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That specificity implies one of these cancers apriori occurs in 5% of the tested population.

Is that about right taking into account pre-screening? We can identify a population that has a 5% chance of having one of these cancers?

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If these represent 70% of cancers overall and ~40% of the US population will get a cancer diagnosis at some point then it seems likely you can find many populations with more than a 5% chance of having cancer.

OK, but if I have a 40% chance of getting a cancer diagnosis at some point in my life, and they run the test as part of my physical every year, then presumably my chance of having cancer at the time they run the test is much less than 5%.

That just means you should not give someone the test every year.

At 70 people have a much higher risk of cancer than 7. Long term smokers have higher risks than non smokers. Combine multiple risk factors and find groups with 5+% risk of these kinds of cancers is not that difficult.

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