Massachusetts became the first state to move toward universal health insurance five years ago. Now, the state is debating how to replace the fee-for-service medical system. Mass Governor Deval L. Patrick (D) is trying to push the health care system here into a new era of cost control. He is proposing a new way of paying for care that would give lump payments to teams of doctors responsible for almost all the care of a group of patients, with bonuses for saving money and dispensing high-caliber services that keep people healthy.

“We did access first,” said state Senate President Therese Murray (D). “Now we have to figure out how we afford that.”

In 2006 created a health insurance exchange, a requirement that most residents carry coverage and subsidies to help them pay for it — central elements now in the federal Affordable Care Act (ACA). As a result, 98 percent of the residents here are now insured, but the first round of health care changes devoted far less attention to medical costs.

Leaders from the state’s insurance and hospital industries, medical society, legislature and governor’s staff served on a special state commission assigned to diagnose the cause of soaring medical spending.

Fee-for-service medicine “is a primary contributor to escalating costs and pervasive problems of uneven quality,” the commission unanimously concluded in 2009.

In 2009 Blue Cross Blue Shield of Massachusetts it began a new payment system called Alternative Quality Contracts. The arrangement is a version of the accountable care organizations that the federal government also is trying to encourage in Medicare. They pay teams of doctors or hospitals a lump sum or what is called a “global budget” for the patients assigned to them. If a team can provide care for less, it keeps some of the savings, assuming it also meets enough of 64 measures of quality that Blue Cross has defined. Today, about one-third of the primary care doctors in Blue Cross’s network are taking part. A half-million HMO patients have been put in them — but not told by the insurer.

At Partners HealthCare, the famous Boston-based medical system that dominates health care locally, Massachusetts General Hospital has been conducting a Medicare experiment in which nurses are assigned to coordinate care for about 2,500 older patients with multiple ailments. The experiment, which began five years ago, so far has reduced hospital re-admissions by one-fifth and cut medical spending by 7 percent.