Can treating sleep apnea fix blood sugar problems?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

General Inclusion Criteria (for all subjects): * Age: ≥30 and ≤70 years, * BMI: ≥30 and ≤45 kg/m2 or body fat ≥ 30 % for women and ≥ 25 % for men, * Maximum body circumference \<170 cm * Weight stable (≤2% change) * Untrained (≤1 h of structured exercise/wk) for at least 3 months before entering the study * No diabetes (fasting blood glucose \<126 mg/dl, 2h oral glucose tolerance test (OGTT) glucose \<200 mg/dl, HbA1c ≤6.5%) Sleep-related inclusion criteria: Subjects without OSA: * AHI \<5/h of sleep; * Oxygen desaturation index \<3/h * No known sleep disorders and periodic limb movement arousal index \<15/h during polysomnography * Reported sleep duration ≥6 h per night * Regular sleep schedules (i.e. bedtime between 8 pm and 12 am and wake-time between 4 am and 8 am on all days of the week) Subjects with OSA * AHI ≥10/h of sleep (i.e., moderate to severe OSA) * Oxygen desaturation index ≥4/h; * No polysomnogram finding that would trigger immediate PAP treatment as per standard operating protocol in our sleep medicine center (a single SaO2 \<50%, SaO2 \<70% for \>2 minutes, electrocardiogram pause \>5 sec, or ventricular tachycardia \>30 sec), because of the risk of a potentially adverse outcome if they are not randomized to the PAP group * Periodic limb movement arousal index \<15/h during polysomnography, * Reported sleep duration ≥6 h per night, * Regular night-time sleep schedules, defined as bedtime between 8 pm and 12 am and wake-time between 4 am and 8 am on all days of the week. General Exclusion Criteria (for all subjects): * Current treatment for previously diagnosed OSA; * Self-reported severe difficulty sleeping in unfamiliar environments; * Metal implants that are incompatible with magnetic resonance imaging; * Controlled substances, tobacco products, dietary supplements, or medications known or suspected to affect sleep, breathing, upper airway muscle physiology, or glucose metabolism * Evidence of disease (e.g., diabetes, congestive heart failure; chronic obstructive pulmonary disease; hypoventilation, defined as daytime partial pressure of carbon dioxide (pCO2) \>45 mm Hg; major neurological or neuromuscular disorders; cancer; uncontrolled hypertension; etc.); * Contraindications to supplemental oxygen or PAP (e.g., recent trans-sphenoidal surgery). * Unwillingness or inability to provide informed consent * Study physician considers subject to be unable to safely complete the study protocol