Statistical Meta-Analysis With Applications

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A complete list of the titles in this series appears at the end of this volume.

Statistical Met a- Analysis With Applications

Joachim Hartung

Guido Knapp

Bimal K. Sinha

Dortmund University of Technology

Dortmund University of Technology

University of Maryland, Baltimore County

WlLEY

A JOHN WILEY &SONS, INC., PUBLICATION

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Library of Congress Cataloging-in-Publication Data:

Hartung, Joachim, Prof. Dr Statistical meta-analysis with applications / Joachim Hartung, Guido Knapp, Bimal K. Sinha.

Includes bibliographical references and index.

I . Statistical hypothesis testing. 2. Meta-analysis. I . Knapp, Guido. 11. Sinha, Bimal K., 1946- 111. Title. QA277.H373 2008 519.5'6-dc22 2008009435

p. cm.

ISBN 978-0-470-29089-7 (cloth)

Printed in the United States of America.

1 0 9 8 7 6 5 4 3 2 1

To my wife Barbel and my children Carola, Lisa, Jan, and Jorn

To my parents Magdalena and Wilhelm

In memory of Professor Shailes Bhusan Chaudhuri for his excellent academic training in statistics and parental love during my Ashutosh College years

CONTENTS

Preface xiii

1 Introduction 1

2 Various Measures of Effect Size

2.1 2.2 2.3 2.4

Effect Size Based on Means Effect Size Based on Proportions Effect Size Based on q Coefficient and Odds Ratio Effect Size Based on Correlation

3 Combining Independent Tests

3.1 Introduction 3.2 Description of Combined Tests

4 Methods of Combining Effect Sizes

13

13 17 19 22

25

25 27

35

vii

viii CONTENTS

5 Inference about a Common Mean of Several Univariate Normal Populations

5.1 Results on Common Mean Estimation 5.1.1

5.1.2 Properties of FGD Asymptotic Comparison of Some Estimates of Common Mean for k = 2 Populations Confidence Intervals for the Common Mean 5.3.1 Approximate Confidence Intervals 5.3.2 Exact Confidence Intervals

Appendix: Theory of Fisher’s Method

Small-Sample Comparison of PGD with Other Estimators

5.2

5.3

5.4 Applications

6 Tests of Homogeneity in Meta-Analysis

6.1 Model and Test Statistics 6.2 An Exact Test of Homogeneity 6.3 Applications

7 One-way Random Effects Model

7.1 7.2

7.3

Introduction Homogeneous Error Variances 7.2.1 Test for g: = 0 7.2.2 Approximate Tests for HO : u: = S > 0 and

Confidence Intervals for 02 7.2.3 Exact Test and Confidence Interval for 0; Based on a

Generalized P-value Approach 7.2.4 Tests and Confidence Intervals for p Heterogeneous Error Variances 7.3.1 Tests for Ho : CT; = 0 7.3.2 Tests for HO : CT: = 6 > 0 7.3.3 Nonnegative Estimation of r ~ ; and Confidence Intervals

43

45

45 48

52 54 55 56 59 60

63

64 67 68

73

73 76 76

77

81 85 85 85 85 87

7.3.4 Inference about p 93

CONTENTS

8 Combining Controlled Trials with Normal Outcomes

8.1 Difference of Means 8.1.1 Approximate Confidence Intervals for the Common

Mean Difference Exact Confidence Intervals for the Common Mean Difference

Analysis in the Random Effects Model

8.1.2

8.1.3 Testing Homogeneity 8.1.4

8.2 Standardized Difference of Means 8.3 Ratio of Means

9 Combining Controlled Trials with Discrete Outcomes

9.1

9.2

Binary Data 9.1.1 Effect Size Estimates 9.1.2 Homogeneity Tests 9.1.3 Binomial-Normal Hierarchical Models in Meta-

Analysis 9.1.4 An Example for Combining Results from Controlled

Clinical Trials 9.1.5 An Example for Combining Results from Observational

Studies Ordinal Data 9.2.1 Proportional Odds Model 9.2.2 Agresti’s ct 9.2.3 An Example of Combining Results from Controlled

Clinical Trials

10 Meta-Regression

10.1 Model with One Covariate 10.2 10.3 Further Extensions and Applications

Model with More Than One Covariate

11 Multivariate Meta-Analysis

1 1.1 1 1.2

Combining Multiple Dependent Variables from a Single Study Modeling Multivariate Effect Sizes 1 1.2.1 Multiple-Endpoint Studies

ix

97

98

100

100 102 103 107 110

113

116 116 118

118

120

121 122 123 124

124

127

128 132 136

139

141 143 144

1 1.2.2 Multiple-Treatment studies 149

X CONTENTS

12 Bayesian Meta-Analysis

12.1 12.2 12.3 12.4

A General Bayesian Model for Meta-Analysis under Normality Further Examples of Bayesian Analyses A Unified Bayesian Approach to Meta-Analysis Further Results on Bayesian Meta-Analysis

