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Nonlinear Mixed Effects Models: Theory

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Book cover Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Abstract

This chapter introduces the theory behind nonlinear mixed effects models through the concept of a structural model or covariate model coupled to both fixed and random effects in a nonlinear manner. Modeling and estimation of model parameters in the face of different sources of variability (between-subject, inter-occasion, inter-study, and residual or within-subject) are discussed, as is modeling the nature of the relationship between the covariate and dependent variable via linear, power, and exponential functions. Model building, identifying significant covariates through covariate screening and covariate modeling, influence analysis, and examination of goodness of fit through both scrutiny of the model building data set and validation via internal and external techniques are discussed.

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Notes

  1. 1.

    Individual predicted values (IPRED) have a special place in nonlinear mixed effects models. If the model is written as Y = f(x;θ;Ω;Σ) then taking into account the random effects in the model, IPRED = Y. Population predicted values (PRED) are computed as Y = f(x;θ;Ω;Σ) when all the random effects are set equal to zero. Many manuscripts publish scatter plots of IPRED vs. Y and PRED vs. Y. Both plots should be scattered around the line of unity and show no systematic trends. By definition, IPRED plots will “look” better than PRED plots because of the extra variability that is accounted for in the former.

  2. 2.

    More recent versions of SAS use a different, more accurate algorithm than the NLMIXED macro released with earlier versions.

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  1. Astellas Pharma Global Development Pharmacokinetics, Modeling, and Simulation, Deerfield, IL, USA

    Peter L. Bonate Ph.D.

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Bonate, P.L. (2011). Nonlinear Mixed Effects Models: Theory. In: Pharmacokinetic-Pharmacodynamic Modeling and Simulation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9485-1_7

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