When his son, Ethan, was a baby, doctors said he had a rare liver disease. The family, which was in a health maintenance organization, had to appeal three times to get approval for the out-of-network surgery that saved the boy, now 10. So Mr. Glaser was overjoyed two years ago when his employer switched to a preferred provider organization that promised out-of-network coverage. Including premiums and deductibles, he and his employer pay about $14,600 a year for family coverage.

But he discovered that at 150 percent of Medicare rates, it fell far short. In the case of a $275 liver checkup, for example, the balance due was $175, almost three times the patient share under Fair Health’s customary rate, and three and a half times what it was five years ago under Ingenix.

If Ethan had to repeat the $200,000 transplant, which used some of his father’s liver in 2003, the plan would pay little of the cost under the Medicare formula. Laws protecting consumers from extra out-of-pocket costs apply only to H.M.O.’s, which require prior approval to go out of network.

“I wish I could tell you that’s a unique case,” said Sandy Praeger, who is chairwoman of the health insurance committee of the National Association of Insurance Commissioners and is Kansas’ insurance commissioner. She said consumers were caught in the middle of a battle between insurers demanding discounts and doctors who resist by billing more than they expect to get paid — a conflict intensified because Medicare tilts its payments toward primary care, while most people go out of network for specialists.

“For some things, Medicare is really a poor payer,” she said. “So if that’s the benchmark, that just magnifies the problem.”

United Healthcare referred questions about the switch to the New York Health Plan Association, an insurance trade group, whose president, Paul F. Macielak, said the Fair Health database was inflated by a subset of physicians. “In an ideal world, everyone would be in network, subject to a contracted rate,” Mr. Macielak added.