Dr. Darrell A. Campbell Jr., the chief medical officer of the University of Michigan Health System, who led the study, said: “The Medicaid patients were sicker, and they did not do as well following surgery. They stayed in the hospital longer, and that increases the cost.”

Michigan has just expanded Medicaid, and nearly half a million people may become eligible for coverage. Since the state began taking applications on April 1, more than 237,000 people have enrolled.

“We supported the expansion of Medicaid because it means that we can get patients into medical care and get them into optimum shape for an operation,” Dr. Campbell said in an interview. “Being a heavy smoker predisposes you to get pneumonia after an operation. For a diabetic, if blood sugar is out of control, that increases the chances of a wound infection after surgery. If we can address these issues preoperatively, we can cut down the problems we see after an operation.”

Dr. Campbell is also the director of the Michigan Surgical Quality Collaborative, which collected and analyzed the data.

About half the states have expanded Medicaid, and the White House is urging others to do so, noting that the federal government will pay the full cost until 2016 and at least 90 percent in later years.