Hierarchical-likelihood approach for nonlinear mixed-effect models

KwangHo Park2, Bo-Hyung Kim1, MD, Namyi Gu1, MD, Kwang-hee Shin1, SoJeong Yi1, Tae-Eun Kim1, MD, Youngjo Lee2, PhD, In-Jin Jang1, MD, PhD

(1)Department of Pharmacology and Clinical Pharmacology, Seoul National University College of Medicine and Hospital, Seoul, Republic of Korea (2)Department of Statistics, Seoul National University, Seoul, Republic of Korea

Objectives: Nonlinear mixed effect models have been widely used for the analysis of pharmacokinetic data. These models frequently lead to an analytically intractable and computationally intensive likelihood that involves multi-dimensional integration. The popular application such as NONMEM^® uses analytical approximation to avoid such numerical difficulties. However, it gives biased estimators. In this study, we used the hierarchical likelihood method ^1,2 to obtain unbiased estimators.

Methods: The one compartment pharmacokinetic model was developed to obtain simulated drug concentrations. This model included inter- and intra-individual variability. The simulated drug concentrations were used to estimate pharmacokinetic parameters, which were calculated using NONMEM^® and new applications based on hierarchical likelihood method.

Results: A total of 270 observations were obtained in 30 subjects, and then PK parameters for these simulated data were estimated using NONMEM^® and H-likelihood method (Table)

Conclusions:  This study suggested that the H-likelihood method showed less unbiased estimators than NONMEM^®.

y_ij = (Dose/η_1i)exp(-η_2it_ij) + ε_ij 1≤ j≤9, 1≤i≤30

η_1i = β₁+b_1i, η_2i = β₂+b_2i

References
[1] Lee and Nelder (1996). Hierarchical generalized linear models (with discussion). Journal of Royal Statistical Society B, 58, 619-656.
[2] Lee, Nelder and Noh (2006). Generalized Linear Models with Random Effects : Unified Analysis via H-likelihood. Chapman & Hall.

Reference: PAGE 18 (2009) Abstr 1661 [www.page-meeting.org/?abstract=1661]

Poster: Methodology- Algorithms