Comment by sethev

Your case #2 doesn't have nearly enough information to say whether it's obviously better for a population of patients. There are a lot of other variables you would need to know:

    - The accuracy of detecting a mass
    - The true distribution of masses in the population
    - The likelihood that of falsely detecting a mass in the same place twice (you seem to implicitly assume that false detections are uncorrelated with each other)
    - The likelihood that a real mass is cancerous (you stipulate that this is 95% in your scenario, but you don't say what other factors are used to determine this - as opposed to just knowing that there's a mass that grew.)
    - The positive effect of treatment in the case of true-positives.
    - The negative effect of treatment or further diagnostics in the case of false-positive.

Saying that doctors are lying about over diagnosis to cope with the fact that diagnostic techniques are too expensive is absurd. They have to actually make decisions in the real world, where your two neat little categories can't be known even if they hypothetically exist.