The false positive rate doesn't depend on the number of true positives in the population. However, as you rightly point out the metric that actually matters for these kinds of screening is the precision/positive predictive value, and that one does.
https://en.m.wikipedia.org/wiki/Positive_and_negative_predic...
P(Having cancer given positive) = P(Positive given having cancer) * P(Having Cancer) / P(Having a Positive in general)
Lets say 1% true positive rate is a "useless test".
0.01 = 0.88 (Detection rate from paper) * X / 0.05 (inverse of specificity)
X = 0.0005
Incident rate of Stomach Cancer (most common) is 27,600 per year in US. The denominator for this fraction is iffy because there are a lot of biases on current detection rates. If we go ahead with "adults in the US" then the rate of cancer is 0.00014 [cite](https://www.cancer.org/cancer/stomach-cancer/about/key-stati...)
Basically, if we applied this test to all adults without other diagnostic factors. This would be worse than 1% true positive detection rate. I don't know about how effective intersecting with other diagnostic criteria would be on increasing the odds a patient actually have the disease and it might or might not still be useful after that.
This sort of study is mostly bullshit anyway. They took a relatively small pile of data, made a small classifier with high accuracy (maybe overtrained, maybe not) and really can't validate it.
...and the test does not determine location, so it's impossible to treat even with a positive test.
So from a clinical standpoint it's nearly useless, except to schedule patients for more frequent traditional testing. ...the counter point is that the stress caused to a patient is probably not trivial, even from a physical health perspective.
...but from a scientific standpoint, it's awesome and well worth further study.
That sounds very useful to me!
Being able to catch a cancer early on because of increased surveillance is hugely valuable. Part of why cancer is so dangerous is because it often grows/spreads for years before you get any symptoms. If you're in the unlucky cohort of <50 years old and have an asymptomatic cancer, it might go decades before anyone thinks to check.
And mind, increased surveillance typically means once a year tests or scans, so it's not so overly onerous. It's possible even that generally being in frequent contact with doctors and more seriously minding your health could have net benefits in preventing other maladies as well.
Unfortunately I can't edit my comment anymore.
If we had a test that detected everyone and they believed it, we'd improve cancer rates.
But, the even more important metric to measure is mortality. Detecting a cancer that is 100% fatal 1 day earlier than traditional tests obviously wouldn't be that impressive. Even if the PPV is very high.
It's also very possible that a cancer that is detected accurately 6 months earlier, but that detection still doesn't improve our ability to treat the cancer. In these cases, it might even look like mortality is improved if you measure time from detection to death ("early detection extended survival by 6 months"). But, actually, it didn't change much.
So, that's all to say that the "Experimental" in the title should temper expectations considerably, because that has real meaning.