 Obstructive sleep apnea OSA is characterized by recurrent episodes of partial or complete loss of airflow during sleep, due to narrowing or closure of the upper airway. The resulting hypoxia has many cardiometabolic consequences, and leads to a disruption of sleep quality including reductions in the expression of rapid eye movement REM sleep and slow wave sleep SWS. Patients also frequently experience excessive daytime sleepiness EDS, which, when present with OSA, defines the clinical entity OSA syndrome OSAS. Obesity is the leading risk factor for the development of OSA. Interestingly, it has been suggested that the disorder itself may contribute to further weight gain, presenting a vicious cycle wherein OSA and obesity perpetuate each other. OSAS may promote weight gain by placing patients in a state of positive energy balance characterized by low levels of physical activity and disrupted patterns of appetite-regulating hormones. Continuous positive airway pressure CPAP, the gold-standard treatment of OSAS, may improve energy balance in these patients, although this has not yet been adequately studied. The current proposal will investigate the effects of 2 months of CPAP on energy balance and cardiovascular risk in obese patients with moderate-to-severe OSA and EDS. Patients will be instructed to use CPAP at home each night throughout the 2-month treatment phases. At baseline and at the conclusion of the 2-month treatment phase, the investigators will measure levels of free-living physical activity, sleepiness, sleep quality, body composition, cardiovascular risk factors, appetite-regulating hormones, hunger, and ad libitum food intake. It is hypothesized that active compared to sham CPAP treatment will result in improvements in energy balance, including increased physical activity, reductions in abnormally high levels of circulating leptin levels, and reductions in hunger, food intake, and cardiovascular risk factors. These improvements are hypothesized to be associated with increases in the expression of REM sleep and SWS, and reduced EDS as a result of CPAP. 