It was a 5.5-cm tumor wrapped around Jason McFarland’s pulmonary artery that threatened to end his 20-year career as a police officer and, possibly, his life. 

He’d sought medical attention after coughing up blood. But at age 42, he never suspected cancer.

The doctors near his hometown of Effingham, Illinois, weren’t optimistic about the diagnosis the X-rays and CT scans revealed: stage IIIA non-small cell lung cancer...