Carole Siesser, a retiree in Delray Beach, Fla., started taking a bone-growth drug made by Eli Lilly & Co. after she fell and fractured her spine. After two years, the medicine helped to heal her back. It also cost her $5,600 of her own money to help cover the roughly $26,000 annual price, even though she has Medicare.

“They really take advantage of the seniors,” Ms. Siesser, 79, said of pharmaceutical companies. “There’s no competition, so they can charge what they want.”

An...