[carlmr]

According to https://www.cancer.org/cancer/cancer-basics/cancer-prevalenc... about 15 million Americans have cancer. That is about 5% of the population. Given those numbers and assuming you have a positive result for a random person, that means according to Bayes:

C being cancer, H healthy, P positive test P(C|P) = [P(P|C) * P(C)] / [P(P|C) * P(C) + P(P|H) * P(H)] = [ 0.7 * 0.05] / [ 0.7 * 0.05 + 0.01 * 0.95] = 0.035 / (0.035 + 0.0095) = 0.7865

That's pretty good. If you have a positive test result, in 4 out of 5 cases it actually is cancer. It gets a bit worse if you account for the fact that this test only works for a subset of the cancers. But this would be useful as a pre-screening.

[nonbel]

Since this is a screening test, I don't think that 15 million number is correct for prevalence.

You are using % of population diagnosed with cancer. The correct value would be the % of population with undiagnosed cancer.

[carlmr]

True. That is really difficult to obtain though. But assuming that most people are eventually diagnosed with cancer (even if just close to death), then a similar maybe a little lower population must have undiagnosed cancers.

In the end you'll need a properly conducted study with random undiagnosed people to get reliable numbers though.

[nonbel]

It seems like pretty basic info to me. There should be some estimate out there somewhere, especially given the billions of dollars spent each year on studying cancer. A quick search didn't lead to anything promising though.