Mr. Victor said that staff members at the Workers Compensation Research Institute, while reviewing data for another project, stumbled over information indicating that entrepreneurial doctors and companies had responded with new strategies. By producing a novel dosage, a manufacturer could also create a new “average wholesale price” for that dose that bore little relation to existing forms of the drug and could be many times higher.

Looking at two states, California and Illinois, the group found that doctors who dispense drugs had quickly embraced those dosage forms. By early 2013, dispensing physicians in California were using the 7.5-milligram version of cyclobenzaprine as often as traditional strengths. Just a year earlier, they had rarely, if ever, prescribed the new dosage and doctors who send patients to pharmacies do not use it, the study found.

Similar trends were seen in California and Illinois for two narcotic painkillers, tramadol and generic Vicodin, which have recently appeared in new dosages at far higher prices, the study found. The new form of tramadol contains 150 milligrams, rather than 100 or 200 milligrams. The new form of generic Vicodin contains 2.5 milligrams of hydrocodone rather than five milligrams.

A small Los Angeles-based company called KLE 2 Pharmaceuticals appears to be a major supplier of the new drug doses, which it promotes on its website. The company uses contract manufacturers to make the drugs, which it sells to middlemen known as repackagers that supply the medications to doctors. The president of KLE 2, Kevin Laxer, who also runs a compounding pharmacy, declined to be interviewed for this article.

Prescribing data reviewed by The New York Times indicates that a Los Angeles physician, Dr. Edwin Haronian, and a Chicago-area physician, Dr. Ronald L. Silver, prescribe the new dosage forms of tramadol and generic Vicodin. They did not respond to telephone calls or email messages sent to their offices.

Alex Swedlow, the chief executive of the California Workers’ Compensation Institute, a research group financed by insurers, said he was unaware of any evidence showing that the new versions of cyclobenzaprine, tramadol or generic Vicodin were more effective than existing ones.

He also added that efforts by California lawmakers to rein in the cost of physician dispensing had largely failed, adding that companies and government officials had begun discussing other options to address the practice. “There is interest in moving towards a formulary,” said Mr. Swedlow, referring to a list of drugs that doctors could dispense for specific conditions.