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In addition to yesterday's CFR piece, here is another estimating the infection fatality ratio in England with @carlheneghan & @oke_jason for @CEBMOxford. Using two national models we produce IFR estimates around late July & early August of 0.30% or 0.49%. https://www.cebm.net/covid-19/estimating-the-infection-fatality-ratio-in-england/
While the CFR is constructed by dividing observed deaths by observed cases, the IFR is constructed by dividing observed deaths by *estimated* infections. The IFR is generally a measure of more interest but obviously requires more assumptions: infections cannot simply be counted.
We take infection estimates published by the ONS & MRC Biostatistics Unit at the University of Cambridge and, as with yesterday's CFR piece, use a distribution based on surveillance data in England to estimate when these infections would have resulted in deaths were they fatal.
As a result we use estimated infections from the previous 40 days along with daily deaths data based on cases in the previous 28 days. This 40 day infection cutoff is chosen to fit the published PHE 88% figure for deaths within 28 days of a positive test so far.
Using the median estimate of infections as per the ONS model, we find an estimated IFR over a seven day period around 4 August that is 0.49%. Using their upper & lower credible interval estimates for infections we obtain 0.36% - 0.67% as a range.
Using the median estimate of infections as per the MRC model, we find an estimated IFR over a seven day period around 28 July that is 0.30%. Using their upper & lower credible interval estimates for infections we obtain 0.22% - 0.40% as a range.
Note that this range is not reflecting any modelling of uncertainty that we conduct & I would not be comfortable interpreting it as /our/ credible intervals for the IFR as such. It solely reflects uncertainty characterised by the ONS & MRC models.
It is notable in the above that the ONS infection estimates suggest a much bigger decline in the IFR (2.63% to 0.49%) compared to the MRC estimates (0.69% to 0.30%). They do seem to be converging to roughly the same sort of range, however.
While Wood's estimate for the infection-to-death distribution appears to be the most appropriate for our purposes, being trained on English data, use of parameters trained on data on deaths in Stockholm yields pretty similar results (0.30% MRC, 0.40% ONS).
I plan to put a detailed draft together based on this piece as a working paper in the next couple of weeks with a full battery of sensitivity analyses. We'll also publish further updates when the MRC & ONS models (or any other credible models we find!) give new estimates.
I did consider inclusion of other daily infection estimates such as the higher ones here, but examination of this data suggests that (AIUI unlike for model estimates produced for the US) the infection estimate is a function solely of announced deaths https://covid19-projections.com/united-kingdom
A really important point to make is that you CANNOT use these estimates and scale up total deaths since March by (1/our estimate) to give total estimated infections in England. Our estimates refer to the more-or-less contemporaneous situation as of late July / early August.
I am now foreseeing lots of replying to misunderstandings/misrepresentations/exaggerations to say "no that's not what we're saying", but hopefully this is clear enough! Public discourse around COVID-19 is so bad & consequences of this so dire that I'd beg people not to add to it.
If I see any egregious misrepresentations of what we are and aren't saying I will be seeking to correct them. Please, please, please do not do this. If anyone has good faith questions I am happy to answer if I can subject to time constraints.
Would definitely be interested in any thoughts anyone had on this or any other sensible modelling estimates for infections anyone is aware of, as there is obviously substantial interest in getting these estimates as accurate as possible.
