Linear mixed effects

The L B90 algorithm proceeds in two alternating steps, a penalized nonlinear least-squares (PNLS) step and a linear mixed effects (LME) step. 

Fig. 13.3 D ose proportionality assessment. The solid line is the predicted exposure based on a linear mixed effects power model having a reference subject. For the tasidotin plots, the predicted line is for a reference patient having a BSA of 1.83 m2.

A population PK evaluation of patients from the safety and efficacy trials can be used to assess the impact of renal function on the disposition of a drug. Special care must be taken that patients with severe renal impairment are adequately represented in the population. The population PK approach assess the impact of various covariates on the disposition of a drug. Non linear mixed effects modeling may be used to model the relationship between various covariates and pharmacokinetic parameters. CLcr as a measure of renal function may be one of the covariates. This type of approach has it advantageous as it involves assessment of the effect of renal impairment on the PK in the target population. 

Hayashi W, Kinoshita H, Yukawa E, Higuchi S. Pharmacokinetic analysis of subcutaneous erythropoietin administration with non-linear mixed effect model including endogenous production. Br J Clin Pharmacol 1998 46 11-9. 

The non-linear mixed effects model is the most widely used method and has proven to be very useful for continuous measures of drug effect, categorical response data, and survival-type data. The nonlinear mixed-effects modeling software (NONMEM) introduced by Sheiner and Beal is one of the most commonly used programs for population analysis. A detailed review of software for performing population PK/PD analysis is available. ... 

The first attempt at estimating interindividual pharmacokinetic variability without neglecting the difficulties (data imbalance, sparse data, subject-specific dosing history, etc.) associated with data from patients undergoing drug therapy was made by Sheiner et al. " using the Non-linear Mixed-effects Model Approach. The vector 9 of population characteristics is composed of all quantities of the first two moments of the distribution of the parameters the mean values (fixed effects), and the elements of the variance-covariance matrix that characterize random effects.f " " ... 

Most of the non-linear mixed-effects modeling methods estimate the parameters by means of ML. The probability of the data under the model is written as a function of the model parameters, and parameter estimates are chosen to maximize this probability. This amounts to asserting that the best parameter estimates are those that render the observed data more probable than they would be under any other set of parameters. 

Other Non-Linear Mixed-Effects Methods. These are less widely used than the above methods and include, but not limited to, alternative first-order (MIXNLIN)... 

Steimer, J.L. Mallet, A. Gohnard, J.L. Boisvieux, J.F. Alternative approaches to the estimation of population pharmacokinetic parameters comparison with the non-linear mixed effects model. Drug. Metab. Rev. 1984, 15 (1-2), 265-292. 

Mentre, F. Geomeni, R. A two-step iterative algorithm for estimation in non-linear mixed-effect models with an evaluation in population pharmacokinetics. J. Biopharm. Stat. 1995, 5, 141-158. 

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

Fattinger, K.E. Sheiner, L.B. Verotta, D. A new method to explore the distribution of interindividual random effects in non-linear mixed effects models. Biometrics 1995, 51, 1236-1251. 

Retout, S. Mentre, E. Bruno, R. Eisher information matrix for non-linear mixed-effects models evaluation... 

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). 

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... 

E. Lipka, I. D. Lee, P. Langguth, H. Spahn-Langguth, E. Mutschler, and G. L. Amidon, Celiprolol double-peak and gastric motility non-linear mixed effect modeling of bioavailability data obtained in dogs. / Pharmacokinet Biopharm 23 267-287 (1995). 

E. I. Ette, Comparing non-hierarchical models apphcation to non-linear mixed effects modeling. Comput Biol Med 26 505-512 (1996). 

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. 

Vd is the volume of distribution, and the negative of (3] is the elimination rate constant. A linear mixed effect model is appropriate for this dataset. In this case, Yj is a 3 x 1 vector of responses for each subject stacked on top of each other creating a Y vector with 12 rows. The other matrices are... 

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