A hypochondriacal person is someone who is excessively preoccupied with and worried about his or her health.
Is there a term for the other end of the spectrum -- somebody extremely carefree, especially with regard to his or her health?
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"stoical" seems to fit.
stoical (adj) "enduring pain and hardship without showing one’s feelings or complaining" ODO
A stoical or phlegmatic kind of person often underestimates symptoms of diseases.
There is the old expression, "hale and hearty" - you could use hale, by itself but I don't think many people (under 40) would understand. "Robust" might also work.
I used to work for a man in his mid-seventies who had the vigor of someone in his twenties, (as pertaining to hard work and cheerfulness) we used to refer to him as a "horse", as in: "That guy is no senior-citizen - he's a horse." (I guess from "work-horse")