REML estimation of variance parameters in nonlinear mixed effects models using the SAEM algorithm. 2007

Cristian Meza, and Florence Jaffrézic, and Jean-Louis Foulley
Laboratoire de Mathématiques, Université Paris-Sud, Bât. 425, 91405 Orsay Cedex, France. cristian.meza@math.u-psud.fr

Nonlinear mixed effects models are now widely used in biometrical studies, especially in pharmacokinetic research or for the analysis of growth traits for agricultural and laboratory species. Most of these studies, however, are often based on ML estimation procedures, which are known to be biased downwards. A few REML extensions have been proposed, but only for approximated methods. The aim of this paper is to present a REML implementation for nonlinear mixed effects models within an exact estimation scheme, based on an integration of the fixed effects and a stochastic estimation procedure. This method was implemented via a stochastic EM, namely the SAEM algorithm. The simulation study showed that the proposed REML estimation procedure considerably reduced the bias observed with the ML estimation, as well as the residual mean squared error of the variance parameter estimations, especially in the unbalanced cases. ML and REML based estimators of fixed effects were also compared via simulation. Although the two kinds of estimates were very close in terms of bias and mean square error, predictions of individual profiles were clearly improved when using REML vs. ML. An application of this estimation procedure is presented for the modelling of growth in lines of chicken.

UI MeSH Term Description Entries
D008137 Longitudinal Studies Studies in which variables relating to an individual or group of individuals are assessed over a period of time. Bogalusa Heart Study,California Teachers Study,Framingham Heart Study,Jackson Heart Study,Longitudinal Survey,Tuskegee Syphilis Study,Bogalusa Heart Studies,California Teachers Studies,Framingham Heart Studies,Heart Studies, Bogalusa,Heart Studies, Framingham,Heart Studies, Jackson,Heart Study, Bogalusa,Heart Study, Framingham,Heart Study, Jackson,Jackson Heart Studies,Longitudinal Study,Longitudinal Surveys,Studies, Bogalusa Heart,Studies, California Teachers,Studies, Jackson Heart,Studies, Longitudinal,Study, Bogalusa Heart,Study, California Teachers,Study, Longitudinal,Survey, Longitudinal,Surveys, Longitudinal,Syphilis Studies, Tuskegee,Syphilis Study, Tuskegee,Teachers Studies, California,Teachers Study, California,Tuskegee Syphilis Studies
D002645 Chickens Common name for the species Gallus gallus, the domestic fowl, in the family Phasianidae, order GALLIFORMES. It is descended from the red jungle fowl of SOUTHEAST ASIA. Gallus gallus,Gallus domesticus,Gallus gallus domesticus,Chicken
D003198 Computer Simulation Computer-based representation of physical systems and phenomena such as chemical processes. Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D003956 Dialysis A process of selective diffusion through a membrane. It is usually used to separate low-molecular-weight solutes which diffuse through the membrane from the colloidal and high-molecular-weight solutes which do not. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed) Dialyses
D000465 Algorithms A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task. Algorithm
D000704 Analysis of Variance A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable. ANOVA,Analysis, Variance,Variance Analysis,Analyses, Variance,Variance Analyses
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D012641 Selection, Genetic Differential and non-random reproduction of different genotypes, operating to alter the gene frequencies within a population. Natural Selection,Genetic Selection,Selection, Natural
D013269 Stochastic Processes Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables. Process, Stochastic,Stochastic Process,Processes, Stochastic
D014462 Ultrafiltration The separation of particles from a suspension by passage through a filter with very fine pores. In ultrafiltration the separation is accomplished by convective transport; in DIALYSIS separation relies instead upon differential diffusion. Ultrafiltration occurs naturally and is a laboratory procedure. Artificial ultrafiltration of the blood is referred to as HEMOFILTRATION or HEMODIAFILTRATION (if combined with HEMODIALYSIS).

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