A highly effective vaccine cannot make things worse

The worst COVID reporting I’ve seen to date: 2 Companies Say their Vaccines Are Effective. What Does That Mean?

Here’s the deck:

You might assume that 95 out of every 100 people vaccinated will be protected from Covid-19. But that’s not how the math works.

In fact, that’s exactly how the math works, which you see if you read the story.

In the case of Pfizer, for example, the company recruited 43,661 volunteers and waited for 170 people to come down with symptoms of Covid-19 and then get a positive test. Out of these 170, 162 had received a placebo shot, and just eight had received the real vaccine.

From these numbers, Pfizer’s researchers calculated the fraction of volunteers in each group who got sick. Both fractions were small, but the fraction of unvaccinated volunteers who got sick was much bigger than the fraction of vaccinated ones. The scientists then determined the relative difference between those two fractions. Scientists express that difference with a value they call efficacy. If there’s no difference between the vaccine and placebo groups, the efficacy is zero. If none of the sick people had been vaccinated, the efficacy is 100 percent.

So here we have a lot of confusing verbiage deployed to obscure middle-school math.

170 people got COVID

162 had taken the placebo 

8 had taken the vaccine

8 ÷ 170 = 5%

95% of the vaccinated participants did not get COVID.

That’s how the math works. 

It’s certainly possible the vaccine will not achieve 95% effectiveness when it’s distributed to the country (though I imagine that, by the same token, it might also protect more than 95%.) But if so, that will have nothing to do with math.  

Next we come to a section asserting that a highly effective vaccine could produce more COVID if people stop wearing masks: 

But if people get vaccinated and then stop wearing masks and taking other safety measures, their chances of spreading the coronavirus to others could increase.

You could get this paradoxical situation of things getting worse,” said Dr. Bar-Zeev.

I’m sorry, but highly effective vaccines do not make things worse.

They make things better. 

More to the point, highly effective vaccines do not depend on masks to be highly effective. They depend on our immune systems functioning as they are designed to function. There is no mask-wearing requirement or condition in any of the vaccine trials, and that is true for the very good reason that neither vaccines nor vaccine campaigns depend on masks to work.

The logic of the piece seems to hinge on the assumption that asymptomatic individuals are deadly.

So, because a highly effective vaccine could conceivably produce more asymptomatic individuals because people who would have been symptomatic are now asymptomatic instead (that would be a good thing, not a bad thing), a vaccine could produce more cases of COVID because more people with asymptomatic COVID are walking around without masks.

But this logic assumes that:

a) vaccinated individuals continue to develop asymptomatic infections (which we don’t know)

b) asymptomatic individuals are just as contagious as symptomatic (not likely to be true, from what I read)

c) asymptomatic vaccinated individuals will somehow produce severe disease in other vaccinated individuals

The logic is a mess. 

The fact is: vaccines work by protecting individuals from other (infected) individuals. If the vaccine works for you, you are now protected from severe disease when you encounter people who have COVID, and this is true regardless of whether those people are symptomatic or asymptomatic. It is also true regardless of whether they’re wearing a mask. Thanks to the miracle of vaccine, you have acquired protection from COVID without having had COVID. That’s the point.

Yes, it’s conceivable you could still catch an asymptomatic case of COVID and be asymptomatically contagious to people who are not vaccinated — but in that case their job is to get vaccinated so they’re protected too. You’ve done your part. There should be no requirement that you wear a mask because you might be asyptomatically contagious to people who haven’t gotten a vaccine.

As a society, of course, you want lots of individuals to be vaccinated because over time those who aren’t protected by vaccine come to be protected by the sheer number of other people who are. An immune-compromised person can be protected not because the vaccine works for him or her, but because s/he encounters fewer infected people in the first place.

But the Times is impervious to the logic of vaccine policy.

What do Pfizer’s 170 people tell us?

They tell us that in the midst of a fast-moving epidemic, only 8 vaccinated people came down w/COVID, and all of their cases were mild.

That is unalloyed good news & should be accurately reported as such.

Instead the Times turns somersaults trying to make lemons out of lemonade.

And see: Why Is All COVID-19 News Bad News?

3 thoughts on “A highly effective vaccine cannot make things worse

  1. I’m guessing we’ll start to see all flavors of vaccine skepticism… particularly as (as I predict) rates of reported autism continue to rise.


  2. Your math is very slightly off. Vaccine efficacy is defined as
    1 – risk_for_vaccinated/risk_for_unvaccinated.

    That would be 1- (8/number_vaccinated)/(162/number_placebo), not 1 – 8/170. To compute the efficacy you need to know how big each group was (or at least the relative sizes).


  3. “95% of the vaccinated participants did not get COVID.”

    Your calculation is actually demonstrating that of the people enrolled in the study who got COVID, 95% were in the placebo group.

    The vast majority of participants in both groups did not get COVID.


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