Keith Taggart noticed a lump the size of a pea in his left cheek in October 2014. He was also experiencing fatigue, weight loss, nausea and incontinence. His primary care physician wasn’t too concerned about the lump but referred him to an oral surgeon to have it removed and biopsied.

Keith was diagnosed with acinic cell carcinoma of the salivary gland 10 days later. But he wasn’t especially worried. “I believed that any future...