Obstructive sleep apnea hypopnea syndrome (OSAS) is a frequent disease with neuropsychological and cardiovascular (CV) consequences. Continuous positive pressure (CPAP), the main treatment for OSAHS, is effective on the majority of symptoms but restrictive, which can promote non-compliance. Treatment interruptions are often observed in connection with intercurrent events such as nasal obstructions or even when patients are on the move. However, randomized trials have shown that stopping treatment, even for a short time, leads to a recurrence of symptoms and significant CV disturbances (increase in blood pressure, endothelial dysfunction, cardiac repolarization disorders). It seems important to consider strategies that promote therapeutic continuity. The mandibular advancement device (MAD) is an interesting tool in this regard. MAD is as effective as CPAP on symptoms and CV data. The investigators want to assess its effectiveness as a complementary treatment during treatment discontinuation on the main consequences of OSAHS.

Patients are recruited during sleep consultations in the Angers University Hospital pneumology department among patients followed for severe OSAHS and treated with CPAP. All of the scheduled examinations are carried out in the sleep laboratory of the CHU d'Angers.

Patients meeting the inclusion criteria and not having any non-inclusion criteria are randomized to the "MAD" group or to the "control" group. For patients in the "MAD" group, an appointment with a stomatologist is organized to make and adjust a thermo-molded type MAD.

An initial assessment is carried out for all patients during a day hospitalization specific to the study (study of endothelial function, blood pressure, Osler test, ECG, venous and urinary sampling, and completion of the study questionnaires).

Patients are then asked to stop CPAP treatment for two weeks. Patients in the OAM group use OAM during this period. Patients in the control group do not receive any specific treatment for their OSAHS during this period.

After 2 weeks of stopping CPAP, a second assessment, identical to the initial assessment, is carried out for all patients. This assessment is carried out during one night of hospitalization which also allows a PSG to be carried out under OAM or without treatment.

At the end of this assessment, the study is terminated and the patients resume their usual use of CPAP.

Inclusion Criteria:

• Patient accepting MAD treatment
• Patient with an apnea-hypopnea index (AHI) greater than 15 events per hour on the initial recording
• Patient with excessive daytime sleepiness during initial treatment (ESE>10)
• Patient treated for more than 12 months by CPAP with average compliance greater than 5 hours per night

Exclusion Criteria:

• Initial severe daytime sleepiness characterized
• OSAS with ≥ 5 central apneas per hour of sleep at baseline recording
• Previously diagnosed severe cardiac and/or respiratory pathology:
• Body mass index ≥ 35 kg/m2
• Known contraindication to OAM treatment