As health care costs keep rising, more people seem to be skipping physician visits.

It's not fear of doctors, however, but more of a phobia about the bills that could follow. Higher deductibles and out-of-network fees are just some of the out-of-pocket costs that can hit a consumer's pockets.

U.S. health care costs keep rising, and hit more than $10,000 a year per person in 2016. According to a recent national poll, over the past 12 months, 44 percent of Americans said they didn't go to the doctor when they were sick or injured because of financial concerns. Meanwhile, 40 percent said they skipped a recommended medical test or treatment.

Also, the study found most people who are delaying or skipping care actually have health insurance. Some 86 percent of those surveyed said they're covered either through their employer, have insurance they purchased directly, or through government programs like Medicare and Medicaid.

"There have been so many changes in the health care landscape in the United States that this news is not entirely surprising," Cleveland Clinic president and CEO Tom Mihaljevic told CNBC's "On the Money" in a recent interview. However, Mihaljevic warned that skipping visits or treatment can be counterproductive.

"One of most important consequences of skipping medical care or delaying care ultimately impacts the quality of care, impacts the outcome," he said. "Untimely visits or delay of visits to the physician ultimately leads to the increased cost of care."

However, the poll, conducted by the University of Chicago and the West Health Institute, found Americans fear large medical bills more than they do serious illness. The data showed 33 percent of those surveyed were "extremely afraid" or "very afraid" of getting seriously ill. About 40 percent said paying for health care is more frightening than the illness itself.

"Part of problem here is healthcare tends to be very complex, and every patient typically requires a number of procedures and tests to be done, so it's really difficult to estimate the upfront cost of care, " Mihaljevic told CNBC.

Additionally, the survey found 54 percent of those polled received one or more medical bills over the past year for something they thought was covered by their insurance. And 53 percent received a bill that was higher than they expected.

Mihaljevic acknowledged the range of different fees for the same services should be made clearer for consumers. "There is an absolute need for increased transparency when it comes to cost and this is one of mandates for our industry as a whole," he said.