Mixed Effects Models for the Population Approach. Models, Tasks, Methods and Tools, by Marc Lavielle
Mixed Effects Models for the Population Approach. Models, Tasks, Methods and Tools, by Marc Lavielle
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总体方法的混合效应模型。
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发表时间：
2015
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通讯作者：
J. Bertrand
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作者：
J. Bertrand
本教材介绍了如何使用基于人群的方法，即使用一组共享MLXTRAN语言的工具来构建和评估纵向（主要是药代动力学和/或药效学）数据的模型。平埃罗和贝茨（2009）对非线性混合效应模型进行了全面介绍，他们描述了现有的估计和推断方法，并使用他们开发的R软件包对药代动力学示例进行了有趣的说明。此外，Simon（2007年和2011年）提供了类似的“如何构建模型”框架，但侧重于NONMEM软件和相关工具。这是第一个为统计学家和数学家提供的“操作”框架，并为具有临床背景的用户提供统计和数学模型的全面描述。第一部分逐步介绍了书中提出的概念，以及它们在建模练习中是如何表达的。第一章简要介绍了这些概念。第二章通过实例介绍了线性模型和非线性模型的区别，并介绍了混合效应层，强调了非线性模型和广义混合效应模型的层次性。在第3章中，作者将展示如何由于这种分层性质，这些模型实际上是概率分布的产物，以及如何使这种公式便于模拟、参数估计、模型选择和设计优化。最后，我们将从MLXHTML脚本中提取第一部分，说明这种语言如何在联合概率分布中体现模型的公式化。第二部分反映了非线性混合效应模型的层次结构，分为（i）观测和（ii）单个参数模型。第4章以非常严格的符号分解和公式化了构成连续、计数、分类和事件发生时间数据的已知模型的每个元素，以及后者的某些组合的联合模型。每种类型的数据分析都有一个例子，读者可以看到手头的数据图、数据集的布局、模型实现和模型拟合图。虽然本节非常面向MLXHTML，但它仍然是对这些模型及其使用和限制的诚实介绍。第5章重点讨论单个参数水平的统计模型，即概率分布，考虑不同性质的协变量和额外的变异性水平。同样，每个案例研究都有一个带有相应MLXTRAN代码的真实案例示例支持。本章的结尾是向建模任务的过渡，以及在给定任务的情况下充分表示模型的需要。值得注意的是，第6章介绍了更先进的
This textbook describes how to build and evaluate a model for longitudinal (mainly pharmacokinetic and/or pharmacodynamic) data using a population-based approach, that is, mixed effects with a set of tools sharing the MLXTRAN language. A thorough presentation of nonlinear mixed effect models is provided in Pinheiro and Bates (2009) who describe the existing estimation and inference methodologies with an anecdotic illustration on a pharmacokinetic example using the R package they developed. Also, Simon (2007 and 2011) provides a similar “how-to build a model” framework but focuses on the NONMEM software and related tools. Here is the first combination of a “how-to” framework for statisticians and mathematicians with a thorough description of the statistical and mathematical models for users with a clinical background. Part I introduces gradually and with detailed notations the concepts presented in the book and how they are articulated in the modeling exercise. The concepts themselves are briefly introduced in Chapter 1. Through real-case examples, Chapter 2 describes the difference between linear and nonlinear models, then introduces the mixed effect layer and highlights the hierarchical nature of nonlinear and generalized mixed effect models. In Chapter 3, the author shows how due to this hierarchical nature these models are indeed the product of probability distributions and how this formulation becomes handy for simulation, parameter estimation, model selection, and design optimization purposes. It ends on the first extract of a MLXTRAN script illustrating how this language embodies the formulation of the model in a joint probability distribution. Reflecting the hierarchical structure of nonlinear mixed effect models, Part II is divided into (i) observations and (ii) individual parameters models. Chapter 4 decomposes and formulates in very rigorous notations every elements constituting known models for continuous, count, categorical, and time-to-event data, as well as for joint models of some combinations of the latter. Each type of data analysis is illustrated with an example and the reader is provided with a plot of the data at hand, a layout of the data set, the model implementation and resulting model fit plots. While being very MLXTRAN oriented, this section is still an honest introduction to these models, their uses and limits. Chapter 5 focuses on the statistical model at the individual parameter level, that is, the probability distribution, accounting for covariates of different nature and additional level of variability. Again, every case study is supported by a real-case example with the corresponding MLXTRAN code. This chapter finishes on a transition toward the modeling tasks and the need to represent the model adequately given the task at hand. Of note, Chapter 6 introduces more advanced