Mixed effects models for the population approach. Models, tasks, methods and tools. With contributions by Kevin Bleakley.

*(English)*Zbl 1341.62034
Chapman & Hall/CRC Biostatistics Series. Boca Raton, FL: CRC Press (ISBN 978-1-4822-2650-8/hbk; 978-1-4822-2651-5/ebook). xviii, 365 p. (2015).

A framework of mixed effects models and their estimation with the stochastic EM algorithm is presented. Most examples are from the area of pharmacokinetic modeling, but the book under review should also be useful for other researchers modeling hierarchical longitudinal data. The book is divided into three parts. After an overview, the introductory part proceeds with a review of (non-)linear mixed effects models and their generalized variants and a motivation of the modeling framework. The second part describes the modeling framework in depth with chapters on distributional assumptions for different data types, models for individual parameters and extensions. The last part covers estimation algorithms and examples. Four appendices contain material on the individual approach, some mathematical results, a brief introduction to pharmacokinetic modeling, and a brief overview of the software packages Monolix, Mlxplore, Datxplore, and Simulx.

Reading the book requires some applied statistics training, especially as the foundations on (generalized) (non-)linear (mixed) models in Chapter 2 are terse. To fully appreciate the technical material in Chapter 9, some probability theory is a prerequesite.

Reading the book requires some applied statistics training, especially as the foundations on (generalized) (non-)linear (mixed) models in Chapter 2 are terse. To fully appreciate the technical material in Chapter 9, some probability theory is a prerequesite.

Reviewer: Philipp Doebler (Münster)

##### MSC:

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62J02 | General nonlinear regression |

62J12 | Generalized linear models (logistic models) |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62N01 | Censored data models |

65C60 | Computational problems in statistics (MSC2010) |

92C60 | Medical epidemiology |

92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |