I believe Alzheimer's disease has recently been linked to chronic hypoxia. My grandfather is suffering from Alzheimer's and one of the things his doctor warned us about was to pay attention to his breathing and to bring him in if we notice shortness of breath. I guess this is one of the symptoms/side effects of Alzheimer's disease.
The danger of this is that sometimes family members or the patient might not realize that there is chronic hypoxia. I heard this happens a lot at the later stages of the disease. Thankfully, my grandfather is doing rather well and I hope it stays that way. He is staying with us and we are monitoring him, making sure he can move around easily with no breathing problems.