(Jason Redmond/Associated Press)

It's one of modern medicine's most frustrating riddles: A person gets sick. She knows how tricky health insurance can be, so she does the smart thing. She goes to a hospital covered by her plan — “in-network,” in the parlance of health care. She gets well. Weeks later, she opens her mail and feels unwell again: An unexpected bill that puts her on the hook for hundreds of extra dollars because, it says, some of the care she got was out-of-network. How could this be?

The answer is simple but frustrating. Doctors who work in hospitals agree to accept certain kinds of insurance. Those may — or may not — be the same insurers that their hospital has decided to accept. That can leave patients with a bill for the rest. Although the problem has been chronicled for years, the scale was unknown.

A study published in the New England Journal of Medicine on Wednesday found that “surprise billing,” when patients unexpectedly find themselves paying for out-of-network care, was common. Researchers examined 2.2 million medical claims covering emergency department visits from an undisclosed large health insurance company over nearly two years. While 99 percent of the visits were in-network, a fifth included treatment by out-of-network emergency physicians.

Zack Cooper, a health economist at Yale University who led the work, said that he was shocked by the result.

“One of the reasons you don’t see policy [to fix this] is no one knows this is happening this frequently,” Cooper said.

The researchers do not know how many of those patients received surprise bills. Some insurers may pay the balance or the patients could live in a state that protects consumers against such bills. But Cooper and study co-author Fiona Scott Morton calculated from their data that patients' potential surprise bills could add up to $623, on average — and found one patient who could have faced a potential bill of more than $19,000.

Those numbers were dismissed as “ludicrous” by Rebecca Parker, the president of the American College of Emergency Physicians. The study relied on data indicating that emergency physicians charged, on average, nearly 800 percent of Medicare rates for out-of-network care. That is “totally out of the realm of what's true,” Parker said.

A spokeswoman for the New England Journal of Medicine said that the study was peer-reviewed.

Parker said her organization has been examining the surprise billing issue for more than a year and often found that patients who receive surprise bills are dealing with the unwelcome discovery that their insurance plans simply cover very little. She said that analysis suggests such bills stem from high deductibles — and that the amount billed to them because of out-of-network care is small.

Cooper's data suggests otherwise. His concern is that those people with insurance plans most likely to leave them on the hook for the charges are those who may be less likely to afford it. With a move toward “narrow network” plans that save costs by limiting coverage to fewer providers, he notes, the issue could become an even bigger burden for patients.

Kristine Grow, a spokeswoman for America's Health Insurance Plans, a trade group for the insurance industry, said in an email that surprise bills resulting from higher out-of-network charges is “a growing problem that puts patients in a frustrating and costly position.”

She said patients would benefit if doctors were covered by the same plans as the hospitals where they work.

Parker said that physicians want to be in-network but must be paid fair rates.

“We don’t want our patients sitting checking their coverage while they're clutching their chest with chest pains,” Parker said. “If you don’t know your coverage and you’re worried about coming in, that’s not insurance coverage. All of us have cases of patients that delayed care because they were worried about deductibles.”

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