The doctor prescribed an obesity drug. Her insurer called it ‘vanity.’

Maya Cohen’s entree into the world of obesity medicine came as a shock.

In despair over her weight, she saw Dr. Caroline Apovian, an obesity specialist at Brigham and Women’s Hospital, who prescribed Saxenda, a recently approved weight-loss drug. Cohen, who is 55 and lives in Cape Elizabeth, Maine, hastened to get it filled.

Then she saw the price her pharmacy was charging: $1,500 a month. Her insurer classified it as a “vanity drug”…