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Taylor & Francis
Multiple Comparisons Using R / Edition 1

Multiple Comparisons Using R / Edition 1


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Product Details

ISBN-13: 9781584885740
Publisher: Taylor & Francis
Publication date: 08/02/2010
Edition description: New Edition
Pages: 205
Product dimensions: 6.20(w) x 9.30(h) x 0.70(d)

About the Author

Frank Bretz is Global Head of the Statistical Methodology group at Novartis Pharma AG in Basel, Switzerland. He is also an adjunct professor at the Hannover Medical School in Germany.

Torsten Hothorn is a professor of biostatistics in the Faculty of Mathematics, Computer Science and Statistics at Ludwig-Maximilians-Universität München in Germany.

Peter Westfall is James and Marguerite Niver and Paul Whitfield Horn Professor of Statistics and associate director of the Center for Advanced Analytics and Business Intelligence at Texas Tech University in Lubbock, USA.

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

What People are Saying About This

From the Publisher

The book is primarily targeted at practitioners who will find the illustrative examples utilizing real data helpful. Methodologically interested readers are provided with interesting concepts and a good survey on multiple comparisons literature in the bibliography.
—Thorsten Dickhaus, Biometrics, September 2012

Nice stand-out features of the book are its clarity and conciseness, its coverage of group sequential and adaptive designs, and the nice illustration through actual problems using R software and the CRAN library of R routines for multiple testing. … useful for statistical consultants and graduate students who perhaps cannot afford a SAS license. … Another nice feature of the book is its organization.
—Michael R. Chernick, Technometrics, August 2011

An excellent first chapter gently explains to the reader why multiple comparison techniques are required. Successive chapters delve into more and more sophisticated scenarios for multiple comparisons. The benefits of applying multiple testing in the context of ordinary linear models are in my opinion not often stressed in undergraduate statistics courses. It was refreshing to see an entire chapter devoted to this idea. The over 150 references make this an excellent entry point into the literature … Do consider it [the book] if you are a user of R, who is also a researcher or teacher of linear modelling, and needs to apply multiple comparisons in their work. Your work will be the better for it.
—Alice Richardson, International Statistical Review (2011), 79

I found the book to be a rare gem; it is very seldom indeed that a reviewer has difficulty finding things to criticize. The book is concise, but covers all the common topics and a little more. It is simply written, yet manages to explain the key concepts remarkably well. Above all, it introduces a comprehensible structure that unifies seemingly different methodologies into a single system. … I believe this book could be useful to all those seeking guidance [on] the multitude of multiplicity correcting procedures. … The authors managed to create a fine balance between theory and practical applications … The book is warmly recommended.
—Vera Lisovskaja, Journal of Biopharmaceutical Statistics, Vol. 21, 2011

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