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Testing statistical hypotheses of equivalence and noninferiority. 2nd ed. (English) Zbl 1219.62002

Boca Raton, FL: CRC Press (ISBN 978-1-4398-0818-4/hbk; 978-1-4398-0819-1/ebook). xvi, 415 p. (2010).
This book deals to a great extent with testing equivalence and non-inferiority. This is the second edition, which differs considerably from the previous one published in 2003, see the review Zbl 1019.62001. It is evident that since the first edition there has been a huge development on testing equivalence and non-inferiority, and thus the number of clinical trials targeting equivalence or non-inferiority increases. The new edition covers all the developments from the first edition in a very satisfactory way. It is much larger than the first one, containing up to date material and covering all the issues worked out so far. Also the issue of testing non-inferiority which has found much more development since 2003 is now more extended in the new edition and is treated in more detail.
The book is organized in eleven chapters. There is also a large appendix with most of the mathematical details and computer programs to support the text. The author provides a guideline how to proceed with reading depending on the needs of the reader in the preface. The first chapter introduces the issues needed further. I found the discussion on why these approaches are needed very interesting and the motivations given are very useful to alert the reader. Chapter 2 discusses non-inferiority. Most of the material is new. Chapter 3 discusses issues related to testing equivalence. The next five chapters discuss equivalence tests in different design settings, like one sample tests (chapter 4), paired sample tests (chapter 5), independent sample tests (chapter 6), multiple sample tests (chapter 7), and multivariate data (chapter 8). Then in chapter 9 issues about testing goodness of fit are given, while chapter 10 discusses bioequivalence and chapter 11 deals with demonstrating relevant differences between treatments. In all chapter mathematical details are kept to a necessary minimum, and most of them have been moved to the appendix. However, the mathematical developments are not superficial, the reader must have a good quantitative background in order to follow.
The appendices contain much of the details of the mathematical derivations and some computer codes including S-PLUS, R, SAS, and FORTRAN, which are very helpful for practical reasons but also for illustration purposes. A helpful table in an appendix lists the programs and cross-references the pages where the programs are discussed, and all programs are available on a web-page controlled by the publisher. Throughout the book there are several occasions where the author uses simulation results to demonstrate the properties of the described tests. Finally I found it interesting that within the various chapters there are discussions of parametric tests based on different distributional assumptions, especially normality, tests of binary and categorical data, and rank based tests, and in general different types of data are treated.
Overall the book is neatly written with a lot of examples, and easy to follow. It is a useful reference for applied statisticians, especially those working in the pharmaceutical industry, as it brings together relevant theoretical results from hypothesis testing with equivalence testing procedures that are useful in many applied settings. It provides a detailed description of the work done in this area and hence it is a must for all libraries of medical schools, pharmaceutical companies and all those working in related areas. I think that this book remains a standard for texts on equivalence studies.

MSC:

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62F03 Parametric hypothesis testing
62P10 Applications of statistics to biology and medical sciences; meta analysis
62N03 Testing in survival analysis and censored data
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics

Citations:

Zbl 1019.62001

Software:

R; S-PLUS; SAS
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