Three factors are threatening to push residents’ annual health care costs up faster than the state’s overall rate of economic growth:

First, health insurers in Massachusetts estimate the “medical cost trend” — an industry measure based on the price of services and the volume of doctor visits, procedures, and tests — will rise between 6 and 12 percent this year. That would be more than double the state’s anticipated rate of economic growth.

Second, organizers of new insurance-buying cooperatives, formed to enable small businesses to band together and negotiate discounts from health plans, say new federal rules will supersede Massachusetts regulations that qualify small businesses for discounts. That will probably drive up premiums for companies with fewer than 100 workers.

Finally, a string of hospital mergers — most recently, Beth Israel Deaconess Medical Center’s deal to acquire Jordan Hospital of Plymouth, as well as the proposed alliance of Partners HealthCare System with South Shore Hospital in Weymouth — raise the prospect that formerly independent community hospitals will have the clout to command higher medical reimbursements.

Reining in health expenses has been a top priority for Massachusetts officials, who view it as a pressing follow-up to the 2006 state law that created near-universal access to health insurance. Governor Deval Patrick last year signed legislation limiting the annual per-capita increase in health care costs to the state’s economic growth, projected to be 3.6 percent in 2013. The measure was applauded by business and consumer groups. Now, there is mounting skepticism about the chances of avoiding a higher increase.

“This goal is completely untested,” said Lynn Nicholas, president of the Massachusetts Hospital Association. “It’s being used for the first time anywhere. This is like turning around a giant tanker in a short amount of time. People totally underestimate how difficult that is.”

Richard C. Lord, a member of the state’s new Health Policy Commission and president of Associated Industries of Massachusetts, a trade group representing about 5,000 employers, said the law does not specifically penalize health care organizations that go over budget. It also lets providers and insurers off the hook in the event the state does not meet its target by calling for public hearings to identify and address the causes of rising prices.

“Nobody thought this was going to be easy,” Lord said. “We set an ambitious target for slowing the rate of growth in health spending. Whether we can meet it, it’s too soon to tell.”

Health care leaders in other states are closely monitoring the effort to control costs.

“People around the country paid a lot of attention to the Massachusetts health care reform in 2006,” said Ric Gross, market analyst for the research firm HealthLeaders-InterStudy, based in Nashville. “People will be watching what happens with this payment reform, as well.”

There are some trends working in the state’s favor. Data released by the Congressional Budget Office last month showed health care spending is growing nationally at the lowest rate in decades. Among the reasons: moves toward more coordinated health care by doctors and hospitals, and changes in insurance products and payment models.

Massachusetts has been at the forefront of those changes. Providers have been grouping themselves into so-called accountable care organizations to manage the care of patients within budgets. At the same time, insurers have been shifting providers toward fixed payments, rather than reimbursing them for every test and procedure. And more employers are offering coverage that allows them to save money by restricting where employees can get care or requiring workers to pay more for expensive doctors and hospitals.

Such factors helped push down average base rate premium increases to 3.6 percent for the first quarter and 2.7 percent for the second quarter in the most regulated segment of the state’s insurance business — the market serving small businesses and individuals.