I think you are not getting the idea of ARR. ARR is dependent on the
background risk of catching covid in the first place. For the lancet article, they had low ARR because during the time they were doing the trials the prevalence of Covid was not as high as during the second wave. you mention 5mil/60 mil population in the UK already infected with Sars2-covid. that is for the entire period since pandemic started in Mar 2020. ARR is always calculated base on a defined period (for eg the vaccine trial period).
If you can imagine that over a period of X years, you will have 100% chance of catching covid, then the vaccine ARR = RRR.
This is also why using ARR is problematic during an ongoing infectious pandemic cycle. ARR would be more appropriate if used during a steady state endemic level situation where the background risk is stable and constant. However during a pandemic, the
force of the infection is dynamic, if its not well controlled by vaccines, SOP etc, the background risk would increase exponentially. The ironic thing is, the higher the background risk, the higher the ARR figures would be.
exactly.
event rate multiply by time would be the real picture.