Crossword Genius

In Madrid, sick after doctor left (4)

Ross

I believe the answer is:

amid

I'm a little stuck... Click here to teach me more about this clue!

'in' is the definition.

'madrid sick after doctor left' is the wordplay.
I cannot quite understand how this works, but
'doctor' could be 'd' (eg in PhD, Doctor of Philosophy) and 'd' is found within the answer.
The remaining letters 'ami' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for amid that I've seen before include "Surrounded by" , "Among" , "Maid (anag)" , "Within" , "In the centre of" .)

I've seen this clue in The Guardian.
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