Drug Effects on Sleep Data from a 28-Day Clinical Study in Insomniac Patients: Covariate Analysis Using a Multinomial Mixed-Effect Markov-Chain Model
R. Bizzotto (1), M. O. Karlsson (2), A. C. Hooker (2), S. Zamuner (3)
(1) Institute of Biomedical Engineering, National Research Council, Padova, Italy; (2) Department of Pharmaceutical Biosciences, Uppsala University, Sweden; (3) Clinical Pharmacology Modelling and Simulation, GlaxoSmithKline, Stockley Park, UK.
Objectives: Sleep quality is objectively assessed through polysomnography (PSG), from which clinical efficacy endpoints like sleep latency (LPS) or wake time after sleep onset (WASO) are evaluated. In previous work a multinomial mixed-effect Markov-chain model has been validated for a thorough description of PSG data [1,2]. The aim of this work is the evaluation of drug effects on sleep architecture using this model.
Methods: 342 subjects with primary insomnia were enrolled in a 28-day placebo-controlled study evaluating the sleep effect of a NCE (two doses). PSG data from nights 1 and 27 were analyzed. Each individual sequence of sleep stages (initial sleeplessness IS, following wake AW, stage 1 ST1,stage 2 ST2, slow-wave sleep SWS and REM sleep) was treated as a Markov chain and transition probabilities were modeled through multinomial logit functions of nighttime and time after last sleep stage change (‘stage time') [1,2]. Stepwise forward inclusion followed by backward elimination based on the log-likelihood ratio test [3] was used on the two nights separately to attempt the inclusion of plasma concentration effects. Linear and piecewise linear functions of concentration were added to the logits and estimated using NONMEM VI.
Results: Several statistically relevant effects were included in the final Markov-chain model, changing the probabilities of most transitions. In summary, in the first part of the night transitions from ST2 to SWS were promoted by lower exposures and reduced by higher exposures. In the later part of night 1, transitions from SWS to ST2 were more likely under drug treatment, mostly at low concentrations. In the second part of night 1 increasing plasma concentrations increased the transition probability ST2 to REM and decreased the transition probabilities ST2 to AW and ST2 to ST1 (the latter was higher at night 27). The probability of transitioning from ST1 to AW was reduced by increasing drug concentrations, at median stage time or high nighttime values.
Conclusions: Stepwise forward inclusion and backward elimination based on statistical criteria was able to develop a second-stage multinomial Markov-chain model including drug effects on many parameters. The final model provided a valuable explanation of the reducing effects observed on the clinical endpoints LPS and WASO and on the concentration-dependent tolerance observed on WASO. The multinomial Markov-chain model appeared a suitable tool for the exploration of drug effects on sleep architecture.
References:
[1] R. Bizzotto, S. Zamuner, G. De Nicolao, M. O. Karlsson, R.Gomeni. Multinomial logistic estimation of Markov-chain models for modeling sleep architecture in primary insomnia patients, J Pharmacokinet Pharmacodyn 37(2):137-155 (2010).
[2] R. Bizzotto, S. Zamuner, G. De Nicolao, R. Gomeni, A. C. Hooker, M. O. Karlsson. Multinomial logistic functions in Markov-chain models for modeling sleep architecture: external validation and covariate analysis, PAGE 19 (2010).
[3] E.N. Jonsson, M.O. Karlsson. Automated covariate model building within NONMEM, Pharm Res 15(9):1463-1468 (1998).
