Everything you say is correct, but I think it's easy to come away with the impression that early detection is not helpful in living longer when I'm certain that's not the case.
I'm certain that expected time of death is a nonincreasing function of detection time -- this would necessarily be the case if the treatment never harmed the patient, and even though that's sadly not the case, prescribing a course of treatment that on average shortens patient lives must surely contradict "First do no harm".
If you assign a low quality-of-life score to time spent undergoing certain harsh treatments like chemo, then you could certainly reduce your "total quality of life" (that is, the integral over your lifetime of quality-of-life-at-each-moment) by starting treatment too early. I think that's a reasonable way to frame it. But in terms of maximising lifespan, the earlier you detect it, the better.
False positive rates are a concern for any widespread medical testing. If you test everyone in the USA for a rare disorder, a super great test might have a 1% false positive rate and 1% false negative rate. It's good that you catch 99% of people with the disorder, but that might only be 10,000 people. At the same time, you'll get 3.3 million false positives which will absolutely swamp the medical systems for follow-up tests, some of which will also have false positives. This costs a ton of money at the very least for unnecessary follow-up testing, and realistically would overwhelm the medical systems designed for just those 10,000 people. It also causes a great amount of undue stress and financial burden on the 3.3 million affected families.
Some people will also be unlucky enough to get false positives on the follow-up test, and eventually you may end up performing unnecessary invasive interventions on 30,000 people who don't have the underlying condition.
It's not to say that:
> the earlier you detect it, the better.
Is wrong, per se. But we'll need to narrow down the criteria for who should be recommended to get these tests in order to minimize harms from false-positives. So you'd want to identify risk factors and have a way to check if someone has those risk factors before testing them.
I'm certain that expected time of death is a nonincreasing function of detection time -- this would necessarily be the case if the treatment never harmed the patient, and even though that's sadly not the case, prescribing a course of treatment that on average shortens patient lives must surely contradict "First do no harm".
If you assign a low quality-of-life score to time spent undergoing certain harsh treatments like chemo, then you could certainly reduce your "total quality of life" (that is, the integral over your lifetime of quality-of-life-at-each-moment) by starting treatment too early. I think that's a reasonable way to frame it. But in terms of maximising lifespan, the earlier you detect it, the better.