Fortunately, researchers are studying how well patients do in these competing types of systems. The 2016 FIRST trial, which received a lot of attention, found that patient safety was not compromised when doctors in training worked longer shifts.

But even when the data show that limiting work hours leads to as good or better care, physicians should not be content to play “doctor tag,” in which a physician or clinic simply designates a new provider to “take over” treatment. Just because a physician takes good care of someone during his or her shift does not mean that responsibility ends there.

It may be helpful to think about specialties within medicine that have long been associated with limited continuity, such as emergency or intensive-care medicine. In both of these venues, patients move in and out of treatment quickly and follow-up may be difficult. But it is not impossible.

In her new book, “You Can Stop Humming Now,” Dr. Daniela Lamas, a critical care specialist, recounts visits she made to patients after they had left her unit. In one case, she attends a party thrown by a man whose severe West Nile virus infection had initially made it unlikely he would ever return home. But now there he was, eating, chatting, “working the crowd” and reminding his son to videotape the event.

Dr. Lamas did this on her own time. But she found it immensely rewarding. “We rarely have the opportunity,” she writes, to follow patients “through long-term acute care hospitals, infections, delirium, readmissions, and maybe, if they are very lucky, back home to a life that looks something like what they left.” The patient and his wife seemed thrilled that she had come — not as his current doctor but as his past doctor who still cared.

And what of my patients? I have made a decision not to try to imitate my father, as much as I admire the type of doctor that he was. But patients deserve to have a “doctor,” despite the caveat to my new patient. Plus I have found that most physicians, at the end of the day, are control freaks, wanting to be in charge of their own patients.

So I try to stay in touch, by phone, computer or other messaging strategies. Patient portals, being implemented at many hospitals, now allow patients to leave messages for their physicians in secure ways that do not threaten confidentiality. And I “sneak in” patients with urgent issues when I am not scheduled in clinic but there are open rooms, such as early in the morning or during lunch. The generous staff members at my clinic help make this happen by registering these patients and getting their vital signs. My clinic is also pursuing strategies to increase the chance that patients can see their regular doctors.