Testing Statistical Hypotheses of Equivalence

Equivalence testing has grown significantly in importance over the last two decades, especially as its relevance to a variety of applications has become understood. Yet published work on the general methodology remains scattered in specialists' journals, and for the most part, it focuses on the relatively narrow topic of bioequivalence assessment. With a far broader perspective, Testing Statistical Hypotheses of Equivalence provides the first comprehensive treatment of statistical equivalence testing. The author addresses a spectrum of specific, two-sided equivalence testing problems, from the one-sample problem with normally distributed observations of fixed known variance to problems involving several samples and multivariate data. The treatment includes a concise review of basic mathematical results on optimal tests for equivalence, and the author makes available on the Internet a collection of computer programs that allow easy implementation of the methods presented. In a field as complex and rich in potential applications as equivalence testing, Testing Statistical Hypotheses of Equivalence stands alone as a coherent reference that furnishes both the theoretical and practical tools needed for dealing with equivalence trials of any complexity and in any phase.

Table of Contents:
INTRODUCTION Demonstration of Equivalence as a Basic Problem of Applied Statistics Formalization of the Statistical Notion of Equivalence Major Fields of Application of Equivalence Tests Choosing the Main Distributional Parameter Numerical Specification of the Limits of Equivalence METHODS FOR ONE-SIDED EQUIVALENCE PROBLEMS Objective of a One-Sided Equivalence Trial and Formulation of Hypotheses Standard Solution for Location Parameter Families Exact Two-Sample Tests for Binomial Distributions GENERAL APPROACHES TO THE CONSTRUCTION OF TESTS FOR EQUIVALENCE IN THE STRICT SENSE The Principle of Confidence Interval Inclusion Bayesian Tests for Equivalence The Classical Approach to Deriving Optimal Parametric Tests for Equivalence Hypotheses Construction of Asymptotic Tests for Equivalence EQUIVALENCE TESTS FOR SELECTED ONE-PARAMETER PROBLEMS The One-Sample Problem with Normally Distributed Observations of Known Variance Test for Equivalence of a Hazard Rate to Some Given Reference Value with Exponentially Distributed Survival Times Testing for Equivalence of a Single Binomial Proportion to a Fixed Reference Success Probability Confidence-Interval Inclusion Rules as Asymptotically UMP Tests for Equivalence EQUIVALENCE TESTS FOR DESIGNS WITH PAIRED OBSERVATIONS Sign Test for Equivalence Equivalence Tests for the McNemar Setting Paired t-Test for Equivalence Signed Rank Test for Equivalence A Generalization of the Signed Rank Test for Equivalence for Noncontinuous Data EQUIVALENCE TESTS FOR TWO UNRELATED SAMPLES Two-Sample t-Test for Equivalence Mann-Whitney Test for Equivalence A distribution-Free Two-Sample Equivalence Test Allowing for Arbitrary Patterns of Ties Testing for Dispersion Equivalence of Two Gaussian Distributions Equivalence Tests for Two Binomial Samples Log-Rank Test for Equivalence of Two Survivor Functions MULTI-SAMPLE TESTS FOR EQUIVALENCE The Intersection-Union Principle as a General Solution to Multi-Sample Equivalence Problems F-Test for Equivalence of k Normal Distributions Modified Studentized Range Test for Equivalence Testing for Dispersion Equivalence of More than Two Gaussian Distributions A Nonparametric k-Sample Test for Equivalence TESTS FOR ESTABLISHING GOODNESS OF FIT Testing for Equivalence of a Single Multinomial Distribution with a Fully Specified Reference Distribution Testing for Approximate Collapsibility of Multiway Contingency Tables Establishing Goodness of Fit of Linear Models for Normally Distributed Data THE ASSESSMENT OF BIO-EQUIVALENCE Introduction Methods of Testing for Average Bioequivalence Individual Bioequivalence: Criteria and Testing Procedures Approaches to Defining and Establishing Population Bioequivalence Bioequivalence Assessment as a Problem of Comparing Bivariate Distributions APPENDIX REFERENCES INDEX

Review :
"The main value of the book is in its rather comprehensive and explicit treatment of various tests for equivalence problems. The book is very carefully written and mathematically correct..applied (bio-)statisticians may find this book a helpful manual for various testing procedures in the field of equivalence testing. These procedures are very carefully described and are accompanied by SAS of Fortran code. More mathematically oriented readers may regard this book as a good source of examples, and the thorough discussion of relevant practical questions in the field might stimulate them to doing further research in this area." -Journal of the American Statistical Association, March 2004 "The book is well organized for the applied statistician with an interest in the theoretical background for statistical procedures. What is especially useful about this book for the applied statistician is that the author weaves into the presentation of the equivalence tests, discussions of power, and sample size as well as simulation results that evaluate the small sample properties of the tests. In addition, a location on the World Wide Web where one can find SAS programs to facilitate the implementation of these tests is provided... Wellek has provided a text on equivalence testing that the applied statistician will find useful both as a theory underlying equivalence testing as well as a source of equivalence tests and tools for their implementation for a wide variety of situations." -Journal of Biopharmaceutical Statistics "The publication of a book specifically dealing with the statistical issues and methods surrounding the assessment of equivalence is timely...the primary objective of this book isstated to be: 'a systematic and comprehensive account of testing procedures for the alternative hypothesis'. It achieves this well." -Current Medical Research Opinion (CMRO) 2004 .." this book provides the reader with the opportunity to do equivalence testing for various statistical problems. The author has helpfully provided a collection of computer programs (in SAS and Fortran) that allow for easy implementation of the methods presented...I was left feeling that this book provides a good grounding in statistical techniques to do hypothesis testing in equivalence trials." -Pharmaceutical Statistics, 2003 "Wellek has done a commendable service to the academic community by providing the first comprehensive treatment of testing hypotheses of equivalence, since most of the work in this area so far is confined to research journals. Overall, this excellent book has great potential for applications and should interest students and researchers alike. Summing Up: Highly recommended." - D.V. Chopra in CHOICE" this book has explained well with examples and case studies the topics Researchers will find this book thought provoking." - Journal of Statistical Computation & Simulation