Remember sitting in the dentist’s office when you were a kid, absentmindedly thumbing through a worn copy of Reader’s Digest as you apprehensively awaited your turn in the chair? If you were like me, you turned to the short, funny sections first: Humor in Uniform; In These United States; All in a Day’s Work; and, of course, Laughter, the Best Medicine. Even then, I instinctively wanted to laugh when I was scared.

Now, hospitals around the country are increasingly treating cancer patients...