Preface

xiii

Abbreviations

xvii

1

Basic Ideas in Clinical Trial Design

1

1.1

Historical Perspective

1

1.2

Control Groups

2

1.3

Placebos and Blinding

3

1.4

Randomisation

4

1.4.1

Unrestricted Randomisation

5

1.4.2

Block Randomisation

5

1.4.3

Unequal Randomisation

6

1.4.4

Stratified Randomisation

7

1.4.5

Central Randomisation

8

1.4.6

Dynamic Allocation and Minimisation

9

1.4.7

Duster Randomization

10

1.5

Bias and Precision

11

1.6

Between- and Within-Patient Designs

12

1.7

Cross-Over Trials

14

1.8

Signal and Noise

15

1.8.1

Signal

15

1.8.2

Noise

15

1.8.3

Signal-to-Noise Ratio

15

1.9

Confirmatory and Exploratory Trials

16

1.10

Superiority, Equivalence and Non-Inferiority Trials

17

1.11

Data Types

18

1.12

Choice of Endpoint

20

1.12.1

Primary Variables

20

1.12.2

Secondary Variables

21

1.12.3

Surrogate Variables

21

1.12.4

Global Assessment Variables

22

1.12.5

Composite Variables

23

1.12.6

Categorisation

23

2

Sampling and Inferential Statistics

25

2.1

Sample and Population

25

2.2

Sample Statistics and Population Parameters

26

2.2.1

Sample and Population Distribution

26

2.2.2

Median and Mean

27

2.2.3

Standard Deviation

28

2.2.4

Notation

29

2.3

The Normal Distribution

29

2.4

Sampling and the Standard Error of the Mean

32

2.5

Standard Errors More Generally

35

2.5.1

The Standard Error for the Difference Between Two Means

35

2.5.2

Standard Errors for Proportions

38

2.5.3

The General Setting

38

3

Confidence Intervals and P-Values

39

3.1

Confidence Intervals for a Single Mean

39

3.1.1

The 95 per Cent Confidence Interval

39

3.1.2

Changing the Confidence Coefficient

41

3.1.3

Changing the Multiplying Constant

41

3.1.4

The Role of the Standard Error

43

3.2

Confidence Intervals for Other Parameters

44

3.2.1

Difference Between Two Means

44

3.2.2

Confidence Intervals for Proportions

45

3.2.3

General Case

46

3.3

Hypothesis Testing

47

3.3.1

Interpreting the P-Value

47

3.3.2

Calculating the P-Value

49

3.3.3

A Common Process

52

3.3.4

The Language of Statistical Significance

55

3.3.5

One-Tailed and Two-Tailed Tests

55

4

Tests for Simple Treatment Comparisons

57

4.1

The Unpaired t-Test

57

4.2

The Paired t-Test

58

4.3

Interpreting the t-Tests

61

4.4

The Chi-Square Test for Binary Data

63

4.4.1

Pearson Chi-Square

63

4.4.2

The Link to a Signal-to-Noise Ratio

66

4.5

Measures of Treatment Benefit

67

4.5.1

Odds Ratio (OR)

67

4.5.2

Relative Risk (RR)

68

4.5.3

Relative Risk Reduction (RRR)

69

4.5.4

Number Needed to Treat (NNT)

