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Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

机译：多元非线性混合效应模型的最大似然估计的近似方法

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Multivariate nonlinear mixed-effects models (MNLMM) have received increasing use due to their flexibility for analyzing multi-outcome longitudinal data following possibly nonlinear profiles. This paper presents and compares five different iterative algorithms for maximum likelihood estimation of the MNLMM. These algorithmic schemes include the penalized nonlinear least squares coupled to the multivariate linear mixed-effects (PNLS-MLME) procedure, Laplacian approximation, the pseudo-data expectation conditional maximization (ECM) algorithm, the Monte Carlo EM algorithm and the importance sampling EM algorithm. When fitting the MNLMM, it is rather difficult to exactly evaluate the observed log-likelihood function in a closed-form expression, because it involves complicated multiple integrals. To address this issue, the corresponding approximations of the observed log-likelihood function under the five algorithms are presented. An expected information matrix of parameters is also provided to calculate the standard errors of model parameters. A comparison of computational performances is investigated through simulation and a real data example from an AIDS clinical study.
机译：多元非线性混合效应模型（MNLMM）由于具有灵活性，可以根据可能的非线性轮廓分析多结果纵向数据而得到越来越多的使用。本文介绍并比较了五种不同的迭代算法，用于MNLMM的最大似然估计。这些算法方案包括与多元线性混合效应（PNLS-MLME）过程耦合的惩罚非线性最小二乘，拉普拉斯逼近，伪数据期望条件最大化（ECM）算法，蒙特卡洛EM算法和重要性采样EM算法。当拟合MNLMM时，很难在封闭形式中精确评估观察到的对数似然函数，因为它涉及复杂的多个积分。为了解决这个问题，提出了在五种算法下观察到的对数似然函数的相应近似值。还提供了预期的参数信息矩阵，以计算模型参数的标准误差。通过仿真和来自AIDS临床研究的真实数据示例研究了计算性能的比较。

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