Models for discrete longitudinal data. (English) Zbl 1093.62002

Molenberghs, Geert; Verbeke, Geert

Springer Series in Statistics. New York, NY: Springer (ISBN 0-387-25144-8/hbk). xxii, 683 p. (2005).

This book provides a comprehensive treatment of modeling approaches for non-Gaussian repeated measures, possibly subject to incompleteness. The authors begin with models for the full marginal distribution of the outcome vector. This allows model fitting to be based on maximum likelihood principles, immediately implying inferential tools for all parameters in the models. At the same time, they formulate computationally less complex slternatives, including generalized estimating equations and pseudo-likelihood methods. They briefly introduce conditional models and move on to the random-effects linear family encompassing the beta-binomial model, the probit model and, in particular, the generalized linear mixed model. Several frequently used procedures for model fitting are discussed and differences between marginal models and random-effects models are given attention. The authors consider a variety of extensions, such as models for multivariate longitudinal measurements, random-effects models with serial correlation, and mixed models with non-Gaussian random effects. They sketch the general principles for how to deal with the commonly encountered issue of incomplete longitudinal data. The authors criticize frequently used methods and propose flexible and broadly valid methods instead, and they conclude with key concepts of sensitivity analysis. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The text is so organized that the reader can skip the software-oriented chapters and sections without breaking the logical flow.
The book is divided into six parts: 1. Introductory Material; 2. Marginal Models; 3. Conditional Models; 4. Subject-specific Models; 5. Case Studies and Extensions; 6. Missing Data. Virtually all the statistical analyses were performed using SAS procedures. The GLIMMIX procedure used here is experimental. Both, the methodological development and the analysis of the case studies are presented in a software-independent fashion. It is a very important, modern and useful book for statisticians.

Reviewer: T. Postelnicu (Bucureşti)

MSC:

62-02	Research exposition (monographs, survey articles) pertaining to statistics
62J12	Generalized linear models (logistic models)
62-04	Software, source code, etc. for problems pertaining to statistics
65C60	Computational problems in statistics (MSC2010)

Keywords:

multivariate longitudinal measurements; discrete longitudinal data; mixed models

Software:

glimmix; SAS