Ken has already replied with medical info, I will add some:
If you do a sleep study (polysomnogram) on people at high altitude, those with high-altitude periodic breathing have a print-out that look like sleep apnea patients. Give Diamox and it improves because Diamox is a central (brain) respiratory stimulant. I don't have a reference handy at the moment, but I recall it was part of a lecture I gave a few years ago.
The link below is to a different interesting article- says if you study sleep apnea patients at altitude you will see it, but if they descend to a lower altitude to do the study, their condition improves, thus altering the results. Importantly, their episodes of central apnea (rather than obstructive apnea) improve the most, just what you would expect with lower altitude. This is applicable to the understanding of high altitude illness. high altitude polysomnography