> But the only way to find out was to have invasive, risky procedures to biopsy or remove what was found.
> And overall, the side effects from all the risky, invasive procedures to track down the over 90% of stuff that was harmless equal or outweigh the benefit from removing the less than 10% of stuff that wasn't harmless.
I accept this (well-used) perspective from a practical, current perspective, but not for abstract diagnostics generally. From the Bayes' theorem, and same logic you use in Kalman filters: More knowledge, if you have data on the confidence, always helps. It only causes these negative outcomes due to acting poorly with the data (e.g. due to emotions and liability concerns, I suspect here)
Tech folks have a very ... unique ... perspective on things. The following conversation would not be unusual for a tech geek--"Oh, they found something on that scan, so I need to get it looked at once a week for a month or two. Okay. Shrug.*
That is NOT a typical patient response. Go run that in front of any doctors and watch them laugh you out of the room.
1) When most people see something medical flagged, their first reaction is PANIC.
My friend's wife had something flag on her mammogram--the biopsy later showed it to be benign. In the meantime, her anxiety drove her blood pressure to something like 175 over 130 and they had to up her anxiety and blood pressure meds until the biopsy came back. Her probability of stroke was way higher than her probability of breast cancer. My grandfather had a little blood in his urine from a slowly growing bladder cancer. He forced them to treat it in spite of the fact that he was in his mid-80s, and the probability that cancer would kill him was zero. Instead, he basically died feeling miserable from the cancer treatments 6 months later.
2) Most working people cannot take off the amount of time necessary to do a weekly set of followup medical appointments for a couple months. Again, this is very different from tech geeks who can pretty much throw their work schedules around pretty flexibly.
The most practical Bayesian counter (indep of matters of confidence) might be the info bottleneck:
The risk (bottleneck) is in throwing out the relevant details