> Would having 6000 false positives be okay for being able to find the 1000 true positives?

I’d say no. That’s 5000 people who are told they might have cancer while in fact they don’t and who will then undergo further testing that is at best traumatic and at worst extremely invasive if not outright damaging.

Take intestinal cancer, for example. You can get screened for that and if you screen positive, they will take a biopsy - a fairly unpleasant and not entirely risk free procedure. Then it gets worse. If the biopsy shows some part of your intestines isn’t quite in order (a likely outcome, though not necessarily one that indicates cancer) they will take out that bit of intestine, just to be safe. This is a very invasive procedure and because it’s your intestines we’re talking about, you digestive system will be seriously out of whack for a while - if it ever heals completely - seriously and significantly degrading your quality of life. All this for a, let’s use your figures, 1 in 6 chance that you might have had cancer.

You're leaving out all choices in your decision pipeline.

If you screen positive, you can elect to have a biopsy or scan.

If your results come back inconclusive, you can elect to pursue surgical (or other) intervention.

That's what medicine is: a selection from among potential procedures, given the information at hand, informed by previous outcomes in similar or applicable situations.

In this case, we simply have more information. If said information turns out to have limited predictive power on the ultimate occurance of cancer, that will be incorporated into detection and treatment practices.

But the important thing is having more information than we had before.

If the patient were a robot, this would make sense. But people are easily scared, especially by the word "cancer," and fright can lead to bad decisions. And this is a decision that's made by individuals, including the doctors, who just want to take the "safe" option.

For example, the United States Preventative Services Task Force, which effectively decides the preventative procedures covered by Medicare and Medicaid, recommended against routine prostate specific antigen testing for prostate cancer in 2012. They backed that up with data on mortality and unnecessary procedures. Prostate doctors around the country flipped out. The doctors are focused on helping their individual patients. That's good, but it keeps them from seeing the overall harm to the entire population.

Why don't you just ask them?

"Based on the results of this test, you have a 1 in 6 chance of having cancer. This is what the biopsy process looks like, would you like one?

It also means that the test fails at detecting cancer more often than not, and will mean that if it detects a true cancer this time doctors will be inclined to not take it seriously because evidence/experience is that the test is useless

I suppose this takes into account the fact that doctors are humans too, and humans are typically not good at statistics. The probability of cancer from a positive test rises from 0.8% to 14.1%, a significant increase, and seems to warrant a closer look, from a layman's point of view at least.