Studies show that the MMA orthognathic surgery can reduce sleep apnea scores (AHI) significantly

This is a great paper that highlights some of the relationships behind sleep apnea and skeletal malocclusion such is maxillary and mandibular rethrognathia.

The author shows that MMA surgeries can predictably reduce AHI Sleep Apnea scores in sleep apnea diagnosed patients.

Here is the publications with a case study.