Learn Dutch: Doordat de verwijsbrief is goedgekeurd, is de afspraak ingepland. - Because the referral letter has been approved, the appointment is scheduled.

You can replace the whole subordinate clause starting with doordat (because) with a prepositional phrase using door (through/due to). The structure is the preposition + het + infinitive + van. This gives you: Door het goedkeuren van de verwijsbrief is de afspraak ingepland. This nominal style is very common in formal or written Dutch as a way to make sentences more concise.

Why does this sentence use doordat instead of omdat?

While both mean because, doordat expresses a strict cause-and-effect relationship where the consequence is automatic or beyond human volition (the system's approval triggers the scheduling). Omdat is used to give a human reason or motivation. In formal written Dutch, this distinction is strictly maintained, though in everyday casual speech, people often just use omdat for everything.

Why is the auxiliary verb is used in is goedgekeurd rather than heeft?

This is the present perfect tense of the passive voice. An active sentence would be something like De arts heeft de brief goedgekeurd (The doctor has approved the letter). To make a perfect tense passive in Dutch, the standard passive auxiliary verb worden is replaced by zijn (to be). Therefore, it becomes is goedgekeurd (has been approved). The same logic applies to is ingepland.