When John Paul Shen, M.D., tells people he studies appendix cancer, many are surprised to learn that you can get appendix cancer in the first place.

Perhaps this response isn’t totally unwarranted. Appendix cancer is rare. There are just over 3,000 cases diagnosed in the United States each year. On top of that, the appendix’s location near the large and small intestine meant appendix cancer was considered — and treated as — colorectal...