Applied Mixed Models in Medicine

A fully updated edition of this key text on mixed models, focusing on applications in medical research 

The application of mixed models is an increasingly popular way of analysing medical data, particularly in the pharmaceutical industry. A mixed model allows the incorporation of both fixed and random variables within a statistical analysis, enabling efficient inferences and more information to be gained from the data. There have been many recent advances in mixed modelling, particularly regarding the software and applications. This third edition of Brown and Prescott’s groundbreaking text provides an update on the latest developments, and includes guidance on the use of current SAS techniques across a wide range of applications. 

• Presents an overview of the theory and applications of mixed models in medical research, including the latest developments and new sections on incomplete block designs and the analysis of bilateral data.
• Easily accessible to practitioners in any area where mixed models are used, including medical statisticians and economists.
• Includes numerous examples using real data from medical and health research, and epidemiology, illustrated with SAS code and output.
• Features the new version of SAS, including new graphics for model diagnostics and the procedure PROC MCMC.
• Supported by a website featuring computer code, data sets, and further material. 

This third edition will appeal to applied statisticians working in medical research and the pharmaceutical industry, as well as teachers and students of statistics courses in mixed models. The book will also be of great value to a broad range of scientists, particularly those working in the medical and pharmaceutical areas.

Robin Prescott, Medical Statistics Unit, University of Edinburgh Medical School, UK.

Preface to Second Edition xiii

Mixed Model Notation xvii

1 Introduction 1

1.1 The Use of Mixed Models 1

1.2 Introductory Example 3

1.3 A Multi-Centre Hypertension Trial 12

1.4 Repeated Measures Data 18

1.5 More about Mixed Models 22

1.6 Some Useful Definitions 27

2 Normal Mixed Models 33

2.1 Model Definition 33

2.2 Model Fitting Methods 45

2.3 The Bayesian Approach 56

2.4 Practical Application and Interpretation 70

2.5 Example 83

3 Generalised Linear Mixed Models 107

3.1 Generalised Linear Models 108

3.2 Generalised Linear Mixed Models 120

3.3 Practical Application and Interpretation 128

3.4 Example 137

4 Mixed Models for Categorical Data 153

4.1 Ordinal Logistic Regression (Fixed Effects Model) 153

4.2 Mixed Ordinal Logistic Regression 158

4.3 Mixed Models for Unordered Categorical Data 163

4.4 Practical Application and Interpretation 166

4.5 Example 169

5 Multi-Centre Trials and Meta-Analyses 183

5.1 Introduction to Multi-Centre Trials 183

5.2 The Implications of using Different Analysis Models 184

5.3 Example: A Multi-Centre Trial 188

5.4 Practical Application and Interpretation 195

5.5 Sample Size Estimation 197

5.6 Meta-Analysis 203

5.7 Example: Meta-analysis 204

6 Repeated Measures Data 215

6.1 Introduction 215

6.2 Covariance Pattern Models 218

6.3 Example: Covariance Pattern Models for Normal Data 228

6.4 Example: Covariance Pattern Models for Count Data 237

6.5 Random Coefficients Models 245

6.6 Examples of Random Coefficients Models 249

6.7 Sample Size Estimation 267

7 Cross-Over Trials 271

7.1 Introduction 271

7.2 Advantages of Mixed Models in Cross-Over Trials 272

7.3 The AB/BA Cross-Over Trial 272

7.4 Higher Order Complete Block Designs 279

7.5 Incomplete Block Designs 284

7.6 Optimal Designs 287

7.7 Covariance Pattern Models 290

7.8 Analysis of Binary Data 299

7.9 Analysis of Categorical Data 303

7.10 Use of Results from Random Effects Models in Trial Design 307

7.11 General Points 308

8 Other Applications of Mixed Models 311

8.1 Trials with Repeated Measurements within Visits 311

8.2 Multi-Centre Trials with Repeated Measurements 330

8.3 Multi-Centre Cross-Over Trials 337

8.4 Hierarchical Multi-Centre Trials and Meta-Analysis 338

8.5 Matched Case-Control Studies 339

8.6 Different Variances for Treatment Groups in a Simple Between-Patient Trial 351

8.7 Estimating Variance Components in an Animal Physiology Trial 355

8.8 Inter- and Intra-Observer Variation in Foetal Scan Measurements 361

8.9 Components of Variation and Mean Estimates in a Cardiology Experiment 363

8.10 Cluster Sample Surveys 365

8.11 Small Area Mortality Estimates 367

8.12 Estimating Surgeon Performance 371

8.13 Event History Analysis 372

8.14 A Laboratory Study Using a Within-Subject  Factorial Design 375

8.15 Bioequivalence Studies with Replicate Cross-Over Designs 378

8.16 Cluster Randomised Trials 392

8.17 Analysis of Bilateral Data xxx

8.18 Incomplete Block Designs xxx

9 Software for Fitting Mixed Models 401

9.1 Packages for Fitting Mixed Models 401

9.2 PROC MIXED 403

9.3 Using SAS to Fit Mixed Models to Non-Normal Data 423

9.4 PROC MCMC xxx

Glossary 431

References 435

Index 441

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