Methods and Applications of Sample Size Calculation and Recalculation in Clinical Trials

ISBN-13: 9783030495275 / Angielski / Twarda / 2020 / 396 str.

Meinhard Kieser

Recenzje

"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)

Spis treści

Part 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

O autorze

Prof. Dr. Meinhard Kieser is a Professor of Medical Biometry and Director of the Institute of Medical Biometry and Informatics at the University of Heidelberg. He studied Mathematics and received his PhD in Medical Biometry in 1992. He then worked for more than 15 years as a biostatistician and Head of Biometrics in the pharmaceutical industry. Professor Kieser has comprehensive experience in the planning and analysis of clinical trials and has been a member of numerous independent data monitoring committees. He serves as an associate editor for Pharmaceutical Statistics and the Journal of Biopharmaceutical Statistics. His main research areas are biostatistical methods for clinical trials, including sample size calculation and recalculation, and methods for evidence synthesis.

Blurb

This 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.