Between 2009 and 2013, overall health-care spending grew at 2.9 percent per year, while the amount shouldered by insured patients when they were hospitalized grew more than twice as fast, according to the study published in JAMA Internal Medicine.

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Patients' out-of-pocket portion of their hospitalization costs rose 6.5 percent each year, from $738 on average in 2009 to more than $1,000 in 2013. To put that in perspective, consider the findings of a recent Federal Reserve survey, which found nearly half of Americans do not have enough money to cover a $400 emergency expense.

The new results echo earlier findings by the Kaiser Family Foundation that looked broadly at the rise in all out-of-pocket health-care costs for people with employer-sponsored insurance.

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However, the most recent federal data that examined all out-of-pocket health care spending in aggregate -- not just limited to people with private insurance -- found that in 2014, out-of-pocket expenses crept up by only 1.3 percent, to reach $329.8 billion. That is the fifth lowest rise in out-of-pocket spending on record. The aggregate federal data on overall out-of-pocket health care spending also shows a much lower annual growth in out-of-pocket costs over the period studied.

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Emily Adrion, a research fellow at University of Michigan Medical School, said her team was motivated to study the patient burden from hospital costs after reading a 26,000-word Time magazine cover story that told the stories of people faced with staggering and obtuse hospital bills.

"If you have high-quality health insurance, you tend to think you're okay, and you read these stories and you think, 'That's terrible, and thank God I have coverage,' " Adrion said. "But nobody really knows what's going on in the black box of health insurance" because the data are proprietary and the complexity is huge.

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Adrion's team examined data from three major insurers covering 50 million people, including 7.3 million hospitalizations. They included employer-sponsored insurance as well as people who bought individual market plans, but the analysis did not extend long enough to capture policies offered on the exchanges by the Affordable Care Act.

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Adrion said she was surprised by the results — the growth in how much patients shouldered was substantial, and what was more interesting was the break-down. Co-payments weren't driving the trend; in fact, over the study period, co-payments, which are a flat fee, were used in fewer hospitalizations. Instead, a growing portion of hospitalizations required either coinsurance or fell under a person's deductible, and the amount paid also increased.

The chart below shows the average out-of-pocket costs per hospitalization:

The shift of health-care costs on to patients is increasing, partly driven by the idea that it will reduce the unnecessary utilization of health care and encourage patients to shop around by giving patients more "skin in the game." It's uncertain whether this shift is having the intended effect, since there's evidence people cut back on all health care when they face a high deductible. A Kaiser study of employer-sponsored insurance plans last year found that deductibles were rising much faster than premiums.

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"I think the increases are very significant given this is a period of low health-care inflation and stagnant wages," said Larry Levitt, a senior vice president at the Kaiser Family Foundation. "It's really about finding the right balance between out-of-pocket costs that don’t discourage people from getting care they need, but also don’t encourage people to use care that is maybe wasteful. I think we are — as a society, we’re struggling to find the right balance."