“We’ve seen over a doubling in the use of stimulant-type medications over the past decade,” said Brian Piper, an assistant professor of neuroscience at Geisinger Commonwealth School of Medicine, who was first author on a 2018 study of trends in the use of stimulants in the United States. “How much of this is an expansion of the criteria for A.D.H.D., how much is driven by more girls being diagnosed, by adult A.D.H.D.?”

His research also points to marked regional variations in the use of stimulants, with much less being prescribed in the western United States than in the east. Prescribing patterns may be affected by local custom, by cultural practices and by many other factors. But marketing and incentives in the form of payments or gifts to providers definitely has an impact, he said. “There is a large body of evidence suggesting that there is no such thing as a free lunch.”

Dr. Piper urged patients — and parents — to check whether a prescriber has accepted compensation of $10 or more from a pharmaceutical company or medical device manufacturer, using this government database or through ProPublica, and to bring up the subject with their doctors: “If they chose to accept that ‘free lunch,’ they should be prepared to have a discussion with their patients about why,” he said.

Doctors who actually do the prescribing must balance not only the potential influence of marketing but also the special anxieties and stigmas surrounding stimulants and the challenges of insurance company regulations.

Dr. Doris Greenberg, a developmental pediatrician in Savannah, Ga., who is associate clinical professor of pediatrics at Mercer University School of Medicine, said that although drug development had led to a much broader array of choices, doctors were severely constrained in their ability to choose the best medication by the restrictions imposed by insurance companies. “They can come out with a thousand new innovative medicines and we still can’t use them,” she said. “We now face a monumental number of rejections from insurance companies.”

Dr. Greenberg said that the insurance companies set arbitrary rules about who can take what, and that she spends much of her time on submissions and resubmissions for insurance authorization, not to mention phone calls with “peer reviewers” who are not in her specialty but must approve her decisions. (Recently, to get approval to prescribe a stimulant to a patient, she said, “I had to talk to an orthopedic surgeon.”)

And then there are the effects of direct marketing: “I have to spend 10 or 15 minutes explaining to a family why I’m not going to use the medicine they saw on TV,” Dr. Greenberg said. “We’re just having a mess of a time trying to treat a very treatable disorder.”