Multinomial logistic estimation of Markov-chain models for modeling sleep architecture in primary insomnia patients

Hypnotic drug development calls for a better understanding of sleep physiology in order to improve and differentiate novel medicines for the treatment of sleep disorders. On this basis, a proper evaluation of polysomnographic data collected in clinical trials conducted to explore clinical efficacy of novel hypnotic compounds should include the assessment of sleep architecture and its drug-induced changes. This work presents a non-linear mixed-effect Markov-chain model based on multinomial logistic functions which characterize the time course of transition probabilities between sleep stages in insomniac patients treated with placebo. Polysomnography measurements were obtained from patients during one night treatment. A population approach was used to describe the time course of sleep stages (awake stage, stage 1, stage 2, slow-wave sleep and REM sleep) using a Markov-chain model. The relationship between time and individual transition probabilities between sleep stages was modelled through piecewise linear multinomial logistic functions. The identification of the model produced a good adherence of mean post-hoc estimates to the observed transition frequencies. Parameters were generally well estimated in terms of CV, shrinkage and distribution of empirical Bayes estimates around the typical values. The posterior predictive check analysis showed good consistency between model-predicted and observed sleep parameters. In conclusion, the Markov-chain model based on multinomial logistic functions provided an accurate description of the time course of sleep stages together with an assessment of the probabilities of transition between different stages.