Mixed Effects Models for the Population Approach. Models, Tasks, Methods and Tools, by Marc Lavielle

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