A nagging pain at the end of Sam Markota’s digestive tract suddenly became unbearable during a business trip to Thailand. The then-55-year-old returned to the U.S. for his first colonoscopy. In April 2015, Sam learned that he had rectal cancer, and it had already spread to his liver and right lung.

“My first oncologist had me dead in a couple years,” Sam recalls. After undergoing chemotherapy, he and his wife sought a second opinion...