I’ve had a rant before about the assumptions made when calculating effectiveness this way so might as well make the same point again. It’s a VERY crude estimation which is significantly flawed. It only holds up assuming the vaccinated and unvaccinated are equally matched cohorts with identical exposure to the virus (obviously not the case).
One very obvious cause of bias in that the vaccinated/fully vaccinated are more likely to be older, less socially active, more likely to WFH or be retired etc etc so will seem to be protected by the vaccine when actually they’re mainly protected by their behaviours. Conversely, the number of cases in the un-vaccinated cohort will be inflated by students and young employees working in e.g. meat packing plants (i.e. two of the most frequent locations of major outbreaks)
One of my bug bears about “covid twitter” are people looking to mathematicians for answers that should come from clinicians that have a much better understandIng of concepts like bias and causality.
To be fair, the trends are encouraging but I wouldn’t be taking the exact %’s mentioned seriously at all.
EDIT: Reading the whole thread he does seem to attempt to take the exposure bias into account but doesn’t show his workings so impossible to know if his approach holds up.
It's flawed, but historically he's also been consistent with the overall stats that the PHE and PH Scotland produce for efficacy (they use more granular data and then create a kind of matching unvaccinated group as a control - except in the oldest cohorts where take-up is so high they can't match people now, there they use historic ratios).
But the hospital stats are interesting because age has been such a massive determinant in hospitalisation whereas they're only a partial one in case numbers. For expected case numbers this twitterer broadly uses Autumn Alpha stats to get ratios (though he says even if he changes those by 50% it scarcely moves the dial by more than 1%)
With the national stats, increasingly Wales are part of the story as well, because the age/dose/deprivation profiles of the vaccinated are different there. It's the epidemiological equivalent of a clinical trial but only the health service are allowed to see the potentially anonymity breaking details while the hospitalisation numbers are so low.
As you say, socialising/work/education patterns are massively different and therefore so are risks. We now have the effect of the most sociable (who are also probably going in to work/education) mostly uncaccinated populations mixing more or less freely again.
Meanwhile the vaccinated older ones will generally socialise with people in their own (probably also vaccinated) age group. Obviously families - particularly families who live in the same household - change the dynamic again, which is why the local demographics come into play so strongly when you try to look at Bolton say. Canary in the mine moment.