1/5. To calculate how unlikely it is to see the cluster of pulmonary haemorrhage deaths in new borns - as discussed in the thread by Scott Mclachlan - it's not enough just to consider the probability of it happening at a single hospital in 1 month ....
https://twitter.com/Dr_ScottMc/status/1450747846970548226
2/5. We have to consider the probability it will happen at at least one hospital somewhere in the UK in one month sometime during, say, a year. Explanation and calculation are in this (3-minute) video
3/5. If it was a cluster of 4 it would be unlikely in a single hospital (about 0.07%, i.e. 1 in 143 chance) but very likely (81% chance) of happening somewhere in a year. But what if we observe a cluster of 8 in the same hospital?
4/5. The probability that happens in 1 hospital in 1 month is 0.00026% (1 in 385,000 chance). Probability it happens somewhere in UK in a year is about 0.063% (1 in 1,600 chance). That's still genuinely unlikely; so there may well be a non-random) causal explanation.
5/5. All done fairly quickly (so it's possible I've made some errors!!). Many assumptions - but all made clear in the video. Blog posting on this is here: normanfenton.com/post/how-unlik…
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