Cognitive dysfunction (impaired memory, thinking, etc) frequently occurs in Parkinson's disease (PD), often progresses to dementia, and profoundly affects quality of life. Obstructive sleep apnea (OSA) is a common disorder in the general population that is treatable with positive airway pressure (PAP) therapy. It is known to impair cognitive function, but whether treatment improves cognitive function is less clear. When already affected by a degenerative process like PD, the brain might be more vulnerable to the effects of OSA, and more responsive to OSA treatment. To date, OSA has not been recognized as a significant factor in PD. In preliminary work in PD patients, the investigators have found an association between OSA and poor cognition, and cognitive improvement with PAP therapy. The investigators now wish to more rigorously evaluate the effect of OSA treatment on cognitive function in PD in a randomized controlled trial. The investigators primary objective is to assess, in PD patients with OSA and cognitive deficit, the effect of OSA treatment on global cognitive function. The investigators will also assess other non-motor symptoms of PD, quality of life, and specific domains of neurocognitive function. PD patients will be recruited from the McGill Movement Disorders Clinic and other Quebec Parkinson Network Centres. Participants will need to have evidence of cognitive deficit and presence of OSA on screening diagnostic polysomnography (sleep study). Ninety subjects will be randomly assigned to PAP or nasal dilator strips. Detailed neuropsychological testing and other measurements (including quality of life) will be done at baseline, 3 months and 6 months. At the end of the study period, subjects will have polysomnography on their respective treatment to assess efficacy with respect to OSA treatment. This study may demonstrate that a non-pharmacologic intervention has the potential to have a marked beneficial impact on cognitive function and quality of life in a significant proportion of PD patients.

Inclusion Criteria:

• Parkinson's disease as perMDS criteria
• Evidence of cognitive dysfunction (clinical impression of mild cognitive impairment and MOCA <=27)
• Presence of OSA (apnea-hypopnea index RDI ≥ 15/h) on screening diagnostic polysomnography (PSG)
• Stable regimen of anti-PD medication for 1 month prior
• Adequate knowledge of English or French for completion of study assessment.

Exclusion Criteria:

• Oxygen saturation <75% for >10% of the diagnostic polysomnography as this should lead to active PAP treatment
• Other major neurological disorder
• Unstable cardiac disease, uncontrolled hypertension, or diabetes
• Active cancer or other disorder with an expected survival < 6 months
• Active treatment of OSA (prior diagnosis of OSA will constitute an exclusion criterion only if the patient is currently being treated for the OSA)
• Significant vision or hearing impairment that could affect performance on neurocognitive assessment tasks.
• Latex allergy.