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I'm actually not well versed in the statistics of extremely low probability events, but it was a red flag for that Pfizer study to me as well. I'm pretty sure you can't just naively apply the standard calculation for standard errors when event counts are that low.
I've only dabbled and never came up with results I was happy with, but you're right about the standard errors. The distributional assumptions are more important when you can't count on the Central Limit theorem applying.
I wish they were more clear about exactly what they did, but I think the authors might not know themselves, as they just reference the STATA package they jammed everything into.
Did you dabble because of a specific project you were working on? Or just out of theoretical interest?
A specific project related to mass shootings. We really need a lot more of those if we want to understand them.
Interesting. One of my department colleagues writes on that topic
Good luck to him or her. I came up with some interesting stylized facts but the actual analysis didn't get very far.
Almost every other discipline has low standards for statistical analysis.
I don't know if you've ever tried to work with these kinds of low probability events, but this claim was an immediate red flag to me.