Here is some of the sort of evidence I base my view on:
https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD004407.pub3/abstract
– “We included five randomised controlled trials (RCTs), one controlled clinical trial (CCT), 27 cohort studies, 17 case‐control studies, five time‐series trials, one case cross‐over trial, two ecological studies, six self controlled case series studies involving in all about 14,700,000 children and assessing effectiveness and safety of MMR vaccine”
I have linked to it in a previous discussion. I have also mentioned cohort studies and case-control studies in this thread.