For men over 70, PSA screening usually isn’t recommended based on USPSTF guidelines. It’s not a hard rule, but more of a general recommendation based on the risks and benefits. If anyone wants to know why, I’m happy to explain.
It’s very likely that President Biden didn’t get a PSA test—which is completely normal for someone his age. He probably started having symptoms from the cancer spreading to his bones, which led doctors to investigate and eventually discover the metastatic prostate cancer.
It doesn’t really make sense to think he knew he had prostate cancer and chose not to treat it, letting it spread. If he had ever had an elevated PSA, it would’ve been worked up and likely treated long before it got to this point.
I know I am oversimplifying here, but there is absolutely no risk to a PSA test beyond the normal risk associated with a blood draw. Biden's PSA, as progressed as his cancer is, would have been extremely, even alarmingly high for a long time.
The primary risk, as I understand it, is from an overreaction to the diagnosis, and a rush to treatment protocols (ADT, radiation, even chemo) that have adverse effects when perhaps those protocols weren't immediately necessary and where a "watchful waiting" period (until treatment is necessary) may have been the least adverse medical treatment. As you have stated, risk/benefit analysis.
I have a hard time believing the President of the United States doesn't have a blood draw at his physical, even if it were for other diagnostic purposes than PSA. I have a harder time believing they wouldn't run a $79 PSA screen on the already collected blood for the President of the US.
The President already knows about our warehousing of Aliens, about the asteroid that will hit us in the next decade, and about
SPECTRE's next plot to seize world control, I am pretty sure he can manage his elevated PSAs without overreacting.
I also find some of Biden's behavior (physically and congnitively) over the last few years to be consistent with side effects of some of the treatment protocols for prostate cancer. That, coupled with the lack of a conclusive statement as to the timing of the actual initial diagnosis, leads me to believe the former President has known about this diagnosis, and very likely received treatment for it, before or during his presidency.