Nonlinear mixed effects models statistical

Wu, H. and Wu, L. Identification of significant host factors for HIV dynamics modelled by nonlinear mixed-effects models. Statistics in Medicine 2002a 21 753-771. 

Various methods are available to estimate population parameters, but today the nonlinear mixed effects modeling approach is the most common one employed. Population analyses have been performed for mAbs such as basiliximab, daclizu-mab and trastuzumab, as well as several others in development, including clenolixi-mab and sibrotuzumab. Population pharmacokinetic models comprise three submodels the structural the statistical and covariate submodels (Fig. 3.13). Their development and impact for mAbs will be discussed in the following section. 

Beyond pharmacokinetics and pharmacodynamics, population modeling and parameter estimation are applications of a statistical model that has general validity, the nonlinear mixed effects model. The model has wide applicability in all areas, in the biomedical science and elsewhere, where a parametric functional relationship between some input and some response is studied and where random variability across individuals is of concern [458]. 

Therefore, 8 = Sy if and only if LR(X,F) = LR(Y,F). Testing this equality can be done by testing the equality of LR(X,F) and LR Y,F). The latter likelihood ratio statistics are the objective functions (i.e., -2 log-likehood of the data) of nonlinear mixed effects models. As a test statistic, the difference of objective functions (log-likelihood difference, LLD) of two nonhierarchical models can therefore be used. 

M. Davidian and A. R. Gallant, The nonlinear mixed effects model with a smooth random effects density. Institute of Statistics Mimeo Series No. 2206, North Carolina State University, Raleigh, NC, 1992. 

Until recently, no method of comparing nonhierarchical regression models has been available. The bootstrap has been proposed because it may estimate the distribution of a statistic under weaker conditions than do the traditional approaches. In general, for nonlinear mixed effects models that are not hierarchical, the preferred model has simply been selected as that with the lower objective function (2). A more rational approach has been proposed for comparing nonhierarchical models, which is an extension of Efron s method (2, 30). The test statistic is the difference between the objective functions (log-likelihood difference—LED) of the two nonhierarchical models. The method consists of constructing the confidence interval for the LLDs. 

Data analyses included data visualization, nonparametric statistical analysis on observations (data from study 1 only), and parametric analysis with nonlinear mixed effects modeling. 

Nonlinear mixed effects models consist of two components the structural model (which may or may not contain covariates) and the statistical or variance model. The structural model describes the mean response for the population. Similar to a linear mixed effects model, nonlinear mixed effects models can be developed using a hierarchical approach. Data consist of an independent sample of n-subjects with the ith subject having -observations measured at time points t i, t 2, . t n . Let Y be the vector of observations, Y = Y1 1, Yi,2,. ..Ynjl,Yn,2,. ..Yn,ni)T and let s... 

Hartford, A. and Davidian, M. Consequences of misspecifying assumptions in nonlinear mixed effects models. Computational Statistics Data Analysis 2000 34 139-164. 

Higgins, K.M., Davidian, M. and Giltinan, D.M. A two-step approach to measurement error in time-dependent covariates in nonlinear mixed-effects models, with application to IGF-1 pharmacokinetics. Journal of the American Statistical Association 1997 93 436-448. 

Pinheiro, J.C. and Bates, D.M. Model building in nonlinear mixed effect models. In ASA Proceedings of the Biophar-maceutical Section. American Statistical Association, Alexandria, VA, 1994, pp. 1-8. 

Retout, S., Mentre, F., and Bruno, R. Fisher information matrix for nonlinear mixed-effects models Evaluation and application for optimal design of enoxaparin population pharmacokinetics. Statistics in Medicine 2002 30 2623-2629. 

Both nonparametric and parametric bootstrap approaches can be pursued depending on whether we are willing to assume we know the true form of the distribution of the observed sample (parametric case). The parametric bootstrap is particularly useful when the sample statistic of interest is highly complex (as one might expect when trying to bootstrap a pharmacokinetic parameter derived from a nonlinear mixed effect model) or when we happen to know the distribution, since the additional assumption of a known distribution adds power to the estimate. 

Unlike the individual model discussed above, a more elaborate statistical model is required to deal with sparse PK data. In formulating the model, it is recognized that overall variability in the measured (response) data in a sample of individuals reflects both measurement error and intersubject variability. The observed response (e.g., concentration) in an individual within the framework of population (regression) nonlinear random mixed effects models can be described as... 

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