Patients fill significantly fewer prescriptions for conditions such as nausea and pain in states where medical marijuana is available, researchers reported Wednesday in one of the first studies to examine how medical cannabis might be affecting approved treatments.

Prescriptions for all drugs that treat pain combined, from cortisone to OxyContin, were nearly 6 percent lower in states with medical marijuana programs. Anxiety medication was 5 percent lower.

The result was a drop of more than $165 million in health care spending in states that had medical marijuana programs running in 2013, according to the analysis of national Medicare data. The savings would equal 0.5 percent of the entire Medicare program’s drug budget if medicinal cannabis was available in every state, the authors projected.

For years, lawmakers in state after state have approved medical marijuana programs after pleas from desperate patients. The debates centered largely on the limited evidence of benefit and concerns about harm and abuse. There was little discussion of how medicinal cannabis would change treatments that patients were already receiving.

The new study, published Wednesday in the journal Health Affairs, is one of the first to hint at that effect.

“When states turned on a medical marijuana law,” use of treatments approved by the Food and Drug Administration went down, said senior author David Bradford, a health economist at the University of Georgia, “suggesting that they were substituting something else — and the plausible thing that they would be substituting was marijuana.”

Although the relationship may seem obvious, he and others made clear that the associated trends do not prove cause and effect. Nor can they suggest whether substitution would be a good thing or a bad thing overall.

“Let’s say a patient comes to my office saying, ‘I’m using marijuana to sleep because your drugs didn’t work for me.’ He tells me he is using marijuana because it really helps him sleep and his antidepressant isn’t working — ‘and by the way, I’ve flunked out of school,’ ” said J. Michael Bostwick, a psychiatrist at the Mayo Clinic in Rochester, Minn.

While there is some evidence that medical marijuana can be helpful for certain conditions, Bostwick said, “you may need to decide whether you want your degree or your drug, and that’s not addressed” by the new study, which he nevertheless called “ingenious.”

To measure the effect of medical marijuana programs, the researchers examined prescriptions filled in the Medicare Part D program in the 17 states plus the District of Columbia that had legalized medicinal cannabis through 2013, compared with those that had not. They analyzed prescriptions for hundreds of drugs that can be used to treat nine conditions for which there is some evidence of benefit from marijuana. More than one condition may be present in some diseases, such as HIV.

For glaucoma and spasticity, the average number of daily doses prescribed by each physician was too small to determine a difference. But all the others were significantly lower in the states with medicinal cannabis: anxiety, depression, nausea, pain, psychosis, seizures, and sleep disorders.

By contrast, there was no difference for four classes of drugs that have no impact on conditions that may be treated by medical marijuana, such as blood-thinners and antibiotics.

The findings were no surprise to Peter Rosenfeld, 61, of Collingswood, N.J., who has struggled with a degenerative spine condition for decades. When New Jersey’s medicinal cannabis program began three years ago, he tried 10 different strains before settling on one, known as Ghost OG.

About an eighth of an ounce a month, administered a few times a week through a vaporizer, reduces the spasticity, pain and dizziness better than the prescription drugs that he used to take, said Rosenfeld, a retired aerospace researcher: “It is just a good balance of effectiveness and lack of side effects.”

Pennsylvania Gov. Tom Wolf signed the state’s new program into law in April but it will not be operational for more than a year. Until it is, Louann Speese has been getting three cannabinoids — CBD, THCA, and THC, each given orally in an oil — sent from different dispensaries in other states for her severely autistic 19-year-old daughter.

Diana Louann Stanley’s seizures now last no more than a minute, down from five to 20 minutes, her mother said. “Now she is more aware of her surroundings. She has eye contact, which she never had before,” said Speese.

Her daughter no longer needs two anti-epileptic medications, Banzel and Lamictal. And while the $150-a-month worth of cannabis has been provided largely by donations through her daughter’s Facebook page, the cost is “a lot cheaper than pharmaceuticals,” said Speese, who lives near Mechanicsburg.

The new study’s estimates of Medicare cost savings from medicinal cannabis programs did not take account of out-of-pocket spending for the marijuana, which is not covered by insurance and is unlikely to be for a long time. Although 24 states plus D.C. have passed programs, the substance remains illegal under federal law, with very limited availability for research.