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A couple of points:

1. PCR positivity rates: without separate PCR positivity rates broken down by vaccine status, it is very difficult to draw firm conclusions from comparisons of infection incidences across vaccine statuses. And yet they do!

Example: (all other things being equal - note: they are not, likely higher incidences of asymptomatic in vaxxed))

Consider infection rate/100k in vaxxed 1/3 of rate in unvaxxed BUT unvaxxed were tested 3x as often...?

If positivity rates are equal then we could infer "true" infection rates are also similar

If positivity rates are not equal then we "true" infection rates of vaxxed and unvaxxed could diverge or converge from to reported rates

2. Cohort composition and selection bias: without more detailed information about the unvaccinated population vs vaccinated, it is very difficult to draw firm conclusions from comparisons of hospitalisation/ICU/death incidences. And yet they try!

E.g. as you point out, we may assume the oldest, sickest, weakest, and most immune compromised are all to be found in the unvaccinated cohort. Previous studies also point to flu shot uptake being greater among the more health conscious and conversely lower among the more vulnerable. Cohorts are thus highly UNmatched! And then there is the issue of vary behaviour due to perceived protection/vulnerability.

3. Variants: how to compare infection/hospitalisation/ICU/death rates within vaxxed/unvaxxed cohorts across variants? Has treatment improved, is variant less virulent, is there selection bias within cohorts (as discussed in 2.)?

I think your approach is at least moving in this direction by comparing percentage increases within vax/unvax cohorts across time. Thank you!

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