Think about the sentence this way:

Having been prescribed a drug at a dosage too low to be effective or having been taken off a drug too soon, some patients who do not respond to therapies for depression may simply have received inadequate treatment.

Notice that having + Past participle (prescribed here) often denotes an action in the past, with reference to another action. For example:

Having worked hard, GMATMadeEasy hoped to scrore well on GMAT. (Having worked hard denotes the action of working hard in the past of the past (hoped). )

Or

Having worked hard, GMATMadeEasy hopes to scrore well on GMAT. (Having worked hard denotes the action of working hard in the past. )

The sense is very similar in this sentence. Hence, A fits well.

EducationAisle Thank you. makes sense. I understand now that B is wrong .

How about E. It conveys meaning correctly.

Lets understand the meaning of the sentence. Some patients who do not respond to therapies for depression may simply have received inadequate treatment (in the past). Examples of these inadequate treatment (received in the past) include:

1. A drug at a dosage too low to be effective or

2. Taken off a drug too soon.

However, E says: they have a drug prescription with a dosage too low to be effective. This is simple present (as in I have a pen). However, we are looking for examples of inadequate treatment in the past.

Hence, E is wrong.

Choice E also has a lack of parallel structure. Don't we need to have parallel elements on both sides of "or"? Choice E says "when they have" and then "or been". "Have" is present tense and is not parallel with "been".

We just need to be a bit careful here. For example, following would be correct:

My classmates have visited the monument or been to the city.

This needs to be interpreted as:

My classmates have visited the monument or (have) been to the city.

Final solution at one place:

Important: The purpose of this post (and all the other posts by me) is to give a complete solution to all GMAT-Prep Verbal questions at one place. Sometimes students have to wade through dozens of posts to get to the final answer. My posts will give one complete and crisp solution required to arrive at the correct answer by eliminating the wrong ones. Some of the content in these posts may have been taken from various other sources (discussion forums).

Some patients who do not respond to therapies for depression may simply have received inadequate treatment, having, for example, been prescribed a drug at a dosage too low to be effective or having been taken off a drug too soon.
(A) having, for example, been prescribed a drug at a dosage too low to be effective or having been
(B) having, for example, a drug prescription that was ineffective because the dosage was too low, or being
(C) as, for example, having too low of a dosage of a prescribed drug for it to be effective, or being
(D) when they have, for example, been prescribed too low a drug dosage for it to be effective, or were
(E) for example, when they have a drug prescription with a dosage too low to be effective, or been

The best way to attack this problem is to remove 'for example' from each of the choices.

A. having been prescribed a drug at a dosage too low to be effective or having been
B. having a drug prescription that was ineffective because the dosage was too low, or being
C. as having too low of a dosage of a prescribed drug for it to be effective, or being
D. when they have been prescribed too low a drug dosage for it to be effective, or were
E. when they have a drug prescription with a dosage too low to be effective, or been

A is parallel 'having been || having been' ... the connector word is 'or' ... as we are joining two similar ideas (and only two ideas), we should not use a comma. This alone is sufficient to eliminate B, C, D, and E.

In B, 'having a drug prescription (refers to patients) can't be parallel to being taken off (refers to a doctor, possibly) ... as the subjects are different, the two are not parallel.

In C, 'having too low of a dosage (refers to patients) can't be parallel to being taken off (refers to a doctor, possibly) ... as the subjects are different, the two words are not parallel.

D is not parallel ('have been' is not parallel to 'were')

E is not parallel ('have a prescription' is not parallel to 'been taken off')

Correct: A