PHILADELPHIA — His patient, a spunky Italian-American woman in her 60s, was waiting in an exam room down the hall for the answer: Was the experimental drug stopping her deadly skin cancer? But as Dr. Keith Flaherty read out the measurements of her tumors from the latest CT scan, he could not keep the distress from his voice. “She’s worse,” he said to the clinical trial nurse at the University of Pennsylvania’s melanoma clinic. Like the 17 other patients on the drug trial — the corporate lawyer, the receptionist with young children, the Philadelphia philanthropist — the woman known in...