Published in

Elsevier, Computational Statistics & Data Analysis, (80), p. 57-69, 2014

DOI: 10.1016/j.csda.2014.06.011

Links

Tools

Export citation

Search in Google Scholar

Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature

Journal article published in 2014 by Thu Thuy Nguyen, France Mentré ORCID
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Orange circle
Postprint: archiving restricted
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO

Abstract

Nonlinear mixed effect models (NLMEM) are used in model-based drug development to analyse longitudinal data. To design these studies, the use of the expected Fisher information matrix (MFMF) is a good alternative to clinical trial simulation. Presently, MFMF in NLMEM is mostly evaluated with first-order linearisation. The adequacy of this approximation is, however, influenced by model nonlinearity. Alternatives for the evaluation of MFMF without linearisation are proposed, based on Gaussian quadratures. The MFMF, expressed as the expectation of the derivatives of the log-likelihood, can be obtained by stochastic integration. The likelihood for each simulated vector of observations is approximated by Gaussian quadrature centred at 0 (standard quadrature) or at the simulated random effects (adaptive quadrature). These approaches have been implemented in R. Their relevance was compared with clinical trial simulation and linearisation, using dose–response models, with various nonlinearity levels and different number of doses per patient. When the nonlinearity was mild, three approaches based on MFMF gave correct predictions of standard errors, when compared with the simulation. When the nonlinearity increased, linearisation correctly predicted standard errors of fixed effects, but over-predicted, with sparse designs, standard errors of some variability terms. Meanwhile, quadrature approaches gave correct predictions of standard errors overall, but standard Gaussian quadrature was very time-consuming when there were more than two random effects. To conclude, adaptive Gaussian quadrature is a relevant alternative for the evaluation of MFMF for models with stronger nonlinearity, while being more computationally efficient than standard quadrature.