Comparison of NONMEM Estimation Methods in the Application of a Markov-Model for Analyzing Sleep Data
Lindauer, A (1); Guo, Z (2); Zajic, S (3); Huang, S (2); Mehta, K (4); Kumar, B (3); Elassaiss - Schaap, J (1); Bauer, R (5); Clements, JD (3)
(1) Clinical PKPD, Merck & Co., Inc. (Oss, NL); (2) Biostatistics, Merck & Co., Inc. (US); (3) Clinical PKPD, Merck & Co., Inc. (US); (4) Informatics, Merck & Co., Inc. (US); (5) Icon Dev. Solutions (US)
Objectives: Nonlinear mixed-effects modeling of polysomnographic (PSG) data has been shown to provide quantitative insight into the time course of transitioning between sleep stages. However, these models are relatively complex and the amount of data is enormous. As part of an effort to assess the utility/feasibility of this modeling approach for in-house development programs, it was of interest to evaluate the performance of the various estimation methods available in NONMEM 7.2 and select the ‘best' method for future analyses.
Methods: The model described by Kjellson et al. has been adapted for this purpose [1]. Parameter estimates were taken from this publication and considered as ‘true' values. 100 PSG datasets with 100 subjects each were simulated using R. A PSG recording consists of a categorical observation (i.e. awake, stage 1, stage 2, slow-wave-sleep, rapid-eye-movement) per 30-sec epoch during an 8-hour-night. All datasets were analyzed with the following estimation methods: BAYES, SAEM, IMP, IMPMAP, ITS, LAPLACE (LAPL). The initial estimates were set to the true value; only for LAPL the analysis was also performed with randomly changed initial values. The relative errors of the parameter estimates were calculated for each run and summarized for each method.
Results: The LAPL-method clearly outperformed the other methods with fixed-effects parameter estimates usually within 1.5-fold of the true value. For some parameters ITS, IMP, and IMPMAP resulted in extremely biased estimates - less so with SAEM. Randomly changing initial values had no significant impact on the accuracy and precision of the estimates obtained with LAPL. With the BAYES-method all runs terminated during the burn-in phase. Over 80% of the LAPL-runs converged successfully, while for the other methods optimization was completed ~60% of the time. The median run time was shortest using SAEM (1.4 h), followed by LAPL (2.2 h), ITS (7.2 h), IMP (9.7 h), and IMPMAP (290 h).
Conclusions: The present evaluation shows that for analyzing PSG data with a Markov-model the LAPL method provides the most accurate parameter estimates and is most efficient regarding run times. However, due to the complex model structure appropriate MU-referencing was not possible which may explain the suboptimal performance of the other methods. Not providing priors to the model parameters was likely the reason for the premature termination of runs using the BAYES-method. The LAPL method will be used for future internal analysis of PSG data.
References:
[1] Kjellson et al., Modeling Sleep Data for a New Drug in Development using Markov Mixed-Effects Models, Pharm Res (2011) 28:2610-2627