You could check for excess mortality among vaccinated and unvaccinated people. I think the data is very clear: vaccination does not lead to excess mortality (unlike COVID).
I think that would be very tricky to decouple variables here. The vaccine seems to reduce mortality from COVID, but if the vaccine were killing x% itself, the vaccine would only have to be more effective at saving from COVID than killing for that safety signal to be lost. In short, comparing vaxxed vs unvaxxed mortality alone isn't likely to tell you if you have a vaccine safety signal.
You're right, you'd have to test whether people in each group are infected with COVID, and correct for that. Should still be doable. Would also need to correct for age and co-morbidities (doable), and also for differences in behaviour (hard).
A study of covering seven sites in the US from December 14, 2020 from July 31, 2021 found lower non-COVID mortality among vaccination individuals:
> During December 2020–July 2021, COVID-19 vaccine recipients had lower rates of non–COVID-19 mortality than did unvaccinated persons after adjusting for age, sex, race and ethnicity, and study site.
The original (official) data shows how likely is someone to die if vaccinated vs unvaccinated. "Rate" part of "Death rate" means the number of deaths is already divided by the population in one of the groups (vaccinated or not), so the size of a group doesn't affect the rate.
I'm convinced you could show data that every single person that received the vaccine died and these people would still say it's safe. Objectivity is gone and health care is now political. The sheer irony that Trump was blamed for everything except for the worst thing that he actually did. Operation Warp Speed rushed the scientific process and caused bad medicine to be released to the general public.
Could anyone point out if how vaccines as the casue could be ruled out by this data?