With concern high about the ability of the Omicron variant to dodge existing vaccines, it's too bad the Guardian newspaper had to run an article beneath the headline, "More than half Omicron cases in England are in the double jabbed." The graf in the story containing the details reads:
Twelve of the 22 cases occurred more than 14 days after the individual had received at least two doses of vaccine. Two cases were more than 28 days after a first dose of vaccine. Six were unvaccinated, while two had no available data.
Let's set aside from consideration the two cases for which vaccination status isn't known. The first and most obvious thing to be said is that a sample size of 20 is so small as to be practically irrelevant. The networks don't call New Hampshire for one candidate or the other after the ballots have been tabulated from that one village that votes at midnight. They report the vote totals but don't pretend they are significant. But the Guardian's headline, the linguistic equivalent of wild hand waving, pretends that the very first returns are significant.
The second thing to be said relates to the so-called base rate fallacy, which I've written about here and here. If everyone were vaccinated, so that every Omicron case was a breakthrough infection, this would not prove the vaccines were worthless against Omicron, right? What if universal vaccination reduced the total case load by 90 per cent? You have to take account of vaccination rates. When you do that, the scary-sounding results from the absurdly small sample size aren't that scary. Here is how I think that works out:
A chart in the Guardian story indicates that, in England, 69.3 percent of the population is fully vaccinated. But the fine print acknowledges that people under 12 aren't yet eligible. According to this BBC story, 90 percent of the eligible population have received at least one shot, and 80 percent have received two. Let's run some numbers using the 80 percent figure. Out of every thousand people, 800 will have been fully vaccinated, and 200 will be either unvaccinated or partly vaccinated—almost all unvaccinated. Of 20 positive Omicron tests in the population, 12 are for fully vaccinated people, and the other 8 are from the unvaccinated group. For purposes of gauging vaccine efficacy, then, the numbers that matter are 12-out-of-800 among the vaccinated, and 8-out-of-200 among the unvaccinated, or 1.5 percent versus 4 percent. The disease is more than 2.5 times more prevalent in the unvaccinated group. Yet the headline, while technically true, encourages people to conclude that, based on what is known so far, existing vaccines are essentially worthless against Omicron. "More than half the cases are among the fully vaccinated!"
Comments