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The importance of control groups in the light of observational data!
The latest data from Israel suggests recent Covid cases are 53% fully vax, 44% unvax, 2% partly vax, 1% convalescent unvax, ~ 0% convalescent vax. Adjusted for their proportions in the overall population, you get something like:
Fully vaccinated 54.6% risk reduction (vs. unvaccinated people who did not have the disease)
Partially vaccinated 78.4% RR
Convalescent unvaccinated 91.8% RR
Convalescent vaccinated 100% RR
That would suggest, on its own, the partly vax are twice as protected as the fully vax! True, most of these are young adults and teenagers to whom a single dose will be very effective, but still, that suggests the fully vax are still overrepresented due to the high vaccination rates in the locations the current outbreak began. If they are twofold overrepresented (just as an example), true VE would be around 77.3%, not 54.6%.
