Orlando, Fla. ? Give people free prescription drugs, and many of them still won’t bother to take their medicine.

Doctors were stunned to see that happen in a major study involving heart attack survivors. The patients were offered well-established drugs to prevent a recurrence of heart trouble, including cholesterol-lowering statins and medicines that slow the heart and help it pump more effectively.

“My God, we gave these people the medicines for free and only half took it,” said one of the study’s authors, Dr. Elliott Antman of Harvard-affiliated Brigham and Women’s Hospital in Boston.

In fact, the researchers had trouble just signing up patients to take part in the study.

Nevertheless, Aetna, the insurance company that footed the bill, thinks this approach will save money in the long run and plans to start offering certain heart drugs free to some patients. In the study, patients offered medicines at no cost suffered fewer heart problems and saved $500 on average over roughly a year.

It is no secret many Americans don’t follow doctors’ instructions. In one survey, one-third said they didn’t fill a prescription or used less medicine than they should because of cost. The researchers in this study wanted to see what would happen if they took cost out of the equation.

The study was led by Dr. Niteesh Choudhry of Brigham and Women’s, who presented the findings Monday at an American Heart Association conference in Florida.