Description
Book SynopsisThis book provides an extensive overview of the principles and methods of sample size calculation and recalculation in clinical trials. Appropriate calculation of the required sample size is crucial for the success of clinical trials. At the same time, a sample size that is too small or too large is problematic due to ethical, scientific, and economic reasons. Therefore, state-of-the art methods are required when planning clinical trials.
Part I describes a general framework for deriving sample size calculation procedures. This enables an understanding of the common principles underlying the numerous methods presented in the following chapters. Part II addresses the fixed sample size design, where the required sample size is determined in the planning stage and is not changed afterwards. It covers sample size calculation methods for superiority, non-inferiority, and equivalence trials, as well as comparisons between two and more than two groups. A wide range of further topics is discussed, including sample size calculation for multiple comparisons, safety assessment, and multi-regional trials. There is often some uncertainty about the assumptions to be made when calculating the sample size upfront. Part III presents methods that allow to modify the initially specified sample size based on new information that becomes available during the ongoing trial. Blinded sample size recalculation procedures for internal pilot study designs are considered, as well as methods for sample size reassessment in adaptive designs that use unblinded data from interim analyses. The application is illustrated using numerous clinical trial examples, and software code implementing the methods is provided.
The book offers theoretical background and practical advice for biostatisticians and clinicians from the pharmaceutical industry and academia who are involved in clinical trials. Covering basic as well as more advanced and recently developed methods, it is suitable for beginners, experienced applied statisticians, and practitioners. To gain maximum benefit, readers should be familiar with introductory statistics. The content of this book has been successfully used for courses on the topic.
Trade Review“The R source code is shown by chapter, well-documented, and easy to find and follow as brief descriptions and necessary specifications for the function calls are given by means of comments. … a wide area of application fields is covered and exhaustive literature references for further reading are given. … The presentation of the material is very reader-friendly, easily accessible and pedagogical … . It is likewise highly recommended … . This is an effective and nicely written reference textbook.” (Oke Gerke, ISCB News, iscb.info, Vol. 72, December, 2021)
Table of ContentsPart I Basics
1 Introduction
1.1 Background and outline
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 II Sample 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 and 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 Background
5.3.2 Fisher-Boschloo test
6 Comparison of two groups for time-to-event outcomes and test for differences 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 Analysis with chi-square test
7.4.2 Analysis with 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
8.2.2 Ratio of means
8.3 Continuous and ordered categorical outcomes
8.4 Binary outcomes
8.4.1 Analysis with asymptotic tests
8.4.1.1 Difference of rates as effect measure
8.4.1.2 Risk ratio as effect measure
8.4.1.3 Odds ratio as effect measure
8.4.2 Exact unconditional tests
8.4.2.1 Background
8.4.2.2 Difference of rates as effect measure
8.4.2.3 Risk ratio as effect measure
8.4.2.4 Odds ratio as effect measure
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
10.3 Ratio of means
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
12.3 Estimating the occurrence probability of an event with specified precision
12.4 Observing at least one event
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 Sample size calculation for demonstrating consistency of global results and results for a specified region
14.3 Sample size calculation for 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 III Sample size recalculation
17 Background
Part IIIA Blinded sample size recalculation in internal pilot study designs
18 Background and notation
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 variance estimation
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 variance estimation
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 and 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 variance estimation
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
23.3 Risk ratio and 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 IIIB Unblinded sample size recalculation in adaptive designs
27 Background and notation
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 estimate of the effect
28.3 Using the initially specified effect
28.4 Using prior information as well as the interim effect estimate
29 Sample size recalculation by optimization
30 Regulatory and operational aspects
31 Concluding remarks
Appendix: Selected R software code
References
