"Outside bed" but inside pelvis: RT still useful. But for sake of argument let outside bed equal M1 disease. The med onc diagnosed M1
purely from these PSAs. The pretest probability--given a PSA <10, primary Gleason of three, stage T2 disease, and negative axumin and bone scan--for being M1 is ~1%. Now let's assume the PPV (positive predictive value) of this patient's PSA doubling from 1 to 2 in 1 month is truly 95% and the sensitivity of the test is 95% (very generous/optimistic)... how high would the specificity of PSA doubling time (DT) need to be to give a PPV of 95%?
.............disease......
..........(+).......(-)...
test(+)....95........x....
test(-)....5.........y....
..........100.......9900..
1. PPV=95/(95+x); assumed PPV=0.95
2. 0.95=95/(95+x)
3. x=5
4. y therefore equals 9895; x+y=9900
5. Specificity = y/(x+y) = 9895/(9895+5) = 99.95%
Therefore, assigning a ~95% PPV for M1 disease on the basis of PSA DT *in this scenario, for this pre-test probability* would make PSA DT the most specific test for M1 prostate cancer known to man. It would make PSA DT one of the most specific tests in medicine.
PSMA scans "only" have a specificity of ~95-99% so PSA DT would be ~2-3 orders magnitude more specific than PSMA scans i.e. no need for PSMA scans anymore just rely on PSA DT. As can be seen, assuming a PPV of 95% on the basis of PSA DT obviously leads to some absurd conclusions, or at least nose-scrunching.
I am saying you still have to consider the other factors in this case outside of the doubling time which is suspicious, granted, but in no way settles the situation to a 95% certainty level. Even if PSA DT has a high 95% sensitivity/specificity you can plug that back in to the 2x2 table and find the PPV is... 50%. If
truly 95+% chance of met dz, the NNT for RT would be so high it would mean RT would be futile. But I do not think RT is futile here. And a ~50% PPV for the PSA DT given the totality of all the other factors is more "believable" than a ~95% PPV.