COVID data from England - focus on vaccines

While I am quite time limited, I plant to at least provide some commentary regarding the technical briefings from Public Health England. There are produced biweekly and provide - in my view - high quality data.

I am particularly concerned about vaccine efficacy - at least with regards to these reports - I am actually more concerned about vaccine safety, but that is for another time.

There are plenty of caveats about the analysis that I do, but for now I want to stress two:

1. I tend to prefer quite simple analysis. Even those can be difficult enough. Insight is what I am looking for.
2. Remember that there are substantially more vaccinated people than unvaccinated, so we need to mind that. I will present absolute numbers - which is what the report gives - but these need to be calibrated as a function of vax/unvax fraction

I will start with a baseline coming from briefing 19 - July 23. These reports present - for the delta variant - a breakdown of cases, hospitalizations and deaths separated by age and vaccination status. I will only be concerned about fully vaccinated and unvaccinated. There are more classes  in between.

age	cases vaccinated	cases NOT vaccinated	hospitalization vaccinated	hospitalization NOT vaccinated	death vaccinated	death NOT vaccinated
<50	15346	119063	103	1105	4	34
>=50	13427	2377	371	196	220	131
all	28773	121402	474	1301	224	165

From table 5 on briefing 19 - Analysis from 1 Feb to 19 Jul. At least one of the columns doesn't add perfectly, but that is what is there.

I will not mind much about the base line. But now we can take reports 20 and 21 and see how things are evolving: these reports also present cumulative values, but we can subtract the previous report to see how things are currently changing. It is also easier to guesstimate the fraction of vaccinated people as there is a smaller timespan to consider.
That being said, and before we proceed to the new reports, I would like to note that, for all ages, there are 19% of vax cases, 26% of vax hospitalizations and 57% of vax deaths. This is mostly caused by the >50 cohort.
I want to avoid taking conclusions and prefer to leave that to the reader, but it seems that there is a clear break in the relationship between hospitalizations and deaths: More people seem to die as a fraction of hospitalizations in the vaccinated group

Lets now just look at percentage of vaccinated deaths across all reports by age cohort. The number on the header is the report number

cohort	19	20	21
<50	11	39	36
>=50	63	70	70
all	58	70	70

The deaths of the <50 cohort are small (between 9 and 24) - so the evolution there is expected to have some variance.
Now this needs to be calibrated as a function of the fraction of people that are vaccinated. This is almost impossible to do correctly, because we would have to track precise vaccination rates for cohorts.
Fortunately we are looking for rough approximations as we want to understand the evolution of data patterns. As I write this - which is later than the report data collection for 21 - there are 77% of people vaccinated in England (two shots), this being skewed towards older individuals.
Take your conclusions....

Finally I want to have a look at hospitalizations, as they might be a leading indicator of deaths (cases are noisy for several reasons). Here are the fraction of hospitalized that are vaccinated per report

cohort	19	20	21
<50	9	12	18
>=50	65	71	73
all	26	40	46

The fraction of hospitalized individuals that are vaccinated is increasing, we will see in the future if there is any impact on deaths...

This is the first analysis that I am committing to text. I am pretty sure there will be problems (for example, there are plenty of assumptions that I have not documented yet). Comments are most appreciated, and I will correct mistakes that are pointed out to me - I am pretty sure there will be quite a few. As we get new reports, I hope the quality of the data analysis evolves.