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

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  • Nguyen, Thu Thuy
  • Mentré, France

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 (MF) is a good alternative to clinical trial simulation. Presently, MF 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 MF without linearisation are proposed, based on Gaussian quadratures. The MF, 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 MF 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 MF for models with stronger nonlinearity, while being more computationally efficient than standard quadrature.

Suggested Citation

  • Nguyen, Thu Thuy & Mentré, France, 2014. "Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 57-69.
  • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:57-69
    DOI: 10.1016/j.csda.2014.06.011
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    References listed on IDEAS

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    1. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482, April.
    2. Cong Han & Kathryn Chaloner, 2004. "Bayesian Experimental Design for Nonlinear Mixed-Effects Models with Application to HIV Dynamics," Biometrics, The International Biometric Society, vol. 60(1), pages 25-33, March.
    3. Abebe, Haftom T. & Tan, Frans E.S. & Van Breukelen, Gerard J.P. & Berger, Martijn P.F., 2014. "Bayesian D-optimal designs for the two parameter logistic mixed effects model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1066-1076.
    4. Kuhn, E. & Lavielle, M., 2005. "Maximum likelihood estimation in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1020-1038, June.
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    1. Ueckert, Sebastian & Mentré, France, 2017. "A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 203-219.

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