Thank you Igor for the reply. Here is a more detailed explanation of my thought on expected rates...
I'm wondering if we can say that the COVID cases among the vaccinated are 25x more than would be expected (if the vaccine was indeed 90% effective).
Please double check my logic and calculation on this...
Consider the latest week 42-45 UKHSA surveillance report. Based on the report, we know that about 76% of 40-49 year olds are vaccinated (and so 24% unvax). We know that there were 15,920 cases in the unvax. So, we can say that the baseline expected infection rate would be 15,920 cases / 24% = 663 cases per 1% of unvax population.
If we assume that vaccines are 90% effective, then we would expect only 10% of that expected rate among the vaccinated, which would be 663 x 10% = 66.3 cases per 1% of the vaccinated population. Therefore, we would expect a total of 66.3 cases x 76% vaccinated = 5,039 expected cases in the 40-49 year old group.
The reported cases among the fully vaccinated group is 125,936. Therefore, the actual vs expected rate is 125,936 actual / 5,039 expected = 25
Please note that I did not include the Unlinked numbers (I assume that they fall along the same lines as the unvax vs vax). Please doublecheck me on this.
The same calculation can be applied to hospitalizations (3x more than expected in 40-49 year olds) and deaths (2.9x and 3.2x more than expected in the 28 day and 60 day groups)
Thank you Igor for the reply. Here is a more detailed explanation of my thought on expected rates...
I'm wondering if we can say that the COVID cases among the vaccinated are 25x more than would be expected (if the vaccine was indeed 90% effective).
Please double check my logic and calculation on this...
Consider the latest week 42-45 UKHSA surveillance report. Based on the report, we know that about 76% of 40-49 year olds are vaccinated (and so 24% unvax). We know that there were 15,920 cases in the unvax. So, we can say that the baseline expected infection rate would be 15,920 cases / 24% = 663 cases per 1% of unvax population.
If we assume that vaccines are 90% effective, then we would expect only 10% of that expected rate among the vaccinated, which would be 663 x 10% = 66.3 cases per 1% of the vaccinated population. Therefore, we would expect a total of 66.3 cases x 76% vaccinated = 5,039 expected cases in the 40-49 year old group.
The reported cases among the fully vaccinated group is 125,936. Therefore, the actual vs expected rate is 125,936 actual / 5,039 expected = 25
Please note that I did not include the Unlinked numbers (I assume that they fall along the same lines as the unvax vs vax). Please doublecheck me on this.
The same calculation can be applied to hospitalizations (3x more than expected in 40-49 year olds) and deaths (2.9x and 3.2x more than expected in the 28 day and 60 day groups)