For Marc Feingold, a family practice doctor in Manalapan, N.J., who is a single practitioner, the medical home concept fits naturally into the way he treats patients, caring for them when they are sick, but also doing what he can to prevent them from becoming ill. When a patient comes in for sinusitis, for example, Dr. Feingold will check that patient’s blood pressure and cholesterol to make sure they are under control. He says he does not treat his patients who are not Horizon members any differently.

The extra money he receives from Horizon and a similar program allows him to remain independent, he said. He recently began offering Weight Watchers meetings in his office and was able to use some of the money to help defray the cost for his 40 patients. “These programs incentivize me to try to incentivize my patients,” Dr. Feingold said.

Horizon says about 500,000 of its patients are in programs like a medical home or accountable care organization, but the insurer says it hopes to increase that number to more than half of its 3.7 million members by 2017. In 2012, patients seen in a medical home had 23 percent fewer admissions to the hospital and 12 percent fewer emergency room visits than Horizon members who were not.

A result for members could be lower costs. Last month, Horizon said it was offering plans in the small-employer market with lower premiums and no deductible if the member sought care from a doctor affiliated with a medical home.

In North Carolina, Mr. Wilson is trying a number of initiatives. He says what has changed is the insurer’s ability to team with providers to try to improve care and lower costs. Under one program, Carolina Advanced Health, Blue Cross joined with UNC Health Care, the academic medical center based in Chapel Hill. The two, which split evenly any savings, offer a clinic where patients are served by doctors, nurses, pharmacists, mental health professionals and others. In the first two years, the clinic avoided any unnecessary hospital stays. It also reported 64 percent fewer emergency room visits among its patients.

Some policy specialists say these experiments are not enough because they do not fundamentally change the way hospitals and doctors make money. Many of the programs, for example, do not put the health system at risk if it mismanages patients by giving poor or costly care.

“Until there’s risk, real financial risk, it doesn’t change anything,” said François de Brantes, the executive director of the Health Care Incentives Improvement Institute, a nonprofit group that encourages the adoption of new payment methods. He said the private insurers should move much more quickly.