Journal of Biopharmaceutical Statistics

ISSN: 1054-3406 (Print) 1520-5711 (Online) Journal homepage: http://www.tandfonline.com/loi/lbps20

Repeated Measures Design with Generalized
Linear Mixed Models for Randomized ControlledTrials
Misoo C. Ellison
To cite this article: Misoo C. Ellison (2017): Repeated Measures Design with Generalized Linear
Mixed Models for Randomized Controlled Trials, Journal of Biopharmaceutical Statistics, DOI:
10.1080/10543406.2017.1362625
To link to this article: http://dx.doi.org/10.1080/10543406.2017.1362625

Accepted author version posted online: 11Sep 2017.
Published online: 11 Sep 2017.
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Date: 01 November 2017, At: 09:24

JOURNAL OF BIOPHARMACEUTICAL STATISTICSBOOK REVIEW

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Repeated Measures Design with Generalized Linear Mixed Models for Randomized Controlled Trials,by Toshiro Tango, Chapman and Hall/CRC Press, 2017, ISBN 978-1-4987-4789-9, 359 pp.
This book provides a new repeated measures approach called S:T repeated measures design combinedwith the generalized linear mixed-eﬀects models in the context of randomized controlled trials(RCT). The letters, S and T, denote the numbers of repeated measures before and after randomization, respectively. For example, if the primary response variable is measured twice at baseline and 3times after randomization, the design would be a 2:3 repeated measures design. Generalized linearmixed-eﬀects models with continuous, count, or binary response variables are presented emphasizing on the practical aspects of the mixed models using real data from RCT. Multiple real examples
with SAS (version 9.3) codes and interpretation of results are included. This book is an excellent
resource for biostatisticians and researchers designing and analyzing repeated measures data ofclinical trials. It will also serve as a nice accompanying textbook for biostatistics graduate students.
The main contributions of the proposed design in this generalized linear mixed models book are
as follows: (1) it can easily handle missing data by applying the likelihood-based ignorable analyses
under the missing at random assumption and (2) it may lead to a reduction in sample size,compared with the conventional repeated measures design. Historically, the analysis of variance(ANOVA) was the starting point of mixed-eﬀects models. Fisher (1925) developed a method ofestimating variance components by computing the mean squares in a standard ANOVA, equatingthese mean squares to their expectations, and solving for the unknown variances. Searle et al. (1992)
noted that the ﬁrst description in the literature of a mixed-eﬀects model was by Jackson (1939),
although it was not called a mixed-eﬀects model then. Eisenhart (1947) made the ﬁrst distinction
between “ﬁxed” and “random” eﬀects models (Models I and II, respectively), and ﬁrst used the term
“mixed.” It was Henderson (1953) who gave a mathematical description of a mixed-eﬀects model touse in animal breeding applications. The mixed-eﬀects model was popularized by Laird and Ware(1982), describing an expectation–maximization algorithm for its implementation. Since thenmixed-eﬀects models were widely used for the analysis of longitudinal data and many authors
extended the application of mixed-eﬀects models. McCullagh and Nelder (1989) described generalized linear model in a great detail in their book and introduced a linear logistic model with random
eﬀects using a salamander mating experiment. Among numerous developments of generalized linear
mixed-eﬀects models in over the past two decades, Tango’s S:T repeated measures design approach,where repeated measures before randomization are incorporated into the model along with repeatedmeasures after randomization is an ingenious idea. When there are situations where baseline
measurements need to be deﬁned so that only one measure is chosen out of multiple measures,
the S:T repeated measures design will ease this limitation.
The ﬁrst chapter introduces the S:T repeated measures design and generalized mixed-eﬀects
models for Normal, Bernoulli, and Poisson distributions in the framework of RCT design. It also
provides an overview of superiority and non-inferiority trial concepts. Chapters 2 and 3 illustraterepeated measures ANOVA and repeated measures analysis of covariance models with various
covariance structures and compare the results using real data. Chapters 4 and 5 extend ANOVA
models to mixed-eﬀects models and discuss the distinction between the two methods with wellchosen examples. Chapter 6 provides a helpful illustration in regards to handling missing data in
mixed-eﬀects models. Chapters 7 through 9 present the proposed mixed-eﬀects models for normal,
logistic and Poisson regressions and sample size formula for each distribution. Chapter 10 presents
Bayesian alternatives. Chapter 11 introduces latent class or proﬁle models as a competitor to themixed models. Chapter 12 considers some generalized linear mixed models for other trial designs.

2BOOK REVIEWAppendices A and B contain statistical background and theory for sample sizes and generalized
mixed-eﬀects models within the framework of the S:T repeated measures design.
The main focus of this book is to introduce the generalized linear mixed-eﬀects models with S:T
repeated measures design, which provide a ﬂexible and powerful tool to deal with longitudinal datawith heterogeneity or variability among subject-speciﬁc responses and missing data. This bookillustrates theoretical methodologies with a focus on the practicality with a wealth of real-life
examples making it easy to understand the topics. It is well organized and contains SAS codes andoutputs as useful references.
In summary, this is an excellent book with a very good selection of examples. It is clearly written
and is enjoyable to read.

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References
Eisenhart, C. (1947). The assumptions underlying the analysis of variance. Biometrics 3:1–21
Fisher, R. A. (1925). Statistical Methods for Research Workers, 1st ed. Edinburgh, Scotland: Oliver & Boyd.
Henderson, C. R. (1953). Estimation of variance and covariance components. Biometrics 9:226–252
Jackson, R. W. B. (1939). Reliability of mental tests. British Journal of Psychology 29:267–287
Laird, N. M., Ware, J. H. (1982). Random eﬀects models for longitudinal data. Biometrics 38:963–974
McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London, UK: Chapman and Hall.
Searle, S. R., Casella, G., McCulloch, C. E. (1992). Variance Components. New Jersey, NJ: John Wiley & Sons, Inc.

Misoo C. Ellison
Merck & Co., Inc., Kenilworth, NJ, USA© 2017 Taylor & Francis
https://doi.org/10.1080/10543406.2017.1362625