Comparison between NONMEM and the Monte-Carlo Expectation Maximization (MC-PEM) Method Using a Physiologically-Based Glucose-Insulin Model
Robert Bauer(1), Serge Guzy(1), Hanna E Silber(2), Petra M Jauslin(2,3), Nicolas Frey(3), Mats O Karlsson(2)
(1)Pop-Pharm Inc.,Berkeley,CA (2)Uppsala University, Uppsala, Sweden and (3)Hoffmann-La Roche Inc., Basel, Switzerland
Objectives: The purpose of this work is to compare the methodologies of NONMEM and MC-PEM (as applied in the software packages PDx-MC-PEM and S-ADAPT) using an advanced model for regulation of glucose and insulin kinetics.
Methods: In NONMEM a linearized form of the likelihood function is maximized. The MC-PEM method, by using Monte-Carlo simulations during the expectation step, allows to maximize the exact likelihood while avoiding complicated integration algorithms. The MC-PEM algorithm consists of two main steps: the first one is the expectation step (E-Step) where Monte-Carlo sampled model parameters contribute to assessing the conditional means and variances for each subject, at the current values of the population parameters and inter-subject variances. The E-Step is then followed by the maximization step which updates the population parameter characteristics.
As the MC-PEM algorithm is particularly suited for complex models with highly dimensioned inter-subject variances the comparison between MC-PEM algorithm and NONMEM algorithm as been conducted by using the physiologically based glucose-insulin model previously developed by HE Silber and PM Jauslin and presented at the PAGE meetings in 2004 and 2005 [1-3].
Results: In a first analysis, the estimation procedure was performed with some predefined constraints as present in the NONMEM version of the glucose-insulin model (disposition parameters following the OGTT fixed to values obtained analyzing the IVGTT). This analysis resulted in similar final estimates across the three programs for the population means and variances that were allowed to vary, with intra-subject variances over-estimated in PDx-MCPEM. In a second analysis, the fit was performed without any constraints on the population means and variances, and a full S-ADAPT analysis was performed successfully with a statistically significant improvement in the objective function. The same analysis is being conducted using NONMEM.
Conclusions: S-ADAPT's ability to optimally combine both Monte-Carlo stochastic algorithms with deterministic optimization algorithms allowed both precise objective function assessment as well as full analysis without any parameter constraints.
References:
[1] PAGE 13 (2004) Abstr 541 [www.page-meeting.org/?abstract=541]
[2] PAGE 14 (2005) Abstr 799 [www.page-meeting.org/?abstract=799]
[3] PAGE 14 (2005) Abstr 826 [www.page-meeting.org/?abstract=826]
