How should I address to an important person:
Is it correct to say:
How are you, Mister Doctor?
or should I say:
How are you, Doctor?
How are you, Mister?
In writing, there's no need to use capitals unless you're giving them their full name. They're not all that 'important', though some of them have an inflated view of their importance (no offence, Raymott).
'How are you, doctor?'
'Good morning, Doctor Procter.'
However, the point I wanted to make is that "How are you, Mister?" is usually just wrong.
I also think the capital is correct in both Doctor and Mister, since they're used as titles.
Also capitalised are other titles like Captain, Constable, Officer, Sergeant, maybe even Teacher etc. when you say "How are you, Officer?" On the other hand, some words are not titles - "How are you, boy?", "How are you, my good fellow?"
You say (write) to a doctor, "How are you, Doctor?" It has nothing to do with importance, but whether it is a substitute name or not.