UJM, thanks for the reference. They compute ER visit and hospitalization reductions of 2 and 3 doses separately for Delta and Omicron periods comparing with unvaccinated. This is done for all mRNA vaccines after correcting for patient and virus prevalence parameters, so looks pretty solid.
Bottom line: 4x reduction in hospitalization at about 5 months and, presumably, higher for deaths (in all data, reduction increases with severity – from infection to ER to hospitalization to deaths).
Here is my summary from their Table 2 on hospitalization:
months <2 2-3 4 >=4 >= 5
Delta 2 doses 17x 11x 10x 5.5
Omicron 2 doses 3.5 3 2.5 2
Delta 3 doses 25x 14x 4x
Omicron 3 doses 11x 8x 4.5x
One question I have on such research is not taking “natural immunity” into account when counting “unvaccinated”. As they would be already more likely to be infected than those with vaccines, this might underestimate the estimate of the vaccine. I do not see this mentioned in the article.