Chapman and Hall/CRC, 2010. – 461 p. – ISBN: 143980818X, 9781439808184While continuing to focus on methods of testing for two-sided equivalence, Testing Statistical Hypotheses of Equivalence and Noninferiority, Second Edition gives much more attention to noninferiority testing. It covers a spectrum of equivalence testing problems of both types, ranging from a one-sample problem with normally distributed observations of fixed known variance to problems involving several dependent or independent samples and multivariate data.
Along with expanding the material on noninferiority problems, this edition includes new chapters on equivalence tests for multivariate data and tests for relevant differences between treatments. A majority of the computer programs are now available not only in SAS or Fortran but also as R scripts or as shared objects that can be called within the R system.
This book provides readers with a rich repertoire of efficient solutions to specific equivalence and noninferiority testing problems frequently encountered in the analysis of real data sets. It first presents general approaches to problems of testing for noninferiority and two-sided equivalence. Each subsequent chapter then focuses on a specific procedure and its practical implementation. The last chapter describes basic theoretical results about tests for relevant differences as well as solutions for some specific settings often arising in practice. Drawing from real-life medical research, the author uses numerous examples throughout to illustrate the methods.Contents:
Introduction
Statistical meaning of the concepts of equivalence and noninferiority
Demonstration of equivalence as a basic problem of applied statistics
Major fields of application of equivalence tests
Role of equivalence/noninferiority studies in current medical research
Formulation of hypotheses
Choosing the main distributional parameter
Numerical specification of the limits of equivalence
General Techniques for Dealing with Noninferiority Problems
Standard solution in the case of location parameter families
Methods of constructing exact optimal tests for settings beyond the location-shift model
Large-sample solutions for problems inaccessible for exact constructions
Objective Bayesian methods
Improved nonrandomized tests for discrete distributions
Relationship between tests for noninferiority and two-sided equivalence tests
Halving alpha?
General Approaches to the Construction of Tests for Equivalence in the Strict Sense
The principle of confidence interval inclusion
Bayesian tests for two-sided 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
Noninferiority analogues of the tests derived in this chapter
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
Two-sample equivalence tests based on linear rank statistics
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
Multisample Tests for Equivalence
The intersection-union principle as a general solution to multisample 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
Equivalence Tests for Multivariate Data
Equivalence tests for several dependent samples from normal distributions
Multivariate two-sample tests 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
Testing for approximate compatibility of a genotype distribution with the Hardy–Weinberg condition
The Assessment of Bioequivalence
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
Tests for Relevant Differences between Treatments
Introduction
Exploiting the duality between testing for two-sided equivalence and existence of relevant differences
Solutions to some special problems of testing for relevant differencesAppendix A: Basic Theoretical Results
Appendix B: List of Special Computer Programs
Appendix C: Frequently Used Special Symbols and Abbreviations
References
Author Index
Subject Index
