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> an unknown side effect that did not come up in the original studies.

You shouldn't expect side-effects this rare to show up in the trials. The AZ trial was based on ~32k participants (https://www.astrazeneca.com/media-centre/press-releases/2021...). Your probability of observing a 1/1,000,000 occurrence in 32k observations is something like 3%.

It's impossible to uncover (with statistical significance) 1/1,000,000 side effects without giving millions of doses.

The fact that a rare side-effect has (maybe!) shown up should not negatively impact your priors for how safe the vaccine is. If anything, the fact that we're talking about 7 / 7,000,000 cases should reassure you that we're catching extremely rare stuff, which means we would have caught anything more serious too.

A more general way of putting this is that, by doing a trial you don't prove there are _no_ side-effects, you just put an upper bound on how common they can be. This is the best that science can do! Epistemologically speaking, you can never prove the non-existence of something, you can just show that it doesn't occur in the places you've taken measurements, at a frequency that your experiments would detect. (This is the "black swan fallacy", as John Stuart Mill originally formulated it.)



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