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For the last four years, Medicare has wielded a big stick: It has fined hospitals if too many of their patients returned to any hospital within weeks of being released.

But many safety-net hospitals, including academic teaching hospitals, say this is unfair because they take care of sicker, poorer patients.

Now data released Monday shows they may be right.

Researchers at Harvard Medical School found that hospitals are being penalized to a large extent based on the patients they serve. The researchers found that nearly two dozen variables, such as patients’ education, income and ability to bathe, dress and feed themselves, explain nearly half of the difference in readmission rates between the best- and worst-performing hospitals.

The worst performing hospitals, for example, have 50 percent more patients with less than a high school education than the best performers, according to the study published in JAMA Internal Medicine.

Education levels make a difference because many patients who are most likely to be readmitted to hospitals tend to have multiple chronic illnesses, such as diabetes and heart failure.

And managing those illnesses requires “a significant amount of health literacy,” said Michael McWilliams, associate professor of health-care policy and medicine at Harvard Medical School, a senior author of the study.

Other studies have looked at the influence of factors, including race, income and education.

But researchers found a broad set of socioeconomic and clinical characteristics of patients by using nationally representative survey data that was linked to Medicare claims data. These characteristics are not included in Medicare’s penalty calculations, which only adjusts for certain demographic characteristics, such as age, sex and sickness of patients.

Hospitals with the highest readmissions had patients who were “less mobile, had more difficulty with activities of daily living, more chronic conditions, less education, lower income, lower assets, and the list goes on and on,” McWilliams said.

“A lot of these individual factors are very familiar to people on an intuitive level, but we incorporated them all together and asked, how did this actually affect how the readmission rate would look for calculating penalties,” said Michael Barnett, a research fellow in medicine at Harvard Medical School and the hospital and the study’s lead author.

The bottom line, the researchers said, is that hospitals treating the most vulnerable patients are being deprived of needed resources.

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For the fiscal year starting Oct. 1, more than 2,600 hospitals will lose a combined total of $420 million, according to a spokesman for the Centers for Medicare and Medicaid Services.

One hospital that has been hit with the maximum penalty since the program began in 2012 is Franklin Medical Center in Winnsboro, La. The 39-bed hospital is in a rural part of the state and serves a predominantly poor population in the region “that is not very educated,” said hospital administrator Blake Kramer.

“It was absurd and foolish for Medicare to essentially apply a one-size-fits-all penalty program and apply across every single population and every single facility,” he said. “We have a lot of very elderly and very poor people.”

For the coming fiscal year, the hospital’s penalty will be $91,000, he said. The hospital’s budget is about $24 million, and although the county-owned hospital has finished in the black for the last three years, it’s been a struggle, he said.

Asked about the findings of the study, CMS’ chief medical officer Patrick Conway said in a statement Monday that the agency is currently researching the impact of socioeconomic status on the readmissions penalty program.

“We will continue to work with all stakeholders to seek feasible ways to encourage hospitals to reduce hospital readmissions while addressing any unintended consequences, particularly for those hospitals serving dual-eligible and low-income beneficiaries,” he said.

The aim of the program, created under the Affordable Care Act, is to lower costs and improve care by spurring hospitals to do a better job taking care of patients, especially after they leave the hospital.

Readmissions are huge and costly — nearly one in five Medicare patients returns to a hospital within a month of discharge, and studies have shown that nearly three-quarters are potentially preventable.

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