More and more, doctors like are looking to parents to help make difficult decisions on how much treatment to give babies born very sick and premature, as well as figuring out when it's time to let them go. There's now more emphasis on parents' values and preferences in such cases.

Anne and Omar Shamiyeh first learned something was wrong with one of their twins during an ultrasound, when Anne was 18 weeks pregnant. "The technician was, like, 'Well, there's no visualization of his stomach,'" Anne recounted. "And I was like, 'How does our baby have no stomach?'"