In the fall of 2015, Dr. Herbert Dardik, chief of vascular surgery at Englewood Hospital and Medical Center in New Jersey, nodded off in the operating room.

Note that Dr. Dardik, then 80, was not performing the operation. He’d undergone a minor medical procedure himself a few days earlier, so he’d told his patient that another surgeon would handle her carotid endarterectomy, in which plaque is removed from the carotid artery to improve blood flow.

But when she begged Dr. Dardik at least to be present during the operation, he agreed to sit in. “I was really an accessory,” he recalled. “It was so boring, I kind of dozed off” — whereupon an alarmed nurse-anesthetist reported the incident to administrators.

Within days, the hospital’s chief of anesthesiology and chief medical officer were in Dr. Dardik’s office, praising his surgical skill while urging him to reduce his workload.

“I got so annoyed, I stood up and opened the door and said, ‘Get out,’” Dr. Dardik said. “Who knows better what I can do but I myself?”

He also resisted the suggestion that he undergo testing at Sinai Hospital in Baltimore, which had established a two-day program to evaluate whether older surgeons could safely continue practicing.

Not long afterward, Dr. Dardik was on a plane when its older-looking captain came aboard. (Federal regulations mandate a retirement age of 65 for commercial pilots.)

“I hope this guy’s still OK,” Dr. Dardik remembered thinking. At which point, “it hit me like a hammer — this is what other people think when they look at me.”

A few weeks later, he became the first doctor evaluated by Sinai Hospital’s aging surgeon program.

The physician work force, like the rest of the population, has grown substantially grayer in recent years. Almost a quarter of practicing physicians were 65 or older in 2015, according to the American Medical Association. In 2017, more than 122,000 physicians in that age group were engaged in patient care.

Health care researchers and analysts are debating what, if anything, to do about this tide of aging practitioners. “We know that human faculties decrease with age,” said Dr. Mark Katlic, the thoracic surgeon who founded Sinai Hospital’s program.

Declining vision, hearing and cognition can affect any health professional (or any human). But Dr. Katlic has expressed particular concern about surgeons, who need to retain exceptional vision, manual dexterity, reaction speed and stamina.

Past age 70, “can you grab a tiny little blood vessel with a forceps and not grab something else?” he asked. “Or use very small instruments for sutures?” Some operations, he pointed out, go on for six or seven hours, even longer.

Studies haven’t produced clear-cut answers to such questions. Cognition and other abilities decrease with age — but the variability between individuals increases.

At 75, “there are sharp, wonderful doctors, and those who need to stop,” said Dr. E. Patchen Dellinger, lead author of a review on aging physicians published in JAMA Surgery.

Whether older surgeons have poorer outcomes than younger ones also remains debatable, because decades of experience and judgment can compensate for modest physical or cognitive declines.

One large study of Medicare patients found surgeons over age 60 had higher mortality rates for several kinds of operations, including coronary bypasses, but not for other procedures. And the differences were small, occurring mostly among doctors who performed few operations.