“You don’t always think you should call the doctor,” Ms. Cox said. But she has no qualms about reaching out to the nurse.

The initiative is part of an overall effort by Geisinger and other insurers to create a so-called medical home  the place where patients’ care is carefully coordinated by a doctor and staff, with particular attention given to the chronically ill.

Geisinger began experimenting with this approach three and a half years ago and now uses it in 37 practices, most of which are part of its own network of doctors’ offices.

But five of the doctors’ offices, including Dr. Kilduff’s, are independent practices that accept Geisinger as one of several insurance plans. Under the arrangement with the outside doctors, Geisinger pays for the nurses and shares with the doctors any savings they can achieve by reducing medical expenses. So far, Geisinger says it is pleased with the early results. In an unpublished review of 2008 data, Geisinger experienced an 18 percent drop in hospital admissions; overall medical expenses fell 7 percent. Geisinger expects to publish a study on its results later this year.

The doctors involved in the Geisinger experiment say they would not hesitate to hospitalize a patient if necessary. Part of the nurses’ work, in fact, is to keep tabs on anyone who is admitted and make sure a treatment plan is in place when a patient is discharged.

Many other insurers are also trying new, similar ways of rewarding primary care doctors.

“What we’re trying to do is get doctors off the traditional fee-for-service hamster wheel,” said Dr. Gus Manocchia, the chief medical officer for Blue Cross and Blue Shield of Rhode Island, a nonprofit insurer that started a program similar to Geisinger’s earlier this year. “A lot of the Blues plans are at least thinking about this, if they haven’t started it already.”

Image Mary Solomon reviewing Marie Jones’s medical information in her office. Geisinger shares with doctors any savings from helping patients avoid costly hospital stays. Credit... Laura Pedrick for The New York Times

WellPoint, Aetna and Cigna, which are some of the nation’s largest for-profit insurers, are also flirting with the concept. In one case, in Texas, a nurse whose salary is paid by Cigna discovered that a diabetic patient was missing check-ups and not filling his prescriptions because he had lost his job. He was insured through his wife, but without his income the couple could no longer afford to pay his share of the cost of prescriptions or the co-payments for the office visit.