The statistics behind breakthrough infections

Consider a theoretical scenario in which 100% of a population is vaccinated. Since vaccines are not perfect, there will be some “breakthrough” infections, and in such a case, 100% of infections will be among vaccinated people! That does not mean vaccines do not work. To determine vaccine efficacy in this case, we would need to know the total number of vaccinated and unvaccinated people who gathered that weekend. If this were known, then the percent of infections in the two populations could be calculated and the efficacy of the vaccine determined. In other words, it is important to know the denominator in such a calculation!

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If out of the 469 cases, 360 (75%) were vaccinated, to find the percent of infections among vaccinated people we would have to make the calculation 360/a X 100 where “a” is the total number of vaccinated people. Similarly, for the unvaccinated, it would be 109/b, X 100 where “b” is the total of unvaccinated individuals. But we do not know “a” or “b,” so the relative effectiveness cannot be calculated. However, given what we know about rates of vaccination in the state, which is roughly 65%, and in Provincetown, the epicentre, a reported 85%, it is a good bet that “a” is much larger than “b,” meaning that the percent of infection among vaccinated people is much less than among the unvaccinated. Such data is available from other studies and formed the basis for the approval of the various vaccines.

What all this means is that given the high vaccination rate, the chilling 75% number is not surprising and is basically meaningless. The really important number is 1.07, which is the percent of infected people (5 out of 469) who ended up in the hospital!

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