Statistical Issues in Drug Development

Professor Stephen Senn (MSc, PhD, CStat) is a statistical consultant, researcher and blogger. He has extensive experience in both academia and industry, and is recognized worldwide for his studies in statistical methodology applied to drug development. Professor Senn has been the recipient of national and international awards, including the 1st George C Challis award for Biostatistics at the University of Florida, and the Bradford Hill Medal of the Royal Statistical Society. He is a Fellow of the Royal Society of Edinburgh and an honorary life member of Statisticians in the Pharmaceutical Industry (PSI) and the International Society for Clinical Biostatistics (ISCB) and has honorary professorships in statistics at The University of Sheffield and the University of Edinburgh.

Preface to the Third Edition

Preface to the Second Edition xiii

Preface to the First Edition xvii

Acknowledgements xxi

1 Introduction 1

1.1 Drug development 1

1.2 The role of statistics in drug development 2

1.3 The object of this book 3

1.4 The author’s knowledge of statistics in drug development 4

1.5 The reader and his or her knowledge of statistics 4

1.6 How to use the book 5

References 6

Part 1 Four Views of Statistics in Drug Development: Historical, Methodological, Technical and Professional 9

2 A Brief and Superficial History of Statistics for Drug Developers 11

2.1 Introduction 11

2.2 Early Probabilists 12

2.3 James Bernoulli (1654–1705) 13

2.4 John Arbuthnott (1667–1753) 14

2.5 The mathematics of probability in the late 17th, the 18th and early 19th centuries 14

2.6 Thomas Bayes (1701–1761) 15

2.7 Adolphe Quetelet (1796–1874) 16

2.8      George Biddell Airy (1801-1892)

2.9 Francis Galton (1822–1911) 16

2.10 Karl Pearson (1857–1936) 17

2.11 ‘Student’ (1876–1937) 17

2.12 R.A. Fisher (1890–1962) 17

2.13 Modern mathematical statistics 18

2.14 Medical statistics 19

2.15 Statistics in clinical trials today 20

2.16 The current debate 21

2.17 A living science 21

2.18 Further reading 23

References 23

3 Design and Interpretation of Clinical Trials as Seen by a Statistician 27

3.1 Prefatory warning 27

3.2 Introduction 27

3.3 Defining effects 28

3.4 Practical problems in using the counterfactual argument 28

3.5 Regression to the mean 29

3.6 Control in clinical trials 33

3.7 Randomization 34

3.8 Blinding 36

3.9 Using concomitant observations 37

3.10 Measuring treatment effects 38

3.11 Data generation models 39

3.12 In conclusion 41

3.13 Further reading 41

References 41

4 Probability, Bayes, P-values, Tests of Hypotheses and Confidence Intervals 43

4.1 Introduction 43

4.2 An example 44

4.3 Odds and sods 44

4.4 The Bayesian solution to the example 45

4.5 Why don’t we regularly use the Bayesian approach in clinical trials? 46

4.6 A frequentist approach 47

4.7 Hypothesis testing in controlled clinical trials 48

4.8 Significance tests and P-values 49

4.9 Confidence intervals and limits and credible intervals 50

4.10 Some Bayesian criticism of the frequentist approach 51

4.11 Decision theory 51

4.12 Conclusion 52

4.13 Further reading 52

References 53

5 The Work of the Pharmaceutical Statistician 55

5.1 Prefatory remarks 55

5.2 Introduction 56

5.3 In the beginning 57

5.4 The trial protocol 57

5.5 The statistician’s role in planning the protocol 58

5.6 Sample size determination 59

5.7 Other important design issues 60

5.8 Randomization 60

5.9 Data collection preview 61

5.10 Performing the trial 61

5.11 Data analysis preview 61

5.12 Analysis and reporting 62

5.13 Other activities 63

5.14 Statistical research 63

5.15 Further reading 64

References 65

Part 2 Statistical Issues: Debatable and Controversial Topics in Drug Development 67

6 Allocating Treatments to Patients in Clinical Trials 69

6.1 Background 69

6.2 Issues 71

References 87

6.A Technical appendix 88

7 Baselines and Covariate Information 95

7.1 Background 95

7.2 Issues 98

References 108

7.A Technical appendix 109

8 The Measurement of Treatment Effects 113

8.1 Background 113

8.2 Issues 114

References 129

8.A Technical appendix 130

9 Demographic Subgroups: Representation and Analysis 133

9.1 Background 133

9.2 Issues 134

References 144

9.A Technical appendix 145

10 Multiplicity 149

10.1 Background 149

10.2 Issues 150

References 161

10.A Technical appendix 162

11 Intention to Treat, Missing Data and Related Matters 165

11.1 Background 165

11.2 Issues 167

References 178

11.A Technical appendix 180

12 One-sided and Two-sided Tests and other Issues to Do with Significance and P-values 183

12.1 Background 183

12.2 Issues 184

References 192

13 Determining the Sample Size 195

13.1 Background 195

13.2 Issues 198

References 211

14 Multicentre Trials 213

14.1 Background 213

14.2 Issues 213

References 230

14.A Technical appendix 231

15 Active Control Equivalence Studies 235

15.1 Background 235

15.2 Issues 237

References 247

15.A Technical appendix 249

16 Meta-Analysis 251

16.1 Background 251

16.2 Issues 253

References 268

16.A Technical appendix 270

17 Cross-over Trials 273

17.1 Background 273

17.2 Issues 275

References 284

18 n-of-1 Trials 287

18.1 Background 287

18.2 Issues 289

References 293

19 Sequential Trials 295

19.1 Background 295

19.2 Issues 302

References 313

20 Dose-finding 317

20.1 Background 317

20.2 Issues 319

References 334

21 Concerning Pharmacokinetics and Pharmacodynamics 337

21.1 Background 337

21.2 Issues 343

References 358

22 Bioequivalence Studies 361

22.1 Background 361

22.2 Issues 362

References 379

23 Safety Data, Harms, Drug Monitoring and Pharmaco-epidemiology 383

23.1 Background 383

23.2 Issues 388

References 403

24 Pharmaco-economics and Portfolio Management 405

24.1 Background 405

24.2 Issues 407

References 429

25 Concerning Pharmacogenetics, Pharmacogenomics and Related Matters 433

25.1 Background 433

25.2 Issues 437

References 450

25.A Technical appendix 451

Glossary 453

Index 483