CDC says vaccines are only 66 percent effective at preventing Delta infection. As far as I can understand, this means 34% of vaccinated people develop a covid infection. I'm having a hard time squaring this with 'vaccines prevent infection' thesis. Perhaps I'm missing something obvious?

(Yes, I'm aware the fraction is better against severe Delta infection. Yes, I agree 3x reduction is infection rate is a good thing.)

https://www.webmd.com/vaccines/covid-19-vaccine/news/2021082...

> this means 34% of vaccinated people develop a covid infection

That's not what "effective" means. It means that if your probability of getting infected without the vaccine is p, your probability of getting infected with the vaccine is .34*p. One way to think about it is that the "ineffectiveness" is the relative risk P[infected|vaccinated]/P[infected|unvaccinated], and effectiveness is 1-ineffectiveness.

A vaccine can be 100% effective even if P[infected] is negligible.

P[infected] is per unit time and does not account for the dynamics of the situation. For example, if the vaccine is not powerful enough to make R<1, then everybody becomes infected eventually regardless of the vaccine.

Thanks!

> CDC says vaccines are only 66 percent effective at preventing Delta infection

WITH A 95% CONFIDENCE INTERVAL OF 26% TO 84%

They only statistically modeled how much their unvaccinated population was already recovered from coronavirus based on estimates of community spread, among other issues with that number.

https://www.cdc.gov/mmwr/volumes/70/wr/mm7034e4.htm

And when you have a CI of something like that size, of course you wind up in the middle of it -- the actual value could very well be closer to 80% due to systematic uncertainties in the modeling.

Or 30%, to be fair.

published on the CDC site today: 77% (74%-80%) VE for pfizer and 92% (89%-93%) VE for moderna. With only some evidence of reduced VE against delta and/or waning in those > 75 years old:

https://www.cdc.gov/mmwr/volumes/70/wr/mm7037e2.htm

That's a very reassuring result, thanks for sharing.

Interesting that moderna continues to do better, and looking forward to seeing the studies VE versus time since vaccination.

Israel is showing per-capita rates by default.. in some of the data... on https://datadashboard.health.gov.il/COVID-19/ to avoid this issue:

e.g. hospitalized above age 60 (חולים קשה - התחסנות)

162/100,000 unvaccinated

40/100,000 2 dose (I think)

5/100,000 2 dose + booster

If you'd just look at the raw numbers, the vaccine doesn't appear so helpful: 226 unvaccinated, 116 with 2 doses, 55 with 3 doses. Looks like it barely helps.

There is also rate data from UK on covid delta (week 32-35 2021), breakdown by vax status & age, see Figure 2a. Cases under 40 is 1/2 vax/unvax, cases over 40 is actually slightly larger for vax than unvax. I had a sense vaccines are not perfect wrt infection, but didn't expect actual numbers to be that close.

Fortunately vaccines are very still very good at preventing severe cases (hospitaliations), see Figure 2d.

https://assets.publishing.service.gov.uk/government/uploads/...

Preventing severe cases really only benefit the vaccinated and perhaps medical providers. It’s a lousy justification for a mandate that forces someone to do something that cannot be undone.

Great document, thanks for the link.

The document says that >97% of the blood-donor population in the UK has some kind of antibodies, either from natural infection or vaccines. This seems like an astonishingly high number.