Design and Analysis of Experiments in the Health Sciences

GERALD VAN BELLE, PhD, is Professor Emeritus in the Departments of Biostatistics and Environmental and Occupational Health Sciences at the University of Washington. A Fellow of the American Statistical Association and the American Association for the Advancement of Science, he has published more than 140 articles in the areas of experimental design and data characterization as well as analysis with application to neurodegenerative diseases, effects of air pollution on health and toxicology, and clinical trials in resuscitation outcomes research. KATHLEEN F. KERR, PhD, is Associate Professor of Biostatistics at the University of Washington. A former Burroughs Wellcome postdoctoral fellow in mathematics and molecular biology, Dr. Kerr currently serves as associate editor of PLoS Genetics and Statistical Applications in Genetics and Molecular Biology. Her research interests include gene expression microarrays, statistical genetics, experimental design, and biomarker research.

Preface xiii

1 The Basics 1

1.1 Four Basic Questions 1

1.2 Variation 4

1.3 Principles of Design and Analysis 5

1.4 Experiments and Observational Studies 9

1.5 Illustrative Applications of Principles 11

1.6 Experiments in the Health Sciences 12

1.7 Adaptive Allocation 15

1.7.1 Equidistribution 15

1.7.2 Adaptive Allocation Techniques 16

1.8 Sample Size Calculations 18

1.9 Statistical Models for the Data 20

1.10 Analysis and Presentation 22

1.10.1 Graph the Data in Several Ways 22

1.10.2 Assess Assumptions of the Statistical Model 22

1.10.3 Confirmatory and Exploratory Analysis 23

1.10.4 Missing Data Need Careful Accounting 23

1.10.5 Statistical Software 24

1.11 Notes 24

1.11.1 Characterization Studies 24

1.11.2 Additional Comments on Balance 25

1.11.3 Linear and Nonlinear Models 25

1.11.4 Analysis of Variance versus Regression Analysis 26

1.12 Summary 26

1.13 Problems 26

2 Completely Randomized Designs 31

2.1 Randomization 31

2.2 Hypotheses and Sample Size 32

2.3 Estimation and Analysis 32

2.4 Example 34

2.5 Discussion and Extensions 36

2.5.1 Preparing Data for Computer Analysis 36

2.5.2 Treatment Assignment in this Example 37

2.5.3 Check on Randomization 37

2.5.4 Partitioning the Treatment Sum of Squares 37

2.5.5 Alternative Endpoints 38

2.5.6 Dummy Variables 38

2.5.7 Contrasts 39

2.6 Randomization 41

2.7 Hypotheses and Sample Size 41

2.8 Estimation and Analysis 41

2.9 Example 42

2.10 Discussion and Extensions 44

2.10.1 Two Roles for ANCOVA 44

2.10.2 Partitioning of Sums of Squares 45

2.10.3 Assumption of Parallelism 46

2.11 Notes 47

2.11.1 Constrained Randomization 47

2.11.2 Assumptions of the Analysis of Variance and Covariance 48

2.11.3 When the Assumptions Don’t Hold 49

2.11.4 Alternative Graphical Displays 50

2.11.5 Sample Sizes for More Than Two Levels 51

2.11.6 Limitations of Computer Output 51

2.11.7 Unequal Sample Sizes 51

2.11.8 Design Implications of the CRD 51

2.11.9 Power and Alternative Hypotheses 52

2.11.10 Regression or Analysis of Variance? 52

2.11.11 Bioassay 52

2.12 Summary 53

2.13 Problems 53

3 Randomized Block Designs 63

3.1 Randomization 64

3.2 Hypotheses and Sample Size 64

3.3 Estimation and Analysis 64

3.4 Example 65

3.5 Discussion and Extensions 67

3.5.1 Evaluating Model Assumptions 67

3.5.2 Multiple Comparisons 69

3.5.3 Number of Treatments and Block Size 71

3.5.4 Missing Data 71

3.5.5 Does It Always Pay to Block? 71

3.5.6 Concomitant Variables 72

3.5.7 Imbalance 74

3.6 Randomization 77

3.7 Hypotheses and Sample Size 77

3.8 Estimation and Analysis 77

3.9 Example 77

3.10 Discussion and Extensions 79

3.10.1 Implications of the Model 79

3.10.2 Number of Latin Squares 79

3.11 Randomization 80

3.12 Hypotheses and Sample Size 81

3.13 Estimation and Analysis 82

3.14 Example 82

3.15 Discussion and Extensions 85

3.15.1 Partially Balanced Incomplete Block Designs 85

3.16 Notes 86

3.16.1 Analysis Follows Design 86

3.16.2 Relative Efficiency 86

3.16.3 Additivity of the Model 87

3.17 Summary 88

3.18 Problems 88

4 Factorial Designs 93

4.1 Randomization 95

4.2 Hypotheses and Sample Size 95

4.3 Estimation and Analysis 96

4.4 Example 1 97

4.5 Example 2 100

4.6 Notes 103

4.6.1 Regression Analysis Approaches 103

4.6.2 Almost Factorial 105

4.6.3 Design Structure and Factor Structure 105

4.6.4 Effect and Interaction Tables 105

4.6.5 Balanced Design 105

4.6.6 Missing Data 106

4.6.7 Fixed, Random, and Mixed Effects Models 106

4.6.8 Fractional Factorials 108

4.7 Summary 109

4.8 Problems 110

5 Multilevel Designs 117

5.1 Randomization 118

5.2 Hypotheses and Sample Size 118

5.3 Estimation and Analysis 119

5.4 Example 121

5.5 Discussion and Extensions 127

5.5.1 Whole-Plot and Split-Plot Variability 127

5.5.2 Getting the Computer to Do the Right Analysis 128

5.6 Notes 129

5.6.1 Fractional Factorials—Example 129

5.6.2 Missing Data 129

5.7 Summary 130

5.8 Problems 130

6 Repeated Measures Designs 135

6.1 Randomization 136

6.2 Hypotheses and Sample Size 136

6.3 Estimation and Analysis 137

6.4 Example 139

6.5 Discussion and Extensions 142

6.6 Notes 143

6.6.1 RBD and RMD 143

6.6.2 Missing Data: The Fundamental Challenge in RMD 143

6.6.3 Correlation Structure 144

6.6.4 Derived Variable Analysis 144

6.7 Summary 144

6.8 Problems 145

7 Randomized Clinical Trials 149

7.1 Endpoints 151

7.2 Randomization 152

7.3 Hypotheses and Sample Size 153

7.4 Follow-Up 154

7.5 Estimation and Analysis 154

7.6 Examples 155

7.7 Discussion and Extensions 159

7.7.1 Statistical Significance and Clinical Importance 159

7.7.2 Ethics 161

7.7.3 Reporting 162

7.8 Notes 163

7.8.1 Multicenter Trials 163

7.8.2 International Harmonization 167

7.8.3 Data Safety Monitoring 167

7.8.4 Ancillary Studies 168

7.8.5 Subgroup Analysis and Data Mining 168

7.8.6 Meta-Analysis 169

7.8.7 Authorship and Recognition 169

7.8.8 Communication 169

7.8.9 Data Sharing 170

7.8.10 N-of-1 Trials 170

7.9 Resources 171

7.10 Summary 171

7.11 Problems 171

8 Microarrays 179

8.1 Introduction 179

8.2 Genes, Gene Expression, and Microarrays 179

8.2.1 Genes and Gene Expression 179

8.2.2 Gene Expression Microarrays 180

8.3 Examples of Microarray Studies 186

8.4 Replication and Sample Size 188

8.5 Blocking and Microarrays 189

8.6 Randomization and Microarrays 190

8.7 Microarray Data Analysis Issues 191

8.7.1 Image Analysis 191

8.7.2 Data Preprocessing 193

8.7.3 Identifying Differentially Expressed Genes 196

8.7.4 Multiple Testing 196

8.7.5 Gene Set Analysis 198

8.7.6 The Class Prediction Problem 198

8.8 Data Analysis Example 200

8.9 Notes 202

8.9.1 Sample Size 202

8.9.2 FDR Estimation 202

8.9.3 Evaluation of Data Preprocessing Methods 203

8.10 Summary 203

8.11 Problems 203

Bibliography 207

Author Index 217

Subject Index 223