Even among men over 80, almost 40 percent were still getting routine P.S.A. tests. An elevated P.S.A. reading can prompt a cascade of subsequent tests and treatments, because “‘cancer’ is an emotionally charged term,” Dr. Sartor acknowledged. He still sees patients, he said, whose response to very low-risk cancer is, “I want it out, now.”

But treatment involves significant side effects, which often ease after the first year or two but may persist or even intensify. The British data showed, for instance, that six months after treatment, urinary leakage requiring pads affected roughly half of the men who’d had a prostatectomy, compared to 5 percent of those who underwent radiation and 4 percent of those under active surveillance.

After six years, 17 percent of the prostatectomy group still needed pads; among those under active surveillance, it was 8 percent, and 4 percent in the radiation group.

Similarly, men under active surveillance were more likely to retain the ability to have erections, though all three groups reported decreased sexual function with age. After 12 years, men in the radiation group were twice as likely, at 12 percent, to report fecal leakage as men in the other groups.

The financial costs of unnecessary testing and treatment also run high, as an analysis of claims from a large Medicare Advantage program demonstrate. The study, recently published in JAMA Network Open, looked at payments for regular P.S.A. screening and related services for men over 70 with no pre-existing prostate problems.

“The initial screening, which is unnecessary, triggers these follow-up services, a series of events catalyzed by anxiety,” said David Kim, a health economist at the University of Chicago and lead author of the study. “The further it progresses, the harder it is to stop.”

From 2016 to 2018, each dollar spent on a P.S.A. test on men over 70 generated another $6 spent for additional P.S.A. tests, imaging, radiation and surgery.