Methods and Applications of Sample Size Calculation and Recalculation in Clinical Trials 3030495272, 9783030495275

Table of contents :
Preface
Contents
Part IBasics
1 Introduction
1.1 Background and Overview
1.2 Examples
1.2.1 The ChroPac Trial
1.2.2 The Parkinson Trial
1.3 General Considerations When Calculating Sample Sizes
2 Statistical Test and Sample Size Calculation
2.1 The Main Principle of Statistical Testing
2.2 The Main Principle of Sample Size Calculation
Part IISample Size Calculation
3 Comparison of Two Groups for Normally Distributed Outcomes and Test for Difference or Superiority
3.1 Background and Notation
3.2 z-Test
3.3 t-Test
3.4 Analysis of Covariance
3.5 Bayesian Approach
3.5.1 Background
3.5.2 Methods
4 Comparison of Two Groups for Continuous and Ordered Categorical Outcomes and Test for Difference or Superiority
4.1 Background and Notation
4.2 Continuous Outcomes
4.3 Ordered Categorical Outcomes
4.3.1 Assumption-Free Approach
4.3.2 Assuming Proportional Odds
5 Comparison of Two Groups for Binary Outcomes and Test for Difference or Superiority
5.1 Background and Notation
5.2 Asymptotic Tests
5.2.1 Difference of Rates as Effect Measure
5.2.2 Risk Ratio as Effect Measure
5.2.3 Odds Ratio as Effect Measure
5.2.4 Logistic Regression
5.3 Exact Unconditional Tests
5.3.1 Basic Concepts
5.3.2 Fisher-Boschloo Test
6 Comparison of Two Groups for Time-to-Event Outcomes and Test for Difference or Superiority
6.1 Background and Notation
6.1.1 Time-to-Event Data
6.1.2 Sample Size Calculation for Time-to-Event Data
6.2 Exponentially Distributed Time-to-Event Data
6.3 Time-to-Event Data with Proportional Hazards
6.3.1 Approach of Schoenfeld
6.3.2 Approach of Freedman
7 Comparison of More Than Two Groups and Test for Difference
7.1 Background and Notation
7.2 Normally Distributed Outcomes
7.3 Continuous Outcomes
7.4 Binary Outcomes
7.4.1 Chi-Square Test
7.4.2 Cochran-Armitage Test
7.5 Time-to-Event Outcomes
8 Comparison of Two Groups and Test for Non-Inferiority
8.1 Background and Notation
8.2 Normally Distributed Outcomes
8.2.1 Difference of Means as Effect Measure
8.2.2 Ratio of Means as Effect Measure
8.3 Continuous and Ordered Categorical Outcomes
8.4 Binary Outcomes
8.4.1 Asymptotic Tests
8.4.2 Exact Unconditional Tests
8.5 Time-to-Event Outcomes
9 Comparison of Three Groups in the Gold Standard Non-Inferiority Design
9.1 Background and Notation
9.2 Net Effect Approach
9.3 Fraction Effect Approach
10 Comparison of Two Groups for Normally Distributed Outcomes and Test for Equivalence
10.1 Background and Notation
10.2 Difference of Means as Effect Measure
10.3 Ratio of Means as Effect Measure
11 Multiple Comparisons
11.1 Background and Notation
11.2 Generally Applicable Sample Size Calculation Methods and Applications
11.2.1 Methods
11.2.2 Applications
11.3 Multiple Endpoints
11.3.1 Background and Notation
11.3.2 Methods
11.4 More Than Two Groups
11.4.1 Background and Notation
11.4.2 Dunnett Test
12 Assessment of Safety
12.1 Background and Notation
12.2 Testing Hypotheses on the Event Probability
12.2.1 Exact Binomial Test
12.2.2 Approximate Score Test
12.3 Estimating the Event Probability with Specified Precision
12.3.1 Exact Clopper-Pearson Confidence Interval
12.3.2 Approximate Wilson Score Confidence Interval
12.4 Observing at Least One Event with Specified Probability
13 Cluster-Randomized Trials
13.1 Background and Notation
13.2 Normally Distributed Outcomes
13.2.1 Cluster-Level Analysis
13.2.2 Individual-Level Analysis
13.2.3 Dealing with Unequal Cluster Size
13.3 Other Scale Levels of the Outcome
14 Multi-Regional Trials
14.1 Background and Notation
14.2 Demonstrating Consistency of Global Results and Results for a Specified Region
14.3 Demonstrating a Consistent Trend Across All Regions
15 Integrated Planning of Phase II/III Drug Development Programs
15.1 Background and Notation
15.2 Optimizing Phase II/III Programs
16 Simulation-Based Sample Size Calculation
Part IIISample Size Recalculation
17 Basic Concepts of Sample Size Recalculation
Part IVBlinded Sample Size Recalculation in Internal Pilot Study Designs
18 Internal Pilot Study Designs
19 A General Approach for Controlling the Type I Error Rate for Blinded Sample Size Recalculation
20 Comparison of Two Groups for Normally Distributed Outcomes and Test for Difference or Superiority
20.1 t-Test
20.1.1 Background and Notation
20.1.2 Blinded Sample Size Recalculation
20.1.3 Type I Error Rate
20.1.4 Power and Sample Size
20.2 Analysis of Covariance
20.2.1 Background and Notation
20.2.2 Blinded Sample Size Recalculation
20.2.3 Type I Error Rate
20.2.4 Power and Sample Size
21 Comparison of Two Groups for Binary Outcomes and Test for Difference or Superiority
21.1 Background and Notation
21.2 Asymptotic Tests
21.2.1 Difference of Rates as Effect Measure
21.2.2 Risk Ratio or Odds Ratio as Effect Measure
21.3 Fisher-Boschloo Test
22 Comparison of Two Groups for Normally Distributed Outcomes and Test for Non-Inferiority
22.1 t-Test
22.1.1 Background and Notation
22.1.2 Blinded Sample Size Recalculation
22.1.3 Type I Error Rate
22.1.4 Power and Sample Size
22.2 Analysis of Covariance
23 Comparison of Two Groups for Binary Outcomes and Test for Non-Inferiority
23.1 Background and Notation
23.2 Difference of Rates as Effect Measure
23.2.1 Blinded Sample Size Recalculation
23.2.2 Type I Error Rate
23.2.3 Power and Sample Size
23.3 Risk Ratio or Odds Ratio as Effect Measure
24 Comparison of Two Groups for Normally Distributed Outcomes and Test for Equivalence
25 Regulatory and Operational Aspects
26 Concluding Remarks
Part VUnblinded Sample Size Recalculation in Adaptive Designs
27 Group Sequential and Adaptive Designs
27.1 Group Sequential Designs
27.2 Adaptive Designs
27.2.1 Combination Function Approach
27.2.2 Conditional Error Function Approach
28 Sample Size Recalculation Based on Conditional Power
28.1 Background and Notation
28.2 Using the Interim Effect Estimate
28.3 Using the Initially Specified Effect
28.4 Using Prior Information as Well as the Interim Effect Estimate
29 Sample Size Recalculation Based on Optimization
30 Regulatory and Operational Aspects
31 Concluding Remarks
Appendix R Software Code
A.1 Output of Sample Size Functions
A.2 Remarks on the Rounding Strategy
A.3 R Code for Chapter 3
A.4 R Code for Chapter 4
A.5 R Code for Chapter 5
A.6 R Code for Chapter 6
A.7 R Code for Chapter 7
A.8 R Code for Chapter 8
A.9 R Code for Chapter 9
A.10 R Code for Chapter 10
A.11 R Code for Chapter 11
A.12 R Code for Chapter 12
A.13 R Code for Chapter 13
A.14 R Code for Chapter 14
A.15 R Code for Chapter 15
A.16 R Code for Chapter 20
A.17 R Code for Chapter 21
A.18 R Code for Chapter 22
A.19 R Code for Chapter 23
A.20 R Code for Chapter 27
A.21 R Code for Chapter 28
A.22 R Code for Chapter 29
References
Index