However, when accounting for additional factors that the researchers believe could more accurately measure prescription spend, the researchers found a 13 percent reduction for drugs used to treat depression, a 17 percent reduction for those used to treat nausea, 12 percent reductions for those used to treat psychosis and those used to treat seizure disorders, and an 11 percent reduction for drugs used to treat pain.

The researchers found no significant associations between having a medical marijuana law and dispensed units of FDA-approved drugs for anxiety, glaucoma, sleep disorders, or spasticity.

The additional factors used in the multivariate analysis were whether the state had a prescription drug monitoring program in effect; the number of active nonfederal physicians per capita; median household income; the percentage of state residents with household incomes below the federal poverty level; the average annual unemployment rate; the state population; whether the state had legalized recreational marijuana; whether the state had expanded eligibility for Medicaid under the Affordable Care Act; and state and year indicator variables, to allow for fixed effects analysis by state and year.

The researchers also found that the states with medical marijuana laws collectively had estimated Medicaid savings that ranged from $260.8 million in 2007 to $475.8 million in 2014.

“If all states had had a medical marijuana law in place in 2014, the national savings for fee-for-service Medicaid would have been approximately $1.01 billion,” the two wrote.

They cited the reason for their research was to add to the literature that shows the potential clinical benefits of marijuana, as currently the federal Drug Enforcement Administration classifies marijuana as a Schedule I drug.

One of the criteria for such a classification spelled out in the Controlled Substances Act of 1970, was that the drug has no “currently accepted medical use[s].”

“Our findings that actual prescription drug use in Medicaid varies in ways consistent with marijuana’s being a substitute product provides additional, albeit indirect, evidence of medical use,” the researchers wrote.

They added a not-so-subtle lobby for the reclassification of marijuana: “In times of significant budget pressure, the possible savings of $1.01 billion nationally in spending on prescriptions in fee-for service Medicaid is significant.”