Vaccine trials run large randomized control experiments to estimate vaccine effectiveness. i.e. they compare a control group to an experiment group, both equally likely to contract the virus, and observe if a smaller percent of the experiment group contracted the virus compared to the control group over a certain time period.

Continued vaccine efficacy data is measured longitudinally, by tracking the cumulative infection rate across populations with similar risk profiles but different preventative measures in place.

The data for vaccine effectiveness is already publicly available and compiled through reports and infographs on the CDC website, the FDA website and the WHO website. xkcd even had a comic about a graph of vaccine efficacy pulled directly from the FDA's preliminary brief about the Moderna vaccine trial results last year. There are papers that have been published regarding longitudinal results for countries - for instance, you might have heard about studies from Israel claiming that vaccine efficacy has dropped by some 60%, while other studies continue to cap the drop at anywhere from 0 to 10%.

It would have to be a multivariate analysis. That's sort of the problem with x over y analysis - the question presupposes a very narrow range of answers.

There are good reasons to believe the vaccines help, but you don't want to beg the question when you start the analysis.

> you might have heard about studies from Israel claiming that vaccine efficacy has dropped by some 60%

Yes, I heard it. 60% is not a constant, the effectiveness keeps dropping over time. So what gives? In country A, everybody has to take a vaccine every 5-6 months with lockdowns in between, while another country doesn't bother vaccinating, and life returns to normal? Is this what you expect from the vaccine?