Linear Mixed Effects Modelling of Oxygen Desaturation after Sleep Apneas and Hypopneas: A Pilot Study

Obstructive Sleep Apnea severity is commonly determined after a sleep polysomnographic study by the Apnea-Hypopnea Index (AHI). This index does not contain information about the duration of events, and weights apneas and hypopneas alike. Significant differences in disease severity have been reported in patients with the same AHI. The aim of this work was to study the effect of obstructive event type and duration on the subsequent oxygen desaturation (SaO₂) by mixed-effects models. These models allow continuous and categorical independent variables and can model within-subject variability through random effects. The desaturation depth dSaO₂, desaturation duration dtSaO₂ and desaturation area dSaO₂A were analyzed in the 2022 apneas and hypopneas of eight severe patients. A mixed-effects model was defined to account for the influence of event duration (AD), event type, and their interaction on SaO₂ parameters. A two-step backward model reduction process was applied for random and fixed effects optimization. The optimum model obtained for dtSaO₂ suggests an almost subject-independent proportion increase with AD, which did not significantly change in apneas as compared to hypopneas. The optimum model for dSaO₂ reveals a significantly higher increase as a function of AD in apneas than hypopneas. Dependence of on event type and duration was different in every subject, and a subject-specific model could be obtained. The optimum model for SaO₂A combines the effects of the other two. In conclusion, the proposed mixed-effects models for SaO₂ parameters allow to study the effect of respiratory event duration and type, and to include repeated events within each subject. This simple model can be easily extended to include the contribution of other important factors such as patient severity, sleep stage, sleeping position, or the presence of arousals.