While Dr. Tate said Ms. Erkes had not shown signs of abusing painkillers, her situation was far from ideal. “She’s in her 20s and she’s on extended-release morphine — it’s just not the pretty story that it was six months ago.”

Many experts who study opioid abuse say they also are concerned about insurers’ limits on addiction treatments. Some state Medicaid programs for the poor, which pay for a large share of addiction treatments, continue to require advance approval before Suboxone can be prescribed or they place time limits on its use, both of which interfere with treatment, said Lindsey Vuolo, associate director of health law and policy at the National Center on Addiction and Substance Abuse. Drugs like Suboxone, or its generic equivalent, are used to wean people off opioids but can also be misused.

The analysis by ProPublica and The Times found that restrictions remain prevalent in Medicare plans, as well. Drug plans covering 33.6 million people include Suboxone, but two-thirds require prior authorization. Even when such requirements do not exist, the out-of-pocket costs of the drugs are often unaffordable, a number of pharmacists and doctors said.

At Dr. Shawn Ryan’s addiction-treatment practice in Cincinnati, called BrightView, staff members often take patients to the pharmacy to fill their prescriptions for addiction medications and then watch them take their first dose. Research has shown that such oversight improves the odds of success. But when it takes hours to gain approval, some patients leave, said Dr. Ryan, who is also president of the Ohio Society of Addiction Medicine.

“The guy walks out, and you can’t blame him,” Dr. Ryan said. “He’s like, ‘Hey man, I’m here to get help. What’s the deal?’”

Have you had trouble paying for prescription drugs? Tell us about it at propublica.org/drugprices.