Multinomial Markov-chain model of sleep architecture in Phase-Advanced Subjects (PAS)
C. Steven Ernest II (1,2), Roberto Bizzotto (3), David J DeBrota (2), Lan Ni (2), Cynthia J Harris (2), Mats O Karlsson (1), Andrew C Hooker (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Sweden; (2) Eli Lilly and Company, Indianapolis, IN, USA; (3) Institute of Biomedical Engineering, National Research Council, Padova, Italy.
Phase-advance is used to induce a state qualitatively similar to insomnia. Subjects are asked to begin trying to sleep several hours before their usual bedtime and remain in bed whether asleep or not. The ability of a drug to allow a subject to sleep during what is otherwise a normal wake time may predict efficacy of the drug in insomnia patients (IP). Recently, a mixed-effect Markov-chain model based on transition probabilities (TP) as multinomial logistic functions was developed on polysomnography (PSG) data after placebo dosing in IP [1,2].
Objectives: The aims were to examine the sleep architecture in PAS compared to IP over the first 8 hours and incorporate model enhancements to describe current PAS data.
Methods: PSG data were collected for 13 hours after placebo dosing to PAS from two studies at different sites. TP between sleep stages were modeled as multinomial logistic functions depending on nighttime (NT) and time elapsed since last change in sleep stage (STE). Modification to the model structure and predictors was investigated to accommodate the current data: 1) number of break points in the piecewise linear logit functions, 2) different likelihood of probability for each study based on relatively infrequent transitions and 3) study effect on individual TP. Model building was guided by log likelihood ratio test and AIC, posterior (PPC) and visual predictive checks (VPC).
Results: PAS generally displayed a lower transition frequency from one sleep stage to another, faster onset of sleep and different total time spent in sleep stages compared to IP. The model was fit to study data to describe the sleep architecture in PAS. There were significant differences between studies 1 and 2 for most transitions, excluding from SWS, during both NT and STE. VPCs and PPCs for the final model demonstrated general agreement between the statistics derived from raw and simulated data.
Conclusions: The PAS and IP displayed different sleep architecture over the first 8 hours. PAS generally had fewer transitions between sleep stages and generally displayed a higher propensity to stay in the existing sleep stage compared to IP. The multinomial mixed-effect Markov-chain model presented for IP was further developed with the intent of providing a useful tool for analyzing sleep data in PAS. The final model VPCs and PPCs demonstrated that the proposed model is sufficiently robust for describing data characteristics and dynamic behavior of the sleep process in PAS.
