Fig. 1

Graphical overview of the implemented approach for quantifying sleep-stage dynamics. Part (a): The study utilized observational data, including hypnograms of subjects with a conclusive diagnosis of either obstructive sleep apnea (OSA) or healthy status. The illustration highlights differences in the overall prevalence of OSA (OSA-affected > healthy) concerning gender (male predominance in OSA), age (higher OSA prevalence in older subjects), and comorbidities (not present in healthy subjects). Part (b): Inverse Probability Weighting (IPW) is applied to balance the data for the primary confounders of age and gender, having distributional overlap between OSA and healthy subjects. Part (c): A sleep fingerprint matrix \(\textbf{P}\) of sleep-stage transition proportions is modelled using Dirichlet regression within a causal S-Learner framework to capture the effects of OSA, its severity (Apnea-Hypopnea Index, AHI), age, gender, and comorbidities. Part (d): the framework quantifies digital markers of OSA (raw \(\textbf{P}\), \(\textbf{P}^M\) as the normalized Markovian \(\textbf{P}\), and derived quantities such as sleep fragmentation), personalized for subjects’ demographics, OSA severity, and comorbidities, and presented in terms of conditional average treatment effect (CATE) and risk-ratio CATE (RR-CATE).