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Chapman and Hall/CRC, 2010. – 461 p. – ISBN: 143980818X,
9781439808184
While 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
differences
Appendix A: Basic Theoretical
Results
Appendix B: List of Special Computer Programs
Appendix C: Frequently Used Special Symbols and
Abbreviations
References
Author Index
Subject Index