Beginning next year, Bristol Hospital could be out of Anthem Blue Cross and Blue Shield’s network, meaning that Anthem members who use the hospital would be charged out-of-network rates for all but emergency care.Bristol hospital gave notice that it will terminate its contract with the insurer after the two sides were unable to agree on reimbursement rates. Unless they reach an agreement, the contract will end Jan. 1.The two sides are scheduled to talk next week but representatives of both the hospital and the insurer said they remain far apart.Bernadette Kelleher, Anthem’s vice president of provider engagement and contracting, said that the company has proposed an increase in rates for the hospital but that the increases the hospital is seeking are “a non-starter.”"It’s not something we could accept,” she said. “The challenge there is that the level of increase right now, with the current economic environment, individual employers, individual customers, they really just can’t continue to absorb very high, double-digit rate increases.”Peter Freytag, Bristol Hospital’s chief financial officer, acknowledged that the hospital is seeking a large rate increase, but said that is because Anthem’s previous contract paid lower rates than other private insurance companies.”They have been underpaying us for years,” he said.Anthem said the hospital is seeking an increase of more than 20 percent. Freytag said the hospital offered 9 percent as part of continuing negotiations.Freytag disputed the idea that an increase in payments from Anthem would require higher insurance rates for Anthem’s customers. He said the increase Anthem offered would make it difficult for the hospital to cover its costs and replace equipment necessary for quality care.Anthem’s proposed increase would still pay the hospital lower rates than the other private carriers, he said.Similar standoffs have happened in Connecticut this year, in one case involving Anthem. Hospitals typically offset some of the money they lose on Medicare and Medicaid coverage through the rates they charge private insurers.Anthem, which has about 1.4 million customers in Connecticut, accounts for 19 percent of the hospital’s business.Last March, Bristol Hospital briefly stopped accepting United Healthcare insurance after negotiations failed to produce an agreement. The two sides reached a new contract the following month.Around the same time, talks between Anthem and Middlesex Hospital over their contract broke down, leading Anthem to send letters telling its members the hospital would no longer be part of its network. The hospital and insurer reached an agreement before that happened.