Linear mixed effects model general

Generalized linear mixed-effects model fit by restricted PQL Family Binomial with Logit link... 

In this chapter we introduce and illustrate the use of linear, nonlinear, and generalized linear mixed effects models within the S-Plus environment. Based on personal experience, the fitting algorithms implemented in these S-Plus functions appear... 

To further delineate a random effect from a fixed effect, suppose a researcher studied the effect of a drug on blood pressure in a group of patients. Ignoring for a moment the specifics of how one measures blood pressure or quantifies the drug effect, if the researcher was interested in only those patients used in the study, then those patients would be considered a fixed effect. If, however, the researcher wanted to make generalizations to the patient population, and the patients that were used in the experiment were a random sample from the patient population, then patients would be considered a random effect. With that distinction now made, any linear model that contains both fixed and random effects is a linear mixed effects model. 

Linear, Generalized Linear, and Nonlinear Mixed Effects Models... 

Biopharmaceutical research often involves the collection of repeated measures on experimental units (such as patients or healthy volunteers) in the form of longitudinal data and/or multilevel hierarchical data. Responses collected on the same experimental unit are typically correlated and, as a result, classical modeling methods that assume independent observations do not lead to valid inferences. Mixed effects models, which allow some or all of the parameters to vary with experimental unit through the inclusion of random effects, can flexibly account for the within-unit correlation often observed with repeated measures and provide proper inference. This chapter discusses the use of mixed effects models to analyze biopharmaceutical data, more specihcally pharmacokinetic (PK) and pharmacodynamic (PD) data. Different types of PK and PD data are considered to illustrate the use of the three most important classes of mixed effects models linear, nonlinear, and generalized linear. 

Linear mixed effects (LME) models express the response variable as a linear function of both the fixed effects and the random effects, with an additive within-unit error, see Laird and Wase (1) or Searle et al. (2) for a good review of methodology. The frequentist approach to LME models is generally Ukelihood-based, with restricted maximum likelihood (REML) being the preferred method of estimation (3). 

LINEAR, GENERALIZED LINEAR, AND NONLINEAR MIXED EFFECTS MODELS... 

Suppose Y = f(x, 0, t ) + g(z, e) where nr] — (0, il), (0, ), x is the set of subject-specific covariates x, z, O is the variance-covariance matrix for the random effects in the model (t ), and X is the residual variance matrix. NONMEM (version 5 and higher) offers two general approaches towards parameter estimation with nonlinear mixed effects models first-order approximation (FO) and first-order conditional estimation (FOCE), with FOCE being more accurate and computationally difficult than FO. First-order (FO) approximation, which was the first algorithm derived to estimate parameters in a nonlinear mixed effects models, was originally developed by Sheiner and Beal (1980 1981 1983). FO-approximation expands the nonlinear mixed effects model as a first-order Taylor series approximation about t) = 0 and then estimates the model parameters based on the linear approximation to the nonlinear model. Consider the model... 

General linear model or mixed effect model procednres are performed on the pharmacokinetic parameters AUC and to test the data for difference within and between test and reference gronps. Eor a general linear model, the statistical model shonld inclnde factors acconnting for varions sonrces of variability, snch as sequence, snbjects, stndy period, and treatment or formnlation depending on the stndy design. 

Faraway, J. Extending the linear model tuith R generalized linear, mixed effects and nonparametric regression models. Chapman HaU/CRC, London, 2005. 

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