A key government experiment that set out to lower costs and coordinate care for Medicare patients — now the blueprint for an innovation the Obama administration is trying to move to a national scale — has failed to save a substantial amount of money.

The five-year test enlisted 10 leading health systems around the country and offered financial bonuses if they could save enough by treating older patients more efficiently while providing high-quality care.

In 2010, the final year, just four of the 10 sites, all long-established groups run by doctors, slowed their Medicare spending enough to qualify for a bonus, according to an official evaluation not yet made public. Two sites saved enough to get bonuses in all five years, the evaluation shows, but three did not succeed even once.

The uneven progress is significant because the experiment involves “accountable care organizations,” one of the hottest trends in health policy and an idea included in the year-old federal law intended to overhaul the nation’s health-care system.

The law calls for the Medicare program to approve teams of doctors or hospitals to run such organizations — a new twist on the old idea of managed care — starting in January. Although important details differ, the basic contours of the experiment and new ACOs are the same: Medicare shares savings with health organizations if they can treat older Americans for less money and attain specific hallmarks of quality.

What can — and cannot — be accomplished by changing the way Medicare pays for and delivers care is particularly relevant now because the Obama administration proposed rules this spring for groups that want to become ACOs under Medicare. Many health-care providers, including the leaders of all 10 sites in the experiment, are complaining that the rules would to too burdensome.

The experiment began in 2005 under the George W. Bush administration. It offered “performance payments” to participants that met most of 32 measures of quality — half as many as in the proposed rule — and spent at least 2 percent less for Medicare patients, compared with a group of similar Medicare patients outside the experiment who lived nearby.

Despite their spotty financial progress, all 10 medical groups in the experiment met the quality requirements. And the program fostered innovations in care, according to administration officials, outside health policy experts and leaders of the groups.

One of the participants, Wisconsin’s Marshfield Clinic, was by far the biggest winner of bonus payments. According to Theodore A. Paxel, Marshfield’s medical director, the experiment prompted the 95-year-old organization to create a telephone line with nurses available day and night, and half of the people who called last year received enough advice that they did not need to visit a doctor. Marshfield also set up a program for patients with congestive heart failure. Every day, the patients are in touch by telephone with an interactive device that asks them to punch in their weight and answer a few questions. If any of their responses are medically suspicious, someone from the clinic calls right away.

In contrast, the Billings Clinic in Montana put into place similar innovations but never qualified for a bonus payment. The medical director, Doug Carr, said the group did not start out as far along with its electronic health records — a vital tool to coordinate care.

The leaders at some of the sites, formally known as the Physician Group Practice Demonstration, say that technical rules for comparing their Medicare patients to ones outside the experiment made it difficult to demonstrate savings. Other health policy experts say that patients in the experiment look sicker on paper than the ones outside, but that it was a false impression, because the experiment gave the medical groups an incentive to submit lots of billing codes.

Either way, recent studies have shown, when a medical group becomes an ACO, the financial investments it must make in record-keeping and other changes have been higher than the government has predicted, causing it to lose money for at least the first few years. “It does give you pause that this is not something you can just create . . . overnight,” Carr said.

ACOs have a significant role in the legislative battle over whether the government should change Medicare — the highly popular federal health insurance program for 47 million elderly and disabled Americans — as part of a broad plan to reduce the U.S. deficit. Congressional Republicans are pushing hard to spend less on Medicare and are advancing a controversial plan to privatize the program.

Democrats counter that the 2010 health-care law contains important tools that will curb spending, citing ACOs as a prime example. Donald M. Berwick, administrator of the Centers for Medicare and Medicaid Services, said in an interview that he is optimistic about the potential of ACOs to lower costs by coordinating care, although he acknowledged that savings from the experiment “were unevenly distributed, and they were modest.”

Gail Wilensky, who ran Medicare and Medicaid under President George H.W. Bush, said the experiment’s results suggest that the idea may not be ready to go nationwide. She said it is “astounding” that savings were not greater among 10 long-established groups that she said “should have blown it out of the water. . . . It’s like, are you kidding me? . . . If it was this tough for this group that I had just assumed would be hands-down winners, what does it say for groups that don’t have a long history of coming together?”

The experiment, she and other health policy experts point out, was less risky financially for the groups than the proposed ACO rules, because the participants were not penalized for overspending. Under the proposal, ACOs that spend too much would have to forfeit some Medicare funding — from the start or by their third year.

Berwick said he is paying attention to criticism of the proposed rules. But it remains unclear how they may be changed. In planning for Medicare ACOs, he said, the government must be careful to balance the need to slow spending in the financially precarious program against the danger of creating such a steep “on-ramp” that doctors and hospitals will be unwilling to take part.

Still, he said, “if care is correctly coordinated, costs fall and quality rises. . . . To me, it’s a matter of how fast we will get there, not whether we will get there.”