2010 - Berlin - Germany

PAGE 2010: Methodology- Other topics
Oliver Ackaert

A true Markov model for sleep disturbance

C. Diack (3), O. Ackaert (3), B. Ploeger (3), P. van der Graaf (1), R. Gurrell (2), M. Ivarsson (2), D. Fairman (1)

(1) Translational Research (2) Research Enabling Group Pfizer Global Research & Development, Sandwich, UK; (3) LAP&P Consultants, Leiden, The Netherlands

Objectives: The circadian sleep pattern in rats and humans is different, with more frequent transitions between different sleep states and from sleep to fully awake in rats [1-2]. As was demonstrated previously in humans, transitions between different sleep states can be described using a Markov approach [3]. To evaluate the effect of three drug candidates, which are expected to show different propensities for disturbing sleep, a true Markov model was developed to describe these treatment effects on the complex sleep pattern in rats.

Methods: To describe the transitions between different sleep states and assess treatment effects on these transitions it is crucial to consider the dependency between observations. For that purpose Markov models are better suited than proportional odds models [4]. In this study, sleep is considered to be a two-state process: asleep or awake. The two-state, continuous time Markov process was defined by the intensity of both states. In contrast to other Markov approaches [3], the transition probabilities from one state to another over a time interval were uniquely defined and were explicitly derived as functions of these intensities. It was assumed that drug effects can change these transition intensities. The predictive performance of the model was analyzed by comparing the rate of true versus false positive and estimating model accuracy.

Sprague-Dawley rats (n=8) were implanted with radiotelemetry transmitters under isoflurane anaesthesia for recording of electroencephalogram (EEG) and electromyogram (EMG). Data were continuously sampled for 12 hours and analyzed in 5 min epochs. Animals were orally dosed at light on-set with either vehicle or drug in a Latin Square design [5]. PK was derived from satellite animals.

Results: As demonstrated by simulations, the Markov model predicted the data better than a proportional odds model. The predictive performance of the Markov model was also better with low probability of misclassification. The true Markov model allowed estimation of the relative propensity of the 3 drugs to disturb sleep.

Conclusions: Markov models allow analysing longitudinal observations with recurring states. However, for Markov models showing goodness of fit is not sufficient to qualify model performance. Therefore, a received operating characteristics (ROC) technique was used to assess predictive performance and misclassification of the model. This ROC technique can also be used to discriminate between competing models.

[1] Savage, V.M. and G.B. West, A quantitative, theoretical framework for understanding mammalian sleep. Proc Natl Acad Sci U S A, 2007. 104(3): p. 1051-6.
[2] Siegel, J.M., Clues to the functions of mammalian sleep. Nature, 2005. 437(7063): p. 1264-71.
[3] Karlsson, M.O., et al., A pharmacodynamic Markov mixed-effects model for the effect of temazepam on sleep. Clin Pharmacol Ther, 2000. 68(2): p. 175-88.
[4] Zandvliet, A., et al., PK-PD model of multiple follicular developments with corifollitropin alfa during controlled ovarian stimulation: application of Markovian elements.PAGE, Marseille-France, 2008.
[5] Ivarsson, M., L.M. Paterson, and P.H. Hutson, Antidepressants and REM sleep in Wistar-Kyoto and Sprague-Dawley rats. Eur J Pharmacol, 2005. 522(1-3): p. 63-71.

Reference: PAGE 19 (2010) Abstr 1823 [www.page-meeting.org/?abstract=1823]
Poster: Methodology- Other topics