Modelling Sleep Using Markov Mixed Effects Models
Maria C. Kjellsson (1), Daniele Ouellet (2), Raymond Miller (2), Mats O. Karlsson (1)
(1) Uppsala University, Uppsala, Sweden (2) Pfizer Global Research & Developement, Ann Arbor, Michigan, USA
Objectives: To characterize the time course of sleep stages and the concentration-effect relationship of Drug X relative to placebo and to an active comparator using Markov models in patients with insomnia.
Methods: Sleep data were obtained in a 4-way crossover study of low and high doses of Drug X, a standard dose of an active control and placebo in 43 patients with primary insomnia. Sleep stages were measured for 8 hrs overnight at screening (baseline) and for 2 nights of dosing following each treatment. Markov models consisting of submodels for baseline, placebo, Drug X and positive control were developed for each transition. All models were merged into a joint sleep model for simulations.
The submodels were developed sequentially, starting with baseline, followed by placebo, and in parallel for each drug. For each additional submodel, the parameters of the previous submodel were fixed. To speed up the model-building process, a number of pre-defined standard models for each submodel were tried. These standard models were chosen based on previous experience with similar data [1] and physiological plausibility.
The model development was done using a population analysis approach in NONMEM V, assessing both between subject and between occasion variability (BSV, BOV).
A posterior predictive check and simulations of 3 alternate study designs were performed.
Results: The baseline model was in most cases best described by a piece-wise linear function (PWL) of both bedtime (0 to 8 hrs) and stage time (duration within a stage). The PLW had two slopes with an internal breakpoint, which was either fixed at the median or estimated. BSV was characterized in most transitions and BOV in about half of the transitions.
Placebo effects were found on 4 transitions, all for transitions between awake, stage 1 and REM. A majority of the drug effects of Drug X were best described as a linear model as a function of drug concentration in the effect compartment. The drug effects of the positive control were described with a linear model changing with the predicted concentrations in central compartment.
The predictive performance of the joint model, assessed by simulations of the realized study design, was good, with 16 of 18 pre-defined efficacy parameters well described.
Simulations with changing the time of dosing from ½ hour to 1 hour prior to bedtime resulted in a 40% reduction in latency to persistent sleep for the higher dose of Drug X.
Conclusions: The proposed reduced model building process resulted in a model that describes the sleep pattern at baseline, and following placebo, low and high dose of Drug X and positive control.
References:
[1] Karlsson MO et al. A pharmacodynamic Markov mixed-effect model for the effect of temazepam on sleep. Clin Pharmacol Ther 2000;68(2):175-88
