We reported last month that Atrius Health was the only “pioneer’’ accountable care organization in Massachusetts that came in over budget in caring for Medicare patients, and would have to pay back the government to make up for some of those losses.

Atrius, a large doctors’ group, said Wednesday that final accounting shows it came in about 1 percent over budget, which means it does not owe Medicare money. “Our loss is small enough that it is considered within the statistical range of error,’’ the organization said in a written statement.

Thirty-two health care systems— including five in Massachusetts—were selected in 2011 to be “pioneer” accountable care organizations, testing a new model in which providers take on more financial risk as an incentive to better manage patient care and prevent unnecessary, costly hospitalizations. The Centers for Medicare and Medicaid Services sets an individual budget, or target, for each participating group.

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