On The Mathematics of Vaccine Efficacy

[Towlie]

Suppose the two vaccine doses that you receive are claimed to reach 95% efficacy by one week after your second dose. Other considerations remaining equal, that would mean your probability of becoming infected would be 5% of what it would have been if you hadn't received the vaccine.

Now consider historical data for the 7-day average number of daily new cases in your location.

It seems to me that once you've achieved the full claimed 95% efficacy value that the vaccine offers, your chance of becoming infected will be the same as it was when the 7-day average number of daily new cases was 5% of the current number.

Looking at the daily infection data for my state (Florida), that would mean that a hypothetical person currently enjoying full vaccine efficacy would have roughly the same probability of infection as people had during May of 2020.

I don't know about you, but back in May I was very worried and had already been in total isolation for well over a month.

[unblock]

1. Personally, we'll stay in bunker mode until we're vaccinated *and* average cases come way down.

[mpcamb]

13. On the plus side, vaccination reduces likelihood of a severe case and ventilator need.

[RobinA]

2. Well, I'm Not A Statistician

but off the top of my head, your (or anybody's) amount of worry does not necessarily correspond with your actual chance of getting sick.

[Hav]

3. That's a good reminder to continue acting responsibly after getting the vaccine

But the vaccine is also supposed to prevent the severe cases of Covid so that's another factor. Further, hopefully the numbers will go down once more people get vaccinated.

[Ms. Toad]

4. Average effectiveness doesn't translate well to individual risk.

It is far more likely that 95% of those vaccinated will have 100% (or near 100%) protection - and 5% will have zero (or near zero) protection. There's no way to tell which camp you fall in.

[Towlie]

8. If there's no way to tell then it doesn't make one bit of difference.

 
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If a deck of cards is shuffled and a card is chosen at random, it has a 1/13 probability of being an ace.

If a deck of cards was shuffled and a card was chosen at random and placed faced down on a table, your calculated confidence that it's an ace would be 1/13.

That's the difference between probability (which only applies to future events) and confidence (which applies to current states of nature), but the mathematics are the same either way.

[Ms. Toad]

10. Not sure what you think doesn't make a difference.

You get the vaccination because you hope you're in the group for which it is largely effective.

You wear your mask and socially distance because you might not be (and because we don't yet know if this very different vaccine prevents you from transmitting the disease to others).

The ultimate goal is for there to be enough protected people so that those who can't vaccinate (or those for whom the vaccination isn't effective) don't bounce into other vulnerable people who might have and transmit the disease to them. (herd immunity)

My response was really about the assumption that the measured effectiveness 95%, a statistic based on how many people who were vaccinated got COVID anyway v how many people in the control group got it translated into a personal prediction of your own chances.

It's like saying you have a 1/100 chance of winning the lottery means that 1/100 of the pot is yours.

[relayerbob]

5. No, that's not how it works

[Towlie]

6. Oh? Well then please tell us how it DOES work.

 
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[relayerbob]

7. See the post right above

[Massacure]

9. Try to think of it as a shift in severity and not a boolean switch on whether you get COVID or not

Pretend you have random number generator to generate a number between 0 and 999,999.

Without the vaccine, nothing happens if you roll a 0, you get a mild case if you roll greater than 1, and a moderate case if you roll greater than 500,000. If you roll greater than 850,000 you will be hospitalized, greater than 950,000 you will need an ICU and greater than 990,000 will result in death.

Now you are given the vaccine. A roll from 0 to 949,999 means nothing happens. You will not get a mild case unless you roll greater than 950,000 and will not get a moderate case unless you roll greater than 975,000. You will not be hospitalized unless you roll greater than 992,500 and need to roll greater than 994,999 to be ill enough to be admitted to the ICU. Only a roll greater than 999,499 will kill you.

Pretend the number you roll is 987,654. Without the vaccine, you'll have been admitted to an ICU but with the vaccine that is a moderate case that does not require hospitalization.

The vaccine not only reduces the chance of you getting COVID, it also reduces severity if you do get it.

[DeminPennswoods]

11. Put the numbers in perspective

Yes 23M is a big number, but it is less than 10% of the total US population and some percentage of that number are recovered covid19 infectees.

[muriel_volestrangler]

12. With herd immunity, the benefits increase with time

Yes, the vaccinated individual may at first have the same chance of infection as in May 2020; but when most people have been vaccinated (or have recovered from an infection), the number of infectious people will continue to decline. Not only is each person less likely to catch it, they're also less likely to pass it on.

As others have said, this means that being vaccinated doesn't mean you should stop other precautions after a few weeks. But it does mean your chances of problems go down a lot, and they'll go down even more as others get the shot. That's why it's both a good thing for you, and a good thing for society.

[Towlie]

14. Thank you. Yes, that exactly what my original post implies.

 
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[retread]

15. A swing and a miss!!

"The Moderna and Pfizer vaccines — the only two approved in the U.S. — are among the best vaccines ever created, with effectiveness rates of about 95 percent after two doses. That’s on par with the vaccines for chickenpox and measles."


"Of the 32,000 people who received the Moderna or Pfizer vaccine in a research trial, do you want to guess how many contracted a severe Covid case? One."
"The Moderna and Pfizer vaccines are “essentially 100 percent effective against serious disease,” Dr. Paul Offit, the director of the Vaccine Education Center at Children’s Hospital of Philadelphia, said. “It’s ridiculously encouraging.”
"“It’s going to save your life — that’s where the emphasis has to be right now,” Dr. Peter Hotez of the Baylor College of Medicine said."