It has long been one of the most vexing causes of America’s skyrocketing health costs: people not taking their medicine.

One-third to one-half of all patients do not take medication as prescribed, and up to one-quarter never fill prescriptions at all, experts say. Such lapses fuel more than $100 billion dollars in health costs annually because those patients often get sicker.

Now, a controversial, and seemingly counterintuitive, effort to tackle the problem is gaining ground: paying people money to take medicine or to comply with prescribed treatment. The idea, which is being embraced by doctors, pharmacy companies, insurers and researchers, is that paying modest financial incentives up front can save much larger costs of hospitalization.

“It’s better to spend money on medication adherence for patients, rather than having them boomerang in and out of the hospital,” said Valerie Fleishman, executive director of the New England Healthcare Institute, a research organization, who said that about one-tenth of hospital admissions and one-quarter of nursing home admissions result from incorrect adherence to medication. “Financial incentives are a critical piece of the solution.”