Association between stage-specific sleep bout durations and obstructive sleep apnea severity: A variable-domain functional regression approach

The apnea-hypopnea index (AHI), the conventional metric of obstructive sleep apnea (OSA) severity, is typically studied using scalar summaries of sleep architecture, such as the total time spent in each sleep stage. Although clinically interpretable, these summaries fail to capture the temporal organization of overnight sleep-stage sequences and may obscure stage-specific associations with OSA severity. Modeling the complete sleep-stage trajectory provides substantially richer temporal information; however, because total sleep duration varies across individuals, sleep-stage trajectories are observed over subject-specific domains, limiting the applicability of conventional functional regression methods that assume a common observation interval. We therefore applied Variable-Domain Functional Regression (VDFR) to overnight polysomnographic data from the APPLES study (n= 1,103), treating the epoch-by-epoch sleep-stage sequence as a continuous, variable-length functional predictor of AHI. We compared three levels of sleep-stage granularity: five stages (Wakefulness, N1, N2, N3, REM), three stages (Wakefulness, Non-REM, REM), and binary staging (Wakefulness vs. Sleep). Functional sleep-stage terms were significant across all staging granularities and model structures (all p-values [≤]0.001). Wake, N1, and N2 were positively associated with AHI, whereas N3 and REM were negatively associated, with REM exhibiting the strongest association. These effects were attenuated under coarser staging representations, highlighting the importance of preserving fine-grained sleep architecture. To our knowledge, this is the first application of VDFR to overnight polysomnographic data in OSA, showing that accommodating subject-specific sleep durations enables the identification of stage-specific temporal associations with AHI severity that are attenuated or obscured by coarser staging and conventional scalar analyses.