An analysis published Wednesday by the American Medical Association said children with attention deficit hyperactivity disorder who take stimulant medication do not have a lower risk over all for later substance abuse, contradicting the longstanding and influential message that such medicines tend to deter those with the disorder from abusing other substances.

The paper, written by three researchers at the University of California, Los Angeles, examined data from 15 previous studies on the subject and determined that, on average, medications like Adderall and Ritalin had no effect one way or the other on whether children abused alcohol, marijuana, nicotine or cocaine later in life.

A 2003 study in the journal Pediatrics had concluded that the introduction of stimulant medication to children with A.D.H.D. reduced the risk of such abuse later in life, a finding that has been repeated by doctors and pharmaceutical companies not only to assuage parents’ fears of medication but also to suggest that the pills would protect their children from later harm.

“I always doubted the whole ‘protection’ argument, and I wasn’t the only one, but that message was really out there,” said Liz Jorgensen, an adolescent addiction specialist at Insight Counseling in Ridgefield, Conn. “Hopefully, this message will be heard loud and clear.”