A,B,C - "which" refers to patients but the clause is talking about analgesics and not patients.

D - their refers to analgesics and has the correct idiom "potential to".

E - incorrect idiom "potential for"

I do not know why (E) is the correct answer.

I took this one off of the psahil's notes

i did not quite get his explanation, thats why posted it here again

Beware of A,B, and C because the 'which' does not refer to anything. If it were to refer to anything it would be the effect of the analgesics, which is why you should be able to cut down the choices to D and E rather quickly. E is the only one that is entirely specific.

Although E does not seem concise, it really is because this type of scientific writing is always less concise, since it is more important to be convey precise scientific principles and research results. E is the choice that combines precise communication with as little extra language as possible.