[graboy]

I kinda agree with you and I understand your point but I also think there is a social-ethical reality that if a doctor finds something they must treat it. The two options are 1. doing nothing, or 2. reducing cancer risk and you get unnecessary biopsies.

You're thinking of this as there being an objective positive utility for not dying of cancer and a objective negative utility for biopsies, and there being an objective optimal "rational" tradeoff that the best radiologist can optimize for to get their "nearly certain" detection threshold.

But frankly - the tradeoff for the value of a human life is perhaps the most uncertain thing one could choose. It lies in the eyes of the patient if the worry and time associated with a false detection is worth their reduced chance of death. The ethical uncertainty expressed in the OP - are these unnecessary biopsies worth it - is warranted.