If a very high percentage of a group is vaccinated, a fairly high percentage of infections may be among vaccinated people even if the vaccines are highly effective.

This is a general statistical (base-rate) claim. True: standard epidemiological reasoning or data confirm that when vaccination coverage is very high, vaccinated people can make up a large share of infections even with a highly effective vaccine. For example, with 95% coverage and 90% efficacy, about two-thirds of infections are among the vaccinated, as illustrated in 2021 UK, Israel or CDC data or explanations. Mostly true: the principle holds, but the phrasing slightly overstates how 'fairly high' the share would be. Mixed or mostly false: the principle holds only under implausible assumptions. False: the arithmetic or the evidence shows the principle is wrong.

Set before the research began.

1. E1 Vaccinated versus unvaccinated, a comparison between cases shows that the vaccine works - ISS Istituto Superiore di Sanità (ISS, Italy's national public health institute) · 20 July 2021

   “in population groups with a very high vaccination coverage, the majority of reported cases could thus occur in vaccinated subjects.”

2. E2 Why are there vaccinated among COVID-19 infected? jmsallan.netlify.app (personal blog) · 31 August 2021

   “With a vaccination rate of 90%, we have only 10,000 infected among a population of 100,000 still unvaccinated, and 18,000 infected among the 900,000 vaccinated. We have now 10,000 + 18,000 = 28,000 infected. Now the 64% of infected are vaccinated people.”

3. E3 COVID vaccines remain highly effective at stopping severe disease amid spread of Delta, L.A. data show - The Boston Globe The Boston Globe · 24 August 2021

   “"Simply, it's math. As we have more people vaccinated, more of our infections that we diagnose are going to be in vaccinated people," Oregon state epidemiologist Dean Sidelinger said.”

Italy's national public health institute says that in groups with very high vaccination coverage, most reported cases could occur among vaccinated people [E1]. A worked example shows that with 90% coverage, 64% of infections would be among the vaccinated [E2]. An Oregon state epidemiologist calls this effect "simply math" [E3]. These sources postdate the claim, but they describe the same base-rate arithmetic, which held equally on the claim date. Together they confirm the principle as the criteria describe it.