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A Review of: “Models for Discrete Longitudinal Data”, by G. Molenberghs and G. Verbeke

Previously, Verbeke and Molenberghs (2000) presented a comprehensive text on the linear mixed model that was devoted to the analysis of continuous longitudinal data. Their current work considers non-Gaussian data, including repeated, clustered, and multivariate data that are binary, ordinal, or represent counts. This is very important from a practical standpoint because study outcomes are often longitudinal and discrete, or even if the primary outcomes are continuous, discrete versions will often be considered. For example, the percentage reduction from baseline in tumor size, a continuous outcome, might also be viewed as a repeated binary outcome that indicates whether or not a 50% reduction since baseline has occurred. The analysis of longitudinal discrete data also represents an active and broad area of current research, stemming in part from the fact that there is no discrete analog of the multivariate normal distribution. As a result, extending the development of theory for linear mixed models to discrete outcomes typically cannot be accomplished by applying standard likelihoodbased approaches for multivariate normal data to one appropriate counterpart for discrete outcomes. The authors write that they “attempt to fill this gap (resulting from prior focus on Gaussian data) with the current text.” Their intended audience includes “applied statisticians and biomedical researchers, particularly in the biopharmaceutical industry, medical and public health research organizations, contract research organizations, and academic departments.” The book is organized as follows. The introduction (Chapter 1) provides an overview and outline for the six sections of the text. Part I (Introductory Material) describes several interesting motivating studies that the authors refer to repeatedly (Chapter 2); provides a brief review of generalized linear models that includes an example of logistic and Poisson regression analysis for the Toenail and Epilepsy motivating studies (Chapter 3); reviews some of the key concepts for analysis of Gaussian longitudinal data using the linear mixed model (Chapter 4); and then describes three important families of models for repeated non-Gaussian data: the marginal models, conditionally specified models, and the subject-specific models (Chapter 5). Part II focuses on marginal models, with a description and application of association models for bivariate outcomes and cross-classified data (Chapter 6); an overview of models based on fully specified likelihoods, including the Bahadur model for correlated binary data (Chapter 7); a description of alternatives to likelihood-based approaches that include generalized estimating equations (GEE) of Liang and Zeger (1986) and methods based on GEE, including GEE1 (Prentice, 1988), GEE2 (Liang et al., 1992; Zhao and Prentice, 1990), and the alternating