Dr Hodson is a non-canonical character created the episode The Red Signal of The Agatha Christie Hour, a TV film adaptation of the short story by the same name. Dr Hodson is a colleague of Sir Alington West. Sir Alington informs his manservant, that if Dr Hodson calls he can contact him at the home of Jack Trent.
Although it is never stated, one can assume, that since Sir Alington is a psychiatrist so is Dr Hodson.
Dr Hodson is not seen, just mentioned.