Expected rates were obtained by participating sites using pre-COVID-19 vaccination healthcare data stratified by age and sex (Faksova et al.).
The original paper seems to be far too ineffective a methodology.
That is not an effective control; at least take the same health data analysis from the unvaccinated population. Given that even folks with the vaccine can catch less severe cases, you really need to root out COVID-19 as the cause of those complications.