Canine, say, is barking regardless (2,3,4)
I believe the answer is:
in any case
'regardless' is the definition.
(thesaurus)
'canine say is barking' is the wordplay.
'is barking' indicates an anagram (UK slang for mad).
'canine'+'say'='caninesay'
'caninesay' with letters rearranged gives 'IN ANY CASE'.
(Other definitions for in any case that I've seen before include "Besides" , "Where a customs officer may search" , "Whatever the facts are, one way or the other" , "No matter what" , "Where customs officers may search" .)