Success Probability Estimation With Applications to Clinical Trials

DANIELE DE MARTINI, PhD, is Assistant Professor in the Department of Statistics and Quantitative Methods at the University of Milano-Bicocca in Italy. He is also a member of the American Statistical Association, Society for Clinical Trials, and Italian Statistical Society.

Preface xv

Acknowledgments xvii

Acronyms xix

Introduction xxi

I.1 Overview of clinical trials xxii

I.2 Success rates of clinical trials xxiv

I.3 Success probability xxv

I.4 Starting from practice xxvii

PART I SUCCESS PROBABILITY ESTIMATION IN PLANNING AND ANALYZING CLINICAL TRIALS

1 Basic statistical tools 3

1.1 Pointwise estimation 4

1.2 Confidence interval estimation, conservative estimation 6

1.3 The statistical hypotheses, the statistical test and the type I error for one-tailed tests 10

1.4 The power function and the type II error 11

1.5 The p-value 14

1.6 The success probability and its estimation 17

1.7 Basic statistical tools for two tailed tests 19

1.8 Other statistical hypotheses and tests 23

2 Reproducibility Probability Estimation 25

2.1 Pointwise RP estimation 26

2.2 RP-testing 29

2.3 The RP estimate and the p-value 32

2.4 Statistical lower bounds for the RP 35

2.5 The stability criterion for statistical significance 37

2.6 Other stability criteria for statistical significance 40

2.7 Comparing stability criteria 43

2.8 Regulatory agencies and the single study 45

2.9 The RP for two-tailed tests 46

2.10 Discussing Situation I in Section I.4.1 49

3 Sample Size Estimation 51

3.1 The classical paradigm of sample size determination 52

3.2 SP estimation for adapting the sample size 55

3.3 Launching the trial in practice 57

3.4 Practical aspects of SSE 60

3.5 Frequentist conservative SSE 67

3.6 Optimal frequentist CSSE 70

3.7 Bayesian CSSE 75

3.8 A comparison of CSSE strategies 80

3.9 Discussing Situations I and II in Section I.4 83

3.10 Sample size estimation for the two-tailed setting 85

4 Robustness and Corrections in Sample Size Estimation 89

4.1 CSSE strategies with different effect sizes in phases II and III 90

4.2 Comparing CSSE strategies in different Scenarios 91

4.3 Corrections for CSSE strategies 94

4.4 A comparison among Corrected CSSE strategies 97

PART II SUCCESS PROBABILITY ESTIMATION FOR SOME WIDELY USED STATISTICAL TESTS

5 General parametric SP estimation 105

5.1 The parametric model 105

5.2 Power, SP and noncentrality parameter estimation 106

5.3 RP estimation and testing 107

5.4 Sample size estimation 108

5.5 Statistical tests included in the model 109

6 SP estimation for Student’s t statistical tests 113

6.1 Test for two means equal variances 114

6.1.1 Power and RP estimation 114

6.2 Test for two means unequal variances 117

6.3 On Student’s t RP estimates 120

7 SP estimation for Gaussian distributed test statistics 123

7.1 Test for two proportions 123

7.2 Test for survival: the log-rank test 127

8 SP estimation for Chi-square statistical tests 133

8.1 Test for two multinomial distributions: 2 x C comparative trial 133

8.2 Test for S couples of binomial distributions: the Mantel-Haenszel test 137

8.3 On χ² RP estimates 141

9 General nonparametric SP estimation with - applications to the Wilcoxon test 143

9.1 The nonparametric model 144

9.2 General nonparametric SP estimation 145

9.3 The Wilcoxon rank-sum test 146

A Tables of quantiles 161

B Tables of RP estimates for the one-tailed Z test 169

References 179

Topic index 185

Author index 193

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