people should be made aware of the degree to which we actually have no idea whether various things are more likely to kill you or save your life, so that they can make their own decisions better, based on their own intuitions. .
As a math guy you should know that it is impossible to calculate all the variables in the equation. Clinical studies are the best educated guess that can be made.
The best advice is to consult your doctor and pay attention to how your own body reacts to certain food and medicines.
I don't mean exact numbers. Obviously we don't know those. I mean presenting people with the data that we do know. Something like this, but of course more streamlined and universally understandable (I'm drafting this in 2 minutes, whereas you would actually spend days or weeks or months making up a template and dialogue):
"Okay Mr. Patient, so there's this vaccine they made this year. Here's what we know: The data suggests that with a high degree of confidence, we can say that the vaccine has some amount less than a 1/157 chance of killing you itself. And we can also say with equally high confidence that the vaccine has some amount less than 1 1/314 chance of saving your life from the flu. To be clear, the actual numbers could be anything lower than those, and the only reason the numbers are different that I just told you is that we ran different numbers of test subjects, not that we are more sure of either relationship. It could actually be 1/50,000 to kill you and 1/70,000 to save you, or 1/70,000 to kill you and 1/50,000 to save you, or 1/1,000,000 and 1/500. Any combination below what I told you at the start."
"Now, do you want to get this vaccine or no? it's up to you given that information."
I.e.
Give people whatever thresholds we ARE 95% confident of, and don't make any other assumptions for them, and let them decide from there on their own intuitions. Then same basic thing for any other medical procedure we have any amount of data on.
Clinical studies are the best educated guess that can be made.
They are the best source of an educated guess we have, but they aren't being USED in an educated manner or their actual results being given to patients to MAKE their own educated guesses.
Doctors aren't better at flipping coins than I am, and they almost certainly have different biases and opinions about quality vs. quantity of life and acceptable risks, etc. than I do.
Thus,
I am more qualified than a doctor to make an intuitive guess for my own medical procedure, if you simply give me the same numbers as them.
So yes fine, run clinical trials, but only if you're actually going to use them correctly.