In large doses, analgesics that work in the brain as antagonists to ce

With this question, you should spot the "comma" in the middle of the sentence with the word "which" next to it.

There are two considerations when evaluating "which."
1) Structural
2) Meaning

The way the sentence is structured, "which" is describing "patients." That's just what the structure of the sentence dictates. But from a meaning perspective, you are trying to describe "psychological disturbances"--not "patients." Since structurally the word "which" is incorrectly describing "patients" we need to change the sentence structure. Therefore (A), (B), and (C) are wrong and now it's between (D) and (E).

Reading (D) we have:

"In large doses, analgesics that work in the brain as antagonists to certain chemicals have caused psychological disturbances in patients, an effect that may limit their potential to relieve."

You see the phrase "which may limit their potential to relieve severe pain."

There are multiple plural words here so we don't know what "their" refers to---does it refer to psychological disturbances, analgesics, or chemicals? Sure you could probably figure out which one it is, but from a structural standpoint, it is not clear which word "their" refers to. Therefore, you must reword the sentence so that it is clear what "their" refers to.
(D) looks unclear so let's look at (E).

(E) an effect that may limit the potential of such analgesics for relieving
This answer choice gets rid of the ambiguity associated with the word "their" and it also does not use the word "which"--which is positioned to incorrectly describe "patients." Although (E) is longer than the other answer choices, it is free of error. Therefore, (E) is correct.