A new study finds that Medicare is spending billions of dollars more than it needs to on prescription drugs for low-income seniors and disabled beneficiaries.

In 2013, an estimated 10 million people who participate in the Medicare prescription drug program, known as Part D, received government subsidies to help pay for that coverage. They account for an estimated three-quarters of the program’s cost. Most of those low-income enrollees are randomly placed in a plan that costs less than the average for the region where the person lives.

But even though these are lower-cost plans, they often end up costing the government and the beneficiary more. If Medicare instead assigned those people to a drug plan based on the actual drugs they took, it could save those patients hassle and money, and potentially save the government billions of dollars, according to the study by researchers from the University of Pittsburgh.  The study appears in the June issue of the policy journal Health Affairs.

Using a 5 percent sample of Medicare drug claims data from 2008 and 2009, the researchers calculated that if Medicare had matched beneficiaries to drug plans using “intelligent reassignment,” rather than random chance,  the government would have saved $5 billion in 2009. That’s because the government is responsible for picking up the copayments for many low-income beneficiaries.

Meanwhile, beneficiaries who are assigned to plans that don’t cover the drugs they take are on the hook for out-of pocket expenses, or have to go back to their doctors to get authorization for specific drugs or specific quantities of medications.

“We found that most people are not in the least-expensive plans that satisfy their medical needs,” said Yuting Zhang, the lead author of the study and an associate professor of health economics at the University of Pittsburgh.

Zhang and her colleagues created an algorithm that used patients’ previous drug claims to match them to a more appropriate plan. It resulted in not just a mean total saving of $743 per individual to the government, but also far fewer prescriptions subject to utilization review (19 percent rather than 29 percent) or quantity limits (19 percent rather than 27 percent).

In an interview, Zhang said it should be relatively simple for the federal government to change the way it assigns low-income beneficiaries to Part D plans. “They have much better data than we do,” she said. “And they’re already doing the assignment.”

But sometimes even simple things aren’t so simple. The random assignment of beneficiaries to plans (if beneficiaries don’t choose a plan) was a decision made specifically at the outset of the law to ensure that no one plan got a disproportionate number of very sick beneficiaries, according to a study from Georgetown University and the University of Chicago.

And changing the way Medicare assigns low-income beneficiaries to Part D plans would actually require a change in the law, according to Medicare officials. That means it would be up to Congress to make the savings happen.