In this manuscript, we consider methods for the analysis of populations of electroencephalogram signals during sleep for the study of sleep disorders using hidden Markov models (HMMs). Notably, we propose an easily implemented method for simultaneously modeling multiple time series that involve large amounts of data. We apply these methods to study sleep-disordered breathing (SDB) in the Sleep Heart Health Study (SHHS), a landmark study of SDB and cardiovascular consequences. We use the entire, longitudinally collected, SHHS cohort to develop HMM population parameters, which we then apply to obtain subject-specific Markovian predictions. From these predictions, we create several indices of interest, such as transition frequencies between latent states. Our HMM analysis of electroencephalogram signals uncovers interesting findings regarding differences in brain activity during sleep between those with and without SDB. These findings include stability of the percent time spent in HMM latent states across matched diseased and non-diseased groups and differences in the rate of transitioning. Copyright © 2013 John Wiley & Sons, Ltd.