Multiple Comparisons Using R / Edition 1

Multiple Comparisons Using R / Edition 1

by Frank Bretz, Torsten Hothorn, Torsten Hothorn, Peter Westfall
     
 

ISBN-10: 1584885742

ISBN-13: 9781584885740

Pub. Date: 08/02/2010

Publisher: Taylor & Francis

Adopting a unifying theme based on maximum statistics, Multiple Comparisons Using R describes the common underlying theory of multiple comparison procedures through numerous examples. It also presents a detailed description of available software implementations in R. The R packages and source code for the analyses are available at CRAN. R-project.org

After giving

Overview

Adopting a unifying theme based on maximum statistics, Multiple Comparisons Using R describes the common underlying theory of multiple comparison procedures through numerous examples. It also presents a detailed description of available software implementations in R. The R packages and source code for the analyses are available at CRAN. R-project.org

After giving examples, of multiplicity problems, the book covers general concepts and basic multiple comparisons procedures, including the Bonferroni method and Simes' test. It then shows how to perform parametric multiple comparisons in standard linear models and general parametric models. It also introduces the multcomp package in R, which offers a convenient interface to perform multiple comparisons in a general context. Following this theoretical framework, the book explores applications involving the Dunnett test, Tukey's all pairwise comparisons, and general multiple contrast tests for standard regression models, mixed-effects models, and parametric survival models. The last chapter reviews other multiple comparison procedures, such as resampling-based procedures.

Features

Covers a range of multiple comparison procedures, from the Bonferroni method and Simes' test to resampling and adaptive design methods

Discusses how to prevent finding artifacts through unreasonable or excessive data manipulation

Examines the ability to state rigorous claims in spite of the hazards of multiplicity

Provides the theoretical framework for various applications

Focuses on classical applications of multiple comparison procedures

Explores how to determine what is a safe and effective does as well as whether a new condition or treatment is successful

This self-contained introduction offers strategies for constructing multiple comparison procedures and illustrates the framework for multiple hypotheses testing in general parametric models. It is suitable for readers with R experience but limited knowledge Of multiple comparison procedures and vice versa.

Product Details

ISBN-13:
9781584885740
Publisher:
Taylor & Francis
Publication date:
08/02/2010
Edition description:
New Edition
Pages:
208
Product dimensions:
6.20(w) x 9.30(h) x 0.70(d)

Table of Contents

List of Figures ix

List of Tables xi

Preface xiii

1 Introduction 1

2 General Concepts 11

2.1 Error rates and general concepts 11

2.1.1 Error rates 11

2.1.2 General concepts 17

2.2 Construction methods 20

2.2.1 Union intersection test 20

2.2.2 Intersection union test 22

2.2.3 Closure principle 23

2.2.4 Partitioning principle 29

2.3 Methods based on Bonferroni's inequality 31

2.3.1 Bonferroni test 31

2.3.2 Holm procedure 32

2.3.3 Further topics 34

2.4 Methods based on Simes' inequality 35

3 Multiple Comparisons in Parametric Models 41

3.1 General linear models 41

3.1.1 Multiple comparisons in linear models 41

3.1.2 The linear regression example revisited using R 45

3.2 Extensions to general parametric models 48

3.2.1 Asymptotic results 48

3.2.2 Multiple comparisons in general parametric model 50

3.2.3 Applications 52

3.3 The multcomp package 53

3.3.1 The glht function 53

3.3.2 The summary method 59

3.3.3 The confint method 64

4 Applications 69

4.1 Multiple comparisons with a control 70

4.1.1 Dunnett test 71

4.1.2 Step-down Dunnett test procedure 77

4.2 All pairwise comparisons 82

4.2.1 Tukey test 82

4.2.2 Closed Tukey test procedure 93

4.3 Dose response analyses 99

4.3.1 A dose response study on litter weight in mice 100

4.3.2 Trend tests 103

1.4 Variable selection in regression models 108

4.5 Simultaneous confidence bands 111

4.6 Multiple comparisons under heteroscedasticity 114

4.7 Multiple comparisons in logistic regression models 118

4.8 Multiple comparisons in survival models 124

4.9 Multiple comparisons in mixed-effects models 125

5 Further Topics 127

5.1 Resampling-based multiple comparison procedures 127

5.1.1 Permutation methods 127

5.1.2 Using R for permutation multiple testing 137

5.1.3 Bootstrap testing - Brief overview 140

5.2 Group sequential and adaptive designs 140

5.2.1 Group sequential designs 141

5.2.2 Adaptive designs 150

5.3 Combining multiple comparisons with modeling 156

5.3.1 MCP-Mod: Dose response analyses under model uncertainty 157

5.3.2 A dose response example 162

Bibliography 167

Index 183

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