At age 62, Tom Jackson was diagnosed with prostate cancer. The diagnosis is common among men his age, so he took it in stride.

But shortly before Tom was scheduled to have his prostate removed, he discovered a lump on his neck. A biopsy and CT scan of the lump revealed that Tom also had squamous cell carcinoma of the tonsil caused by the human papillomavirus (HPV).

“Prostate cancer for any man over the age of 60 is acceptable...