Patients, even those with employer-sponsored health plans, may face another condition after they are discharged from a hospital stay -- acute sticker shock.

Out-of-pocket hospitalization costs rose 37 percent from 2009 to 2013, with the average patient paying more than $1,000 per hospital visit, according to a study conducted by the University of Michigan.

Driven by an 86 percent rise in deductibles and a 33 percent increase in coinsurance -- the part of the hospital bill patients are expected to pay -- the out-of-pocket costs are rising faster than health insurance premiums.