In the summer of 2012, doctors removed a mole from Vince Leseney’s shoulder. After a biopsy, the musical theater voice instructor and actor was diagnosed with stage IIIB melanoma.

Vince was devastated when his doctors in Oklahoma said there wasn't much that they could do to treat melanoma. But when one of Vince’s former students heard about his diagnosis, she introduced him to her father, Jagan Sastry, M.D., a professor in...