In reply to Michael Hood:
The "proper" data is the "longitudinal" data - records for each individual with the date of their +ve test, the date of their hospitalisation (if there was one) and the date of their death. All that data is presumably available to the NHS and as far as I know, they don't publish any outputs from it. As far as I know, this dataset is not made public, although from what I can tell, an anonymised version could be so published. Analysing this data would give the "true" case fatality rate.
So, we're left scrabbling round making assumptions about lag from infection to death in the data that is published. I prefer not to assume a probability distribution for the time from infection to deaths any choice is provably wrong (the distribution can be shown to change over time) and so has some sort of bias. Instead I do the same measurement as you for every day in a period, and for a range of lags - plot below. When cases are rising or falling, this approach under- or over- estimates the 'true" fatality rate depending on the lag and what the cases are doing. All the curves converge on the right - this is because we have had a plateau phase of cases and then a corresponding plateau of deaths, where the rates are ~constant with time. This means that the measurement is no longer sensitive to lag and so the lag "drops out" of the analysis. So, from this plot I could say with some certainty that the CFR around 13th November was about 2%.
How close is this 2% to the actual CFR? I think the "plateau" phase means that these simple approaches are currently quite accurate. But notice how none of the lines remains on 2% throughout the time period - this suggests either the CFR is changing or the distribution of times from test to death is changing; you can infer this from the demographic data on cases having ages changing and what's known about IRF vs age - so I don't think we can get better estimates of CFR without making a bunch of dodgy assumptions.
I also put a similar plot for IFR below that uses the ONS random sapling data as a measure of true infection levels. To my shame they're not identically laid out so flip booking between them isn't so satisfying. I'm scratching my head about why the CFR is tailing off on the right hand side of my CFR plot; I think it's probably because I'm using too-recent datapoint subject to reporting lag. It could also be a sign of test-and-trace catching up to real infections as it improves.
Edit: So a lot of work and words to get to the same place your quick measurement does; but when I gave such a quick measurement for IFR the other day I was snootily informed that my methodology was not anywhere near as good as that of the CEBM. Hint: The CEBM method was not good. Not good at all.
Post edited at 18:48