Just 24 weeks into her pregnancy, Sharrissa Cook gave birth to a critically ill baby boy. Dreshan weighed in at a fragile 1 pound, 11 ounces. He lay motionless in the incubator, connected to tubes and monitors in the neonatal intensive care unit at the University of Alabama at Birmingham Hospital. “He was so tiny,” Cook recalls. “I was a first-time mom. I didn’t have a clue. I didn’t know what to expect.” It was Oct. 11, 2006. Medical personnel asked Cook, then a 26-year-old single mother, to enroll little Dreshan in a study. She says they described it as...