A Bayesian Approach to Nonlinear Random Effects Models

Abstract

Nonlinear random effects models are considered from the Bayesian point of view. The method of analysis follows closely that of Lindley and Smith (1972, Journal of the Royal Statistical Society, Series B 34, 1-42). The numerical method is related to the EM algorithm.

Monoamine oxidase‐A: pharmacodynamics in humans of moclobemide, a reversible and selective inhibitor.

“…The expectation maximization (EM) algorithm proposed by Racine-Poon [15] for calculation of population characteristics would have the advantage that it uses not only the individual parameter estimates but also their covariance matrices and, therefore, makes better use of the data. However, it cannot handle repeated measurements and only gives joint estimates for the three dose levels.…”

“…An attempt was made to use the EM method described by Racine-Poon [15] to obtain improved population parameter estimates. The EM method takes the accuracy and correlation of the individual estimates into account using the covariance matrix associated with individual parameter estimates.…”

Applications of population approaches in toxicology

“…Another classification of the relevant statistical methods differentiates maximum likelihood (Beal and Sheiner, 1980) and Bayesian approaches (Racine-Poon, 1985) . Modelling in toxicology ought to be particularly well served by a Bayesian approach.…”

Non‐linear mixed regression models

“…For the cluster specific models considered here, V B is not a consistent estimator of var (&) since it does not include the sampling error in the bk (6). The jack-knife estimator of variance for clustered data defined by The jack-knife method was selected for purposes of variance estimation since it provides a simple estimator of the variance of the regression and dispersion parameters based on the variation on the subsample estimators &-k. The jack-knife method performs well in relation to other methods of variance estimation,22 and is consistent for clustered data as K --+ 0 0 .~~ An alternative consistent estimator of var (6) for the population average model is given by (1 S), since the marginal expectation is not a function of the estimates of the random effects.…”