The most common and most likely answer to this crossword clue is the 8 letter word CASELOAD
I've seen this crossword clue in The Guardian
C
A
S
E
L
O
A
D
Buddy explains!
The straight part
We know that "Perhaps doctor’s responsibility" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case perhaps doctor’s responsibility = caseload.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CASELOAD mean?
CASELOAD noun- The workload of a person or group that handles cases; the relative volume of cases expected to be worked upon.