I have been studying and treating cancer for 35 years, and here’s what I know about the progress made in that time: There has been far less than it appears. Despite some advances, the treatments for most kinds of cancer continue to be too painful, too damaging, too expensive and too ineffective. The same three methods—surgery, chemotherapy and radiotherapy—have prevailed for a half-century.

Consider acute myeloid leukemia, the bone-marrow malignancy that is my specialty. AML accounts for a third of all leukemia cases. Currently,...