Meza Cristian, Jaffrézic Florence, Foulley Jean-Louis
Laboratoire de Mathématiques, Université Paris-Sud, Bât. 425, 91405 Orsay Cedex, France.
Biom J. 2007 Dec;49(6):876-88. doi: 10.1002/bimj.200610348.
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.
非线性混合效应模型如今在生物统计学研究中被广泛应用，尤其在药代动力学研究或用于分析农业及实验物种的生长性状方面。然而，这些研究大多常基于极大似然（ML）估计程序，而众所周知该程序存在向下偏差。已经提出了一些限制极大似然法（REML）的扩展方法，但仅适用于近似方法。本文的目的是基于固定效应的积分和随机估计程序，在精确估计方案内给出非线性混合效应模型的REML实现方法。该方法通过随机期望最大化（EM）算法，即模拟退火期望最大化（SAEM）算法来实现。模拟研究表明，所提出的REML估计程序显著降低了ML估计中观察到的偏差，以及方差参数估计的残差均方误差，尤其是在不平衡情况下。还通过模拟比较了基于ML和REML的固定效应估计量。尽管两种估计在偏差和均方误差方面非常接近，但与ML相比，使用REML时个体概况的预测明显得到改善。本文给出了该估计程序在鸡品系生长建模中的应用。