13 Publication Bias

14 Recovery of lnterblock Information

14.1 Notation and Test Statistics 14.2 BIBD with Fixed Treatment Effects

14.2.1 14.2.2 14.2.3 A Numerical Example

Combined Tests When b > u Combined Tests When b = v

15 Combination of Polls

15.1 Formulation of the Problem 15.2 Meta-Analysis of Polls

15.2.1 Estimation of Q 15.2.2 Confidence Interval for 6' 15.2.3 Hypothesis Testing for 6'

16 Vote Counting Procedures

17 Computational Aspects

17.1 Extracting Summary Statistics 17.2 Combining Tests 17.3 Generalized P-values 17.4 Combining Effect Sizes

17.4.1 Graphics 17.4.2 Sample Program in R 17.4.3 Sample Program in SAS

155

156 159 164 167

171

179

180 183 184 187 188

191 192 196 196 198 200

203

21 3

213 214 215 217 218 218 220

CONTENTS xi

18 Data Sets

18.1 Validity Studies 18.2 18.3 Dentifrice Data 18.4 18.5

Effects of Teacher Expectance on Pupil IQ

Effectiveness of Amlodipine on Work Capacity Effectiveness of Cisapride on the Treatment of Nonulcer Dyspepsia

Effectiveness of Misoprostol in Preventing Gastrointestinal Damage

18.6 Second-hand Smoking 18.7

18.8 Prevention of Tuberculosis

225

225 226 227 228

229 230

230 230

References

Index

233

245

PREFACE

Statistical Meta-Analysis with Applications combines our experiences on the topic and brings out a wealth of new information relevant for meta-analysis. Meta-analysis, a term coined by Glass (1976), and also known under different names such as research synthesis, research integration, and pooling of evidence, deals with the statistical analysis of a large collection of analysis results from individual studies fo r the purpose of integrating thefindings.

It is a common phenomenon that many studies are carried out over time and space on some important global issues with a common target or goal. As an example, we can cite the 19 studies carried out in the context of effects of second-hand smoking on women! Sometimes the studies may correspond to different experiment settings with one objective in mind. The main reason that many studies on a research topic are carried out rather than a single study is to strengthen the overall conclusion about a certain hypothesis or to negate it with a stronger conviction. When the results of these component studies, either in full or in summary form, are available, it is desirable that we combine the results of these studies in a meaningful way so as to arrive at a valid conclusion about the target parameter. The main object of statistical meta-analysis is precisely to provide methods to meaningfully combine the results from component studies.

There are many aspects of statistical meta-analysis which must be addressed in a book. Most of the concern arises from the nature of the underlying studies, the

xiii

xiv PREFACE

nature of information available from these studies, and also the nature of assumptions about the distributions of random variables arising in the studies. We have provided a complete treatment of all these aspects in this book.

Several new features of this book are worth mentioning. We have indicated a wide variety of applications of statistical meta-analysis ranging from business to education to environment to health sciences in both univariate and multivariate cases. Our treat- ment of the statistical meta-analysis about (1) the common mean of several univariate normal populations, ( 2 ) tests of homogeneity, (3) one-way random effects model, (4) categorical data, (5) recovery of interblock information, and (6) combination of polls is entirely new, based on many recent results by us and others on these topics. Other topics such as meta-regression, multivariate meta-analysis, and Bayesian meta- analysis also appear in completely new forms in our book. Another special feature of the book is the incorporation of a detailed discussion about computational aspects and related softwares to carry out statistical meta-analysis in practice. Readers will find many extra useful features in this book compared to the existing books on this subject. Our book complements the statistical methods and results described in an excellent Academic Press text Statistical Methods for Meta-Analysis by Hedges and Olkin (1985). We put it on record our indebtedness to this book and also to the ex- cellent edited volume The Handbook of Research Synthesis by Cooper and Hedges (1994) for many ideas on statistical meta-analysis. We have freely used some of the data sets and basic ideas from these two sources, and indirectly we owe a lot to Professors Harris Cooper, Larry Hedges, and Ingram Olkin!

Although some topics and chapters covered in this book require the knowledge of advanced statistical theory and methods, most of the meta-analysis methods de- scribed in the book can be understood and applied with a solid master's level back- ground in statistics. Parts of the book can also be used as a graduate text on this topic. We believe that practitioners of statistical meta-analysis will benefit a lot from this book owing to a host of worked-out examples from various contexts. The example data