There’s a body of research showing that painkiller abuse and overdose are lower in states with medical marijuana laws. But that’s always been just an assumption.

Now a new study validates these findings by providing 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, 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 meds.

But most strikingly, the typical physician in a medical-marijuana state prescribed 1,826 fewer doses of painkillers in a year.

The tanking numbers for painkiller prescriptions in medical marijuana states are likely to cause some concern among pharmaceutical companies. These companies have long been at the forefront of opposition to marijuana reform, funding research by anti-pot academics and funneling dollars to groups that oppose pot legalization.

Pharmaceutical companies have also lobbied federal agencies directly to prevent the liberalization of marijuana laws.

In what may be the most concerning finding for the pharmaceutical industry, the Bradfords estimated the cost savings to Medicare from the decreased prescribing. They found that about $165 million was saved in the 17 medical marijuana states in 2013. In a back-of-the-envelope calculation, the estimated annual Medicare prescription savings would be nearly half a billion dollars if all 50 states were to implement similar programs.