69

4.5.5

Confidence Intervals

70

4.5.6

Interpretation

71

4.6

Fisher’s Exact Test

71

4.7

The Chi-Square Test for Categorical and Ordinal Data

73

4.7.1

Categorical Data

73

4.7.2

Ordered Categorical (Ordinal) Data

75

4.7.3

Measures of Treatment Benefit for Categorical and Ordinal Data

76

4.8

Extensions for Multiple Treatment Groups

77

4.8.1

Between-Patient Designs and Continuous Data

77

4.8.2

With In-Patient Designs and Continuous Data

78

4.8.3

Binary, Categorical and Ordinal Data

79

4.8.4

Dose Ranging Studies

79

4.8.5

Further Discussion

80

5

Multi-Centre Trials

81

5.1

Rationale for Multi-Centre Trials

81

5.2

Comparing Treatments for Continuous Data

82

5.3

Evaluating Homogeneity of Treatment Effect

84

5.3.1

Treatment-by-Centre Interactions

84

5.3.2

Quantitative and Qualitative Interactions

87

5.4

Methods for Binary, Categorical and Ordinal Data

88

5.5

Combining Centres

88

6

Adjusted Analyses and Analysis of Covariance

91

6.1

Adjusting for Baseline Factors

91

6.2

Simple Linear Regression

92

6.3

Multiple Regression

94

6.4

Logistic Regression

96

6.5

Analysis of Covariance for Continuous Data

97

6.5.1

Main Effect of Treatment

97

6.5.2

Treatment-by-Covariate Interactions

99

6.5.3

A Single Model

101

6.5.4

Connection with Adjusted Analyses

102

6.5.5

Advantages of Analysis of Covariance

102

6.6

Binary, Categorical and Ordinal Data

104

6.7

Regulatory Aspects of the Use of Covariates

106

6.8

Connection Between AN0VA and ANC0VA

109

6.9

Baseline Testing

109

7

Intention-to-Treat and Analysis Sets

111

7.1

The Principle of Intention-to-Treat

111

7.2

The Practice of Intention-to-Treat

115

7.2.1

Full Analysis Set

115

7.2.2

Per-Protocol Set

117

7.2.3

Sensitivity

117

7.3

Missing Data

118

7.3.1

Introduction

118

7.3.2

Complete Cases Analysis

119

7.3.3

Last Observation Carried Forward (LOCF)

119

7.3.4

Success/Failure Classification

120

7.3.5

Worst Case/Best Case Imputation

120

7.3.6

Sensitivity

121

7.3.7

Avoidance of Missing Data

121

7.4

Intention-to-Treat and Time-to-Event Data

122

7.5

General Questions and Considerations

124

8

Power and Sample Size

127

8.1

Type I and Type II Errors

127

8.2

Power

128

8.3

Calculating Sample Size

131

8.4

Impact of Changing the Parameters

134

8.4.1

Standard Deviation

134

8.4.2

Event Rate in the Control Group

135

8.4.3

Clinically Relevant Difference

135

8.5

Regulatory Aspects

136

8.5.1

Power > 80 per Cent

136

8.5.2

Powering on the Per-Protocol Set

137

8.5.3

Sample Size Adjustment

137

8.6

Reporting the Sample Size Calculation

138

9

Statistical Significance and Clinical Importance

141

9.1

Link Between P-Values and Confidence Intervals

141

9.2

Confidence Intervals for Clinical Importance

143

9.3

Misinterpretation of the P-Value

144

9.3.1

Conclusions of Similarity

144

9.3.2

The Problem with 0.05

145

10

Multiple Testing

147

10.1

Inflation of the Type I Error

147

10.2

How does Multiplicity Arise

148

10.3

Regulatory View

148

10.4

Multiple Primary Endpoints

149

10.4.1

Avoiding Adjustment

149

10.4.2

Significance Needed on All Endpoints

149

10.4.3

Composite Endpoints

150

10.4.4

Variables Ranked According to Clinical Importance

150

10.5

Methods for Adjustment

152

10.6

Multiple Comparisons

153

10.7

Repeated Evaluation Overtime

154

10.8

Subgroup Testing

155

10.9

Other Areas for Multiplicity

157

10.9.1

Using Different Statistical Tests

157

10.9.2

Different Analysis Sets

158

11

Non-Parametric and Related Methods

159

11.1

Assumptions Underlying the t-Tests and Their Extensions

159

11.2

Homogeneity of Variance

160

11.3

The Assumption of Normality

160

11.4

Transformations

163

11.5

Non-Parametric Tests

166

11.5.1

The Mann-Whitney U-Test

166

11.5.2

The Wilcoxon Signed Rank Test

168

11.5.3

General Comments

169

11.6

Advantages and Disadvantages of Non-Parametric Methods

169

11.7

Outliers

170

12

Equivalence and Non-Inferiority

173

12.1

Demonstrating Similarity

173

12.2

Confidence Intervals for Equivalence

175

12.3

Confidence Intervals for Non-Inferiority

176

12.4

A P-Value Approach

178

12.5

Assay Sensitivity

180

12.6

Analysis Sets

182

12.7

The Choice of Δ

182

12.7.1

Bioequivalence

183

12.7.2

Therapeutic Equivalence

133

12.7.3

Non-Inferiority

184

12.7.4

The 10 per Cent Rule for Cure Rates

185

12.7.5

Biocreep and Constancy

186

12.8

Sample Size Calculations

187

12.9

Switching Between Non-Inferiority and Superiority

189

13

The Analysis of Survival Data

193

13.1

Time-to-Event Data and Censoring

193

13.2

Kaplan-Meier (KM) Curves

195

13.2.1

Plotting KM Curves

195

13.2.2

Event Rates and Relative Risk

196

13.2.3

Median Event Times

196

13.3

Treatment Comparisons

197

13.4

The Hazard Ratio

200

13.4.1

The Hazard Rate

200

13.4.2

Constant Hazard Ratio

201

13.4.3

Non-Constant Hazard Ratio

201

13.4.4

Link to Survival Curves

202

13.4.5

Calculating KM Curves

203

13.5

Adjusted Analyses

204

13.5.1

Stratified Methods

204

13.5.2

Proportional Hazards Regression

204

13.5.3

Accelerated Failure Time Model

207

13.6

Independent Censoring

208

13.7

Sample Size Calculations

209

14

Interim Analysis and Data Monitoring Committees

213

14.1

Stopping Rules for Interim Analysis

213

14.2

Stopping for Efficacy and Futility

214

14.2.1

Efficacy

214

14.2.2

Futility and Conditional Power

215

14.2.3

Some Practical Issues

216

14.2.4

Analyses Following Completion of Recruitment

217

14.3

Monitoring Safety

218

14.4

Data Monitoring Committees

219

14.4.1

Introduction and Responsibilities

219

14.4.2

Structure

220

14.4.3

Meetings and Recommendations

222

14.5

Adaptive Designs

223

14.5.1

Sample Size Re-Evaluation

223

14.5.2

Flexible Designs

224

15

Meta-Analysis

229

15.1

Definition

229

15.2

Objectives

231

15.3

Statistical Methodology

232

15.3.1

Methods for Combination

232

153.2

Confidence Intervals

233

15.3.3

Fixed and Random Effects

234

15.3.4

Graphical Methods

234

15.3.5

Detecting Heterogeneity

236

15.3.6

Robustness

236

15.4

Ensuring Scientific Validity

237

15.4.1

Planning

237

15.4.2

Publication Bias and Funnel Plots

238

15.5

Metd-Analysis in a Regulatory Setting

240

15.5.1

Retrospective Analyses

240

15.5.2

One Pivotal Study

241

16

The Role of Statistics and Statisticians

245

16.1

The Importance of Statistical Thinking at the Design Stage

245

16.2

Regulatory Guidelines

247

16.3

The Statistics Process

249

16.3.1

The Statistical Methods Section of the Protocol

250

16.3.2

The Statistical Analysis Plan

250

16.3.3

The Data Validation Plan

251

16.3.4

The Blind Review

251

16.3.6

Statistical Analysis

252

16.3.6

Reporting the Analysis

252

16.3.7

Pre-Planning

253

16.3.8

Sensitivity and Robustness

255

16.4

The Regulatory Submission

256

16.5

Publications and Presentations

257

References

261

Index

267