The thrill of delivering newborns helped pull Dr. Jack Feltz into the field of obstetrics and gynecology. More than 30 years later, he still enjoys treating patients, he said. But now, Feltz is also working to change the way doctors are paid for maternity care. Feltz’s New Jersey-based practice, Lifeline Medical Associates, recently partnered with the insurer UnitedHealthcare to test a new payment model. The insurer sets a budget with the practice to pay doctors one lump sum for prenatal services, delivery and 60 days of care afterward. If the costs come in below that amount, the medical practice gets to keep some of the savings. (Hospitals aren’t a part of this contract; the insurer pays them separately for their services.) “We’ve always been taught to take care of patients as if they were our mothers and our daughters,” said Feltz, who also leads a coalition of obstetricians called the U.S. Women’s Health Alliance that advocates for high-quality, affordable care. “But now we have ...