The J&J and AstraZeneca vaccines have been associated with very rare but severe blood clots, which led to a pause in the use of the J&J vaccine in the US last month. People with severe allergies may be more likely to get anaphylactic shock from the mRNA-based two-dose vaccines.

All these complications create a fog around the decision-space, making some people’s risk-benefit calculations more complex—or creating a space for people who perceive themselves to be at low risk from Covid-19, or who are more concerned about side effects than they need to be, to think it’s OK to not get vaccinated. “Most people aren’t sitting there with numbers worrying about the decimal point, thinking, ‘I’m going to weigh up the risk-benefit ratio,’” says Alexandra Freeman, executive director of the Winton Centre for Risk & Evidence Communication at the University of Cambridge. But just because most folks aren’t doing math doesn’t mean they’re not chewing on the problem. As Freeman says, “a risk is very subjective.”

So, OK, let’s talk about those blood clots. Freeman’s group put together a bunch of infographics that weaved a few of these threads into a useful tapestry. Instead of comparing the risk of getting Covid to the risk of getting vaccinated—an apples-to-oranges problem—they instead published a document comparing the potential blood-clot risk of the AstraZeneca vaccine to its actual benefit, the number of Covid-related intensive care unit admissions prevented by its use. And then they diced that up by age group and exposure risk. (In real life, exposure risk would differ from country to country and even across professions … and the group assumed 80% efficacy for the vaccine across the board, a necessary simplification … and they used a fixed timespan of 16 weeks, because all of these risks shift over time as infection rates wax and wane. Statistics!)

In 100,000 people with low exposure risk, they calculated, the AstraZeneca vaccine might be expected to cause 1.1 people to get blood clots and avoid just 0.8 ICU admissions. If you’re an only-looking-out-for-number-one sort of person, that looks like a reason to avoid the AstraZeneca vaccine—and indeed, European regulators have limited its use. Lucky there’s all those other vaccines.

At the other extreme, among people who for some reason have a high exposure risk—lots of infection running rampant in their county, let’s say—in 60-to-69 year olds, the vaccine might cause just 0.2 cases of blood clots (which seem mostly to affect younger people) but keep 127.7 people out of the ICU. It makes a stark case. In most of the Winton Centre groupings, the risk of the AstraZeneca vaccine pays off.

Again, though, the US and Europe ceded the power to evaluate these vaccines to the companies that made them. Each one used slightly different protocols and different populations. A multi-arm study of all of them might have ironed out these statistical kinks. The WHO actually announced such a trial in 2020; nothing seems to have come of it.

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