What does 95% vaccine efficacy mean?

Filed under: Math, Medicine
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I’ve seen several web pages that explain how to calculate vaccine efficacy, but most of them explain it in terms of a formula rather than explaining what the formula means.

Here’s the simplest conceptual explanation I’ve seen:

a VE of 90% indicates […] a 90% reduction from the number of cases you would expect if they [had] not been vaccinated.

(From a CDC page.)

A NYT lesson plan gives some concrete numbers, which I think helps:

The Pfizer study included 43,661 people, of whom half were in the control/placebo group and half were in the group who received two doses of the vaccine.

“In the placebo group […] 162 [people] became infected with the coronavirus and showed symptoms.” In the group that received the vaccine, only 8 people became infected and symptomatic. (For the rest of this post, I’m just going to say “infected” as shorthand; but we don’t know for sure whether people who receive the vaccine can be asymptomatic carriers.)

The placebo group and the vaccine group were essentially the same size in this case, so you can think about those numbers as the vaccine preventing 154 of the infections that would have happened without it. (That’s 162 infections in the control group, minus 8 infections in the vaccine group.) (Probably if the vaccine group hadn’t received the vaccine, they wouldn’t have had exactly the same number of infections as the control group; but for the purposes of this calculation, we assume that they would have.)

If you divide that 154 number (the number of infections that were prevented by the vaccine) by 162 (the number of infections in the control group), you get 95.06%, which is the efficacy of the Pfizer vaccine. Or to put that another way, about 95% of the people who would have been infected without the vaccine were kept from being infected by the vaccine.

(If the control group and the vaccine group are different sizes, then you have to do a slightly more complicated calculation: first you determine the percentage of the control group that were infected (0.7421% in the Pfizer case); then you determine the percentage of the vaccine group that were infected (0.0366% in the Pfizer case; then you subtract the latter from the former (0.7055%), and divide by the former (95.06%). That’s the real formula; but when the two groups are the same size, various things cancel out such that you can skip some steps if you want to, and you can use the numbers of people infected instead of the percentages of people infected. The efficacy number comes out the same either way.)

For more details, see Wikipedia’s Vaccine efficacy entry.

One Response to “What does 95% vaccine efficacy mean?”

  1. Jed

    Someone I don’t know, from Florida, posted a comment here in which they implied that less than 1% of people get COVID. That’s just not true. And they were using that statistic to recommend against getting the vaccine, which I consider to be irresponsible bordering on dangerous, and I didn’t want to host such a comment. So I’ve deleted it.

    The facts: so far, about 30 million people in the US have been infected. That’s not under 1%; that’s nearly 10%.

    Worldwide, about 128 million people have been infected. That’s about 1.6% of the total world population. But that’s still not a reason to not get the vaccine.

    A couple of good reasons to get vaccinated:

    • Even if you’re not worried about yourself, getting vaccinated reduces the likelihood of infecting others.
    • The percentages aren’t really helpful. For example, the fact that 10% of people in the US have been infected doesn’t mean that everyone in the US has a 10% chance of being infected, because the chance of getting infected varies hugely by location and behavior and various other factors. For example, if you do risky things when you’re in a small enclosed space with someone who’s infected, then your chance of getting infected goes way up.
    • So far, there’s no indication that any of the three vaccines that have been approved in the US for emergency use are dangerous. They hugely reduce the risk of getting a symptomatic infection, and today’s news suggests that they hugely reduce the risk of getting even an asymptomatic infection. They don’t reduce the risk to zero by any means, but they do reduce it a lot.
    • The only way that the world is going to get past this pandemic and return to any semblance of normal life is by vaccinating most of the world’s population.
    reply

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