Quantifying sleep apnea heterogeneity using hierarchical Bayesian modeling

TL;DR

This work tackles the heterogeneity of obstructive sleep apnea (OSA) that is not captured by the standard apnea-hypopnea index (AHI) by developing a hierarchical Bayesian model that jointly analyzes sleep-stage dynamics and event rates in polysomnography data. The model yields patient-specific random effects for transitions between sleep stages and the impact of apnea events, with a factor-model covariance to capture shared variation across patients. A Bayes-optimal clustering approach under K-means loss partitions patients into clinically interpretable phenotypes, demonstrated on the APPLES dataset, revealing four distinct profiles and an association between sleep-disruption patterns and cognitive performance not detected by AHI alone. The framework enables uncertainty quantification for cluster membership and can be extended to time-varying dynamics and alternative event-time distributions, offering a principled path toward disruption-based phenotyping and personalized OSA risk assessment and treatment planning.

Abstract

Obstructive Sleep Apnea (OSA) is a breathing disorder during sleep that affects millions of people worldwide. The diagnosis of OSA often occurs through an overnight polysomnogram (PSG) sleep study that generates a massive amount of physiological data. However, despite the evidence of substantial heterogeneity in the expression and symptoms of OSA, diagnosis and scientific analysis of severity typically focus on a single summary statistic, the Apnea-Hypopnea Index (AHI). We address the limitations of this approach through hierarchical Bayesian modeling of PSG data. Our approach produces interpretable random effects for each patient, which govern sleep-stage dynamics, rates of OSA events, and impacts of OSA events on subsequent sleep-stage dynamics. We propose a novel approach for using these random effects to produce a Bayes optimal clustering of patients. We use the proposed approach to analyze data from the APPLES study. Our analysis produces clinically interesting groups of patients with sleep apnea and a novel finding of an association between OSA expression and cognitive performance that is missed by an AHI-based analysis.

Figures (5)

• Figure 1: Posterior predictive distributions of time spent in non-REM sleep (left) and the number of events occurring during non-REM sleep (right). Black dots are observed values; orange dots are posterior predictive means; blue lines are $95\%$ posterior predictive intervals.
• Figure 2: Posterior summaries of the Markov model fixed effects (top left) and random effect variances (top right), and the apnea and hypopnea inter-event time model fixed effects (bottom left) and random effect variances (bottom right). Dots represent posterior means, and intervals represent 95% posterior credible intervals.
• Figure 3: Posterior mean correlation matrix for the random effect vectors $\theta_i$.
• Figure 4: Bayes-optimal point estimate of cluster assignments based on expected K-means loss for random effect vectors $\theta_i$ (left), and posterior probability of assignment to cluster 1, computed with equation \ref{['uq_prob']} (right). pc1 refers to the first principal component vector computed with the posterior means of the dynamics model random effects.
• Figure 5: Cluster assignments computed using the K-means algorithm with REM AHI, non-REM AHI, time in REM, and time in non-REM as input variables, plotted on the same axes from Figure \ref{['fig_cluster_2panel']}.

Theorems & Definitions (1)

• Proposition 3.1