Mixed Effects Markov Models for Modelling Sleep in Insomniac Patients Treated with Placebo in a 28 Days Trial: Emphasis on the Break Points Selection
Bizzotto R (1), Zamuner S (2), Nucci G (2), Cobelli C (1), Gomeni R (2)
(1) Department of Information Engineering, University of Padova, Padova, Italy; (2) Clinical Pharmacokinetics/Modeling&Simulation, GlaxoSmithKline, Verona, Italy
Objectives: A Mixed Effect Markov Model has been proposed in order to characterize the time course of sleep stage transitions in patients with insomnia over a 2 days treatment . The aim of this work was 1) to characterize the time course of the sleep stages transitions in insomniac patients randomized to placebo in a 28 days trial and 2) to evaluate the impact, and hence optimize the selection, of the time intervals in which the night is divided to allow the transition probabilities identification.
Methods: Data were obtained from a placebo-controlled, parallel study with 116 patients affected by primary insomnia. PSG recordings were available at screening and for 3 sessions of two consecutive nights during the trial. The probability of transitioning from a sleep stage to another was modelled in each session for the placebo group. Transition probabilities between sleep stages were modelled as Markov processes using a population approach implemented with NONMEM VI. To identify the Markov models the night-time needs to be divided into different intervals selecting few break points for which population values and inter-individual variability can be estimated. Transition probabilities between break points were derived applying linear interpolation. In , Karlsson et al. proposed to fix the break points so that: (1) they are almost equidistant in time and (2) intervals between break points contain an approximately equal amount of data. With our dataset these criteria were not simultaneously met; therefore we analyzed how the number and placement of break points selection impacts the estimation of transition probabilities during the night. Performance was evaluated through visual inspection of model fitting, Akaike information criterion and accuracy estimation (RMSE).
Results: Break points selection with equally spaced intervals in the night period provided convergence of the estimation only when very few intervals were considered (3 to 4). When allowing intervals to contain the same amount of data (i.e. to be equi-informative), the number of break points could be markedly increased (up to 10). Such modification of the model resulted in a better fit, as proved by the Akaike information criterion and the RMSE results; in addition, a more granular description of the time course of transition probabilities was obtained. The optimized model was applied to assess the time course of transition probabilities under placebo treatment for chronic dosing.
Conclusions: The distribution of breakpoints influences the results of the Mixed Effect Markov modelling of the sleep stage transitions time course. The choice of break points according to an even distribution of available information results in accurate and more dynamic descriptions of transition probabilities between sleep stages. The definition of a criterion to choose the optimal number of break points is in progress.
 Karlsson M O et al. A pharmacodynamic Markov mixed-effect model for the effect of temazepam on sleep. Clin Pharmacol Ther 2000; 68(2):175-88