Exploratory Subgroup Analyses in Clinical Research

Preface xi

Acknowledgments xiii

Acronyms xv

About the Companion Website xix

Introduction xxi

1 Some History of Subgroup Analysis 1

1.1 Introduction 1

1.2 Questionable Subgroup Analyses 5

1.2.1 Star Signs May Matter 5

1.2.2 Unjustified Under-treatment 7

1.2.3 Misinterpretation of Center Effects 8

1.2.4 The End of a Career 10

1.3 Encouraging Subgroup Analyses 12

1.3.1 Higher Efficacy 12

1.3.2 Harm Prevention 13

1.3.3 Avoiding Unnecessary Treatment 16

1.4 Subgroups and Drug Approvals 18

1.4.1 A Convincing Subgroup 18

1.4.2 Inconsistencies Across Regions 19

1.4.3 Detecting Non-responders 22

1.4.4 In Search for Benefit 26

1.5 Concluding Remarks 29

2 Objectives and Current Practice of Subgroup Analyses 31

2.1 Introduction 31

2.2 Objectives of Subgroup Analyses 32

2.3 Definitions Around Subgroups 34

2.4 Confounding 37

2.5 Two Types of Subgroup Analyses 39

2.6 Reporting of Subgroups 43

2.7 Concluding Remarks 45

3 Pitfalls of Subgroup Analyses 47

3.1 Introduction 47

3.2 Extreme Effect Estimates 48

3.3 Selection Bias 51

3.4 Reversal of Effects 53

3.5 Regression to the Mean 57

3.6 Simpson's Paradox 60

3.7 Post-hoc Analyses 63

3.8 Concluding Remarks 65

4 Subgroup Analysis and Modeling 67

4.1 Introduction 67

4.2 Modeling and Prediction 69

4.3 Subgroups and Hierarchical Models 72

4.3.1 Stein's Discovery 72

4.3.2 The Normal-Normal Hierarchical Model 73

4.4 Subgroups and Regression Models 76

4.4.1 Subgroups Defined in Terms of Variables 76

4.4.2 The Predicted Individual Treatment Effect 79

4.4.3 Comparison of the Two Options 83

4.5 Variable Selection in Regression 85

4.5.1 Classical Variable Selection 86

4.5.2 Regularized Estimators 87

4.5.3 Variable Selection and Confounding 88

4.6 Concluding Remarks 89

5 Hierarchical Models in Subgroup Analysis 91

5.1 Introduction 91

5.2 A General Hierarchical Model 94

5.2.1 Robbins' Theorem and Tweedie's Formula 94

5.2.2 Mixture Priors 97

5.2.3 The False Discovery Rate 100

5.3 Parameter Estimation 101

5.3.1 Posterior Means and Variances 101

5.3.2 Estimation Bias 104

5.3.3 Selection Bias 106

5.4 Case Studies 111

5.4.1 The Toxoplasmosis Dataset 111

5.4.2 The BCG Dataset 113

5.4.3 The Prostate Cancer Dataset 119

5.5 Concluding Remarks 124

6 Selection Bias in Regression 129

6.1 Introduction 129

6.2 Correction for Selection Bias 131

6.3 Variance Estimation 136

6.4 A Case Study 139

6.5 Concluding Remarks 144

7 The Predicted Individual Treatment Effect 147

7.1 Introduction 148

7.2 Definition of the PITE 149

7.3 Confidence Intervals of the PITE 150

7.3.1 MLE for the Full Model 151

7.3.2 MLE Under a Reduced Model 151

7.3.3 Scheffé Confidence Bounds 152

7.3.4 LASSO with Post-selection Intervals 152

7.3.5 Randomized LASSO 154

7.3.6 Simulation Study 154

7.3.7 Extension to Other Endpoints 157

7.4 Case Studies 159

7.4.1 An Alzheimer Dataset 160

7.4.2 The Prostate Cancer Study Again 161

7.4.3 Renal Safety of Contrast Media 165

7.5 Concluding Remarks 173

8 Prediction models 175

8.1 Introduction 176

8.2 Prediction Error 177

8.3 Model Selection or Averaging 180

8.4 Prediction Error of the PITE 182

8.5 A Case Study 187

8.6 Concluding Remarks 190

9 Outlook 193

Bibliography 197

Index 217