STOCKHOLM - Andemariam Beyene sat by the hospital window, the low Arctic sun on his face, and talked about the time he thought he would die.

Two and a half years ago doctors in Iceland, where Mr. Beyene was studying to be an engineer, discovered a golf-ball-size tumor growing into his windpipe. Despite surgery and radiation, it kept growing. In the spring of 2011, when Mr. Beyene came to Sweden to see another doctor, he was practically out of options. ‘I was almost dead,