A complicated patient is one with many apparent inconsistencies in his life or character.
A tough patient is one that bears illness well.
A difficult patient is one that causes trouble to his medics, usually by his behaviour.
A hard patient is either a tough or a difficult one, depending on context.
If the focus is on the serious medical condition, it is perhaps better to say "a complicated, difficult, tough, or hard CASE". "A hard case" is quite common.
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