Two-time widower Paul Nielsen was in excellent health at age 67. So the former marathon runner knew something was wrong when he started feeling tired all the time in the fall of 2015.

“I had to nap for a couple of hours almost every afternoon,” he says. “I couldn’t even make it to supper.”

Though concerned by his fatigue, Paul put off investigating it until his regular annual physical in January 2016. That’s when blood tests...