During a particularly long wait to see his dermatologist, Parker Oks, 18, thought there had to be a better way. "They know approximately how long an appointment will take," said Mr. Oks, a freshman at Boston University. "But the problem is that they don't know how long it will actually take." That realization led Mr. Oks to create Appointment Status, a Web site devoted to improving appointment efficiency and providing patients with information to avoid long waits. Working with three teenagers from Staten Island Technical High School, where he had gone, Mr. Oks aims to make it easier for patients to schedule appointments—and to find out how far behind the doctor may be before settling into a waiting room chair.