If option A is regular blood tests with an endoscopy to confirm should the blood test come back positive and option B is getting endoscopies on a regular basis, option A is a no brainer. While it might not be super invasive, I'd definitely like to keep the number of times a tube has to be shoved down my throat to a minimum.
No, the false positive rate is irrelevant. Let's say you want to check for cancer annually and the blood test has a 50% false positive rate:
If you only get endoscopies after positive results, you get an endoscopy every other year. If you skip the test and go straight to the endoscopy, you get one every year. Thus you get half as many tubes shoved down your throat if you get the blood test.
For a more reasonable false positive rate like 5%, you would have a 50/50 chance of getting a false positive any given decade. I'd much rather get 4 endoscopies than 40.
Indeed, for any false positive rate less than 100% (which isn't really a test to begin with) still on average decreases the number of endoscopies you need.
Really the metric that's important is the false negatives: if that's too high then I can't safely forego the endoscopy just because this year's blood test was negative. Even then though, if the blood test has a long lead time then maybe it's safe to wait and see how next year's blood test goes.
