There’s a body of research showing that painkiller abuse and overdose are lower in states with medical marijuana laws. These studies have generally assumed that when medical marijuana is available, pain patients are increasingly choosing pot over powerful and deadly prescription narcotics. But that’s always been just an assumption.

Now a new study, released in the journal Health Affairs, validates these findings by providing clear evidence of a missing link in the causal chain running from medical marijuana to falling overdoses. Ashley and W. David Bradford, a daughter-father pair of researchers at the University of Georgia, scoured the database of all prescription drugs paid for under Medicare Part D from 2010 to 2013.

They found that, in the 17 states with a medical-marijuana law in place by 2013, prescriptions for painkillers and other classes of drugs fell sharply compared with states that did not have a medical-marijuana law. The drops were quite significant: In medical-marijuana states, the average doctor prescribed 265 fewer doses of antidepressants each year, 486 fewer doses of seizure medication, 541 fewer anti-nausea doses and 562 fewer doses of anti-anxiety medication. [Read more at The Washington Post]