One thing that is also noteworthy in the Week 7 publication is that they are now comparing boosted rates instead of double vaxxed rates in the Table 13 data, as the differential between those with any vaccination and the unvaccinated is hardly discernable (because over 90% of the population of the UK has COVID antibodies at this point, either through vaccination or prior infection), so now they are focusing on the boosted to try to show efficiency. Even looking at the boosted rates, there is hardly any difference in hospitalization rates between the unvaccinated and boosted in the 18-49 demographic [in that demographic, the rate among those with any vaccination is actually higher (9.25 per 100k) among the vaccinated than the unvaccinated (8.84 per 100k)]. If you compare data between the unvaccinated and vaccinated, you find some surprising things:
Case Rates 18+: Vaccinated - 2,883.55 per 100k, Unvaccinated - 1,390.13 per 100k
Hospitalizations 18+: Vaccinated - 17.91 per 100k, Unvaccinated - 15.62 per 100k
Deaths 18+: Vaccinated - 15.80 per 100k, Unvaccinated - 9.74 per 100k
Obviously, there is a little bit of Simpson's Paradox when you look at that broad of an age range, but as I noted above, there are actually age groups where the vaccinated hospitalization rate is higher for vaccinated individuals than unvaccinated individuals. For the 18-29 age group, the vaccinated hospitalization rate (7.87) is higher than the unvaccinated hospitalization rate (7.34). For the 30-39 age group, the vaccinated hospitalization rate (10.45) is higher than the unvaccinated hospitalization rate (9.68).
When you get into the higher age groups, where the vaccination rate is extremely high, you run into another statistical issue, whereby unvaccinated rates are elevated because the denominator is so low, so any cases, hospitalizations or deaths wrongly attributed to the unvaccinated category (which happens, even with the best database management due to human error) dramatically inflate unvaccinated numbers.