The Effects of Successful OSA TreatmENT on Memory and AD BIomarkers in Older AduLts (ESSENTIAL) study is a 5-year, multicenter randomized open-label trial that will screen 400 cognitively normal older adults recruited from well-established sleep clinics at 4 academic medical centers, with newly diagnosed moderate-severe OSA. An expected 200 OSA patients will be then randomized to one of two groups: i) a 3-month OSA treatment by any combination of PAP, OAT, and positional therapy that results in an effective AHI4%\< 10/hour and AHI3A\<20/hour (see below); ii) a waitlist control group to receive treatment at the conclusion of the 3-month intervention period. Both groups will continue follow-up for 24 months on stable therapy to determine if sustained improvements in sleep are associated with improvement in cognitive function and AD biomarkers.