Meilin Keen was studying for the bar exam and preparing to move to New York City last June when she started throwing up blood. Keen, 27 years old, learned days later that she has gastric cancer. She postponed the bar exam. Brain fog from chemotherapy made it hard to do her legal work. Surgeons removed her stomach in December. Keen is coming to terms with all that means for her diet, her health, even her dating life. “That’s a fun icebreaker: I don’t have a stomach anymore,” she said. Cancer is hitting more young people in the U.S. and around...