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So let's have a look at the Gangelt paper. In general, this is a well done study investigating an early outbreak of #SARSCoV2 in a small community of 12,597 people. They estimate an infection attack rate of 15.5% corresponding to 1,956 people. (4/n)
Then, they estimate the IFR based on 7 deaths (7/1956 = 0.36%). You might say: Wait, what? How can you estimate an IFR based on 7 deaths only? Doesn't chance come into play here? You're right. With such a small number of deaths, you can't get precise estimates of the IFR. (5/n)
Assuming binomial sampling, one obtains a 95% CI of 0.14%-0.74%. While the authors report such a CI in the main text, they hide it for the numbers in the abstract. What is the rationale of presenting numbers with a precision that does not exist? This is somewhat concerning (6/n)
But there is more. According to this article from @hfeldwisch, they did not include all deaths that stem from infections up until the end of the study period. Instead of 7, there were probably 13 deaths. (7/n)https://medwatch.de/2020/11/26/die-ungezaehlten-todesfaelle-aus-gangelt/ …
This would result in an IFR of 13/1956 = 0.66% (95% CI: 0.35%-1.13%). That's interesting, because this estimate is in good agreement with the results from our statistical modeling study and the seroprevalence study from Munich. (8/n)
While that's an interesting turn of events, I still would not put too much trust into an IFR from such a small community and with such a small number of deaths. Especially when there are much bigger studies around that are based on hundreds or thousands of deaths. (9/n)
I am confused, why does the precision of the estimate depend on the number of deaths and not just the number of observations? If I have a million cases and only observe 7 deaths, i get a pretty tight CI. Am I missing something?
With 7 deaths and a million cases, you get 7e-6 and a confidence interval from 2.8e-6 to 1.4e-5. So uncertainty over almost an order of magnitude.
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