[DennisP]

Right the numbers for "positive test" should include false positives. That's part of my point. I've worked out a sample calculation if you want to see it. We could get fancy with error bars but I don't think that's necessary for any common cancer, and rare cancers shouldn't be tested for anyway since you'll mostly have false positives.

As I said above, I don't think that screening is automatically good because in some cases, working out the above numbers will tell you not to treat even if you had a positive test. Those cases should not be tested since they're not actionable anyway. That would likely be the case for a rare cancer.

I agree that a false positive is not great. But if you have the data, then the impact of false positive tests is already included in your data. You're comparing the total rates of death and other unpleasant outcomes for a tested population vs. an untested population.