A small study involving 15 adults with moderate-to-severe obstructive sleep apnea and 19 controls with mild or no sleep apnea has found that predicted peak oxygen uptake (VO2), a measure of aerobic physical fitness, was significantly lower in those people with moderate to severe obstructive sleep apnea. Moreover, the number of times a person stopped breathing, for 10-seconds or more, per hour of sleep, predicted 16% of the variability observed in the group's peak VO2.
People who suffer from apnea are more likely to be obese and thus would be expected to be less fit as well, but even compared to people with similar BMI, the apnea patients had a reduced aerobic fitness. It's suggested that the sleep apnea itself causes structural changes in muscle that contributes to exercise problems.
VO2 max measurements may be an early marker for those who are at higher risk of stroke and heart attack
Beitler JR, Awad KM, Bakker JP, Edwards BA, DeYoung P, Djonlagic I, Forman DE, Quan SF, Malhotra A. Obstructive sleep apnea is associated with impaired exercise capacity: a cross-sectional study. J Clin Sleep Med 2014;10(11):1199-1204.