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Medical treatment is getting pricier every year, and a new study shows that patients are carrying a bigger and bigger share of the cost.

It found that even people with health insurance pay, on average, more than $1,000 out of their pockets for a hospital stay.

These are not from surprise medical bills for expenses insurance refuses to cover, but rather from the co-pays and deductibles that insurance plans increasingly require, the team at the University of Michigan found.

“From 2009 to 2013, total cost sharing associated with hospitalizations grew by more than 37 percent, from $738 to $1,013, ” Emily Adrion and colleagues wrote in the Journal of the American Medical Association’s JAMA Internal Medicine.

Related: How to Protect Yourself From Surprise Medical Bills

“This increase represents an annual growth rate of 6.5 percent compared with the 5.1 percent growth in health insurance premiums reported during this same period.”

Out-of-pocket costs for having a baby were fairly low at $259 in 2013, they found, even though that was a 63 percent increase over 2009.

"Increasing out-of-pocket spending for unavoidable, necessary care is counter to the goals of a health insurance system."

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But the cost of something new and unexpected, like a heart attack, was much higher: $1,586, the team found. An appendicitis attack cost the patient $1,509 on average.

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“Our findings are particularly notable given recent research suggesting that most Americans lack a basic understanding of the different forms of cost sharing associated with medical care,” the team wrote.

These co-pays and deductibles almost defeat the purpose of having health insurance, argued Dr. Mitchell Katz, deputy editor of the journal.

“It seems to me that if certain procedures do not have to be performed or can be substituted with something less expensive, it is right to ask the insuree to pay a portion of the procedure. I feel the same way about expensive drugs. However, that is clearly not the issue when we are speaking of emergency hospitalizations,” Katz wrote.

Related: Feds Relent on Cutting Bare-Bones Health Insurance Plans

“Instead, it seems that out-of-pocket costs are being used so that the premiums of health insurance plans are lower,” he added.

“There are no easy answers for how to deal with the rising cost of medical care, but increasing out-of-pocket spending for unavoidable, necessary care is counter to the goals of a health insurance system.”

To calculate what people are paying, Adrion’s team looked at records from 7.3 million hospitalizations between 2009 and 2013 covered by three giant insurance companies: Aetna, UnitedHealthcare, and Humana.

The most expensive plans tended to be those that people bought as individuals, as opposed to large, group plans offered by employers. Many of these are bare-bones plans that have low premiums and were designed to provide catastrophic care only. Health policy experts had criticized them for charging high co-pays and deductibles.

“Our findings are particularly notable given recent research suggesting that most Americans lack a basic understanding of the different forms of cost sharing associated with medical care."

The 2010 Affordable Care Act, widely known as Obamacare, was designed to change some of that.

“Beyond the cost-sharing implications of extending health insurance coverage to millions of previously uninsured Americans, the ACA also allowed many individuals who previously could purchase insurance coverage only through the individual market to take advantage of risk pooling and premium subsidies through participation in the health insurance marketplaces,” the team wrote.

Obamacare originally forced insurers to drop some of these pricey, low-coverage plans but the administration relented after an outcry from people who said they wanted to keep them.