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Applied Mixed Models in Medicine

Helen Brown and Robin Prescott
John Wiley
Publication Date: 
Number of Pages: 
Statistics in Practice
[Reviewed by
Sarah Boslaugh
, on

Mixed modeling has become a popular technique for the analysis of many types of medical data, because those data often do not meet the assumptions of conventional fixed effects models, in particular the assumption that residuals are independently and identically distributed. A major factor in the rise of popularity of mixed modeling is its incorporation into common statistical packages such as SAS and R, so that running mixed models no longer requires purchasing and learning to use an additional software package. The main barrier which prevents mixed models from being more widely used is their exclusion from many statistics courses and textbooks.

Applied Mixed Models in Medicine should largely close that gap by presenting the basic theory behind mixed modeling, examples of the application of different types of models to typical types of medical data. There are many examples which discuss how to apply mixed modeling to typical medical analytical problems, and the presentation includes both theoretical discussion and SAS code and output for each type of analysis; the procedures most often used are PROC MIXED, PROC GENMOD AND PROC GLIMMIX. Data sets and SAS code used in the text are available electronically from There is a brief discussion of statistical programs other than SAS which may be used for mixed modeling, but this text's usefulness would be diminished for people working in any language other than SAS.

Applied Mixed Models in Medicine takes a practical rather than theoretical approach and requires understanding of only basic statistics. It is intended primarily for applied statisticians who work with medical data and need to learn how to use mixed models in their work. Others who may be interested in using this text include teachers and students in advanced biostatistics courses and principal investigators who need to understand mixed modeling even if they will hire a statistician to actually perform the analyses for them.

Helen Brown is a Principal Statistician for NHS Scotland (National Health Service for Scotland), and Robin Prescott is Professor of Health Technology Assessment and Director of the Medical Statistics Unit for the Public Health Sciences Section of the Divison of Community Health Sciences of the University of Edinburgh.

Sarah Boslaugh, PhD, MPH, ( is a Performance Review Analyst in the Center for Healthcare Quality and Effectiveness at BJC HealthCare in St. Louis, MO. She wrote An Intermediate Guide to SPSS Programming: Using Syntax for Data Management for Sage Publications in 2005 and is currently writing Secondary Data Sources for Public Health: A Practical Guide for Cambridge University Press. She is also Editor-in-Chief of The Encyclopedia of Epidemiology which will be published by Sage in 2007.

Preface to Second Edition.

Mixed Model Notations.

1 Introduction.

1.1 The Use of Mixed Models.

1.2 Introductory Example.

1.3 A Multi-Centre Hypertension Trial.

1.4 Repeated Measures Data.

1.5 More aboutMixed Models.

1.6 Some Useful Definitions.

2 NormalMixed Models.

2.1 Model Definition.

2.2 Model Fitting Methods.

2.3 The Bayesian Approach.

2.4 Practical Application and Interpretation.

2.5 Example.

3 Generalised Linear MixedModels.

3.1 Generalised Linear Models.

3.2 Generalised Linear Mixed Models.

3.3 Practical Application and Interpretation.

3.4 Example.

4 Mixed Models for Categorical Data.

4.1 Ordinal Logistic Regression (Fixed Effects Model).

4.2 Mixed Ordinal Logistic Regression.

4.3 Mixed Models for Unordered Categorical Data.

4.4 Practical Application and Interpretation.

4.5 Example.

5 Multi-Centre Trials and Meta-Analyses.

5.1 Introduction to Multi-Centre Trials.

5.2 The Implications of using Different Analysis Models.

5.3 Example: A Multi-Centre Trial.

5.4 Practical Application and Interpretation.

5.5 Sample Size Estimation.

5.6 Meta-Analysis.

5.7 Example: Meta-analysis.

6 RepeatedMeasures Data.

6.1 Introduction.

6.2 Covariance Pattern Models.

6.3 Example: Covariance Pattern Models for Normal Data.

6.4 Example: Covariance Pattern Models for Count Data.

6.5 Random Coefficients Models.

6.6 Examples of Random Coefficients Models.

6.7 Sample Size Estimation.

7 Cross-Over Trials.

7.1 Introduction.

7.2 Advantages of Mixed Models in Cross-Over Trials.

7.3 The AB/BA Cross-Over Trial.

7.4 Higher Order Complete Block Designs.

7.5 Incomplete Block Designs.

7.6 Optimal Designs.

7.7 Covariance Pattern Models.

7.8 Analysis of Binary Data.

7.9 Analysis of Categorical Data.

7.10 Use of Results from Random Effects Models in Trial Design.

7.11 General Points.

8 Other Applications of MixedModels.

8.1 Trials with Repeated Measurements within Visits.

8.2 Multi-Centre Trials with Repeated Measurements.

8.3 Multi-Centre Cross-Over Trials.

8.4 Hierarchical Multi-Centre Trials and Meta-Analysis.

8.5 Matched Case–Control Studies.

8.6 Different Variances for Treatment Groups in a Simple Between-Patient Trial.

8.7 Estimating Variance Components in an Animal Physiology Trial.

8.8 Inter- and Intra-Observer Variation in Foetal Scan Measurements.

8.9 Components of Variation and Mean Estimates in a Cardiology Experiment.

8.10 Cluster Sample Surveys.

8.11 Small AreaMortality Estimates.

8.12 Estimating Surgeon Performance.

8.13 Event History Analysis.

8.14 A Laboratory Study Using aWithin-Subject 4 × 4 Factorial Design.

8.15 Bioequivalence Studies with Replicate Cross-Over Designs.

8.16 Cluster Randomised Trials.

9 Software for Fitting MixedModels.

9.1 Packages for Fitting Mixed Models.

9.2 Basic use of PROC MIXED.

9.3 Using SAS to Fit Mixed Models to Non-Normal Data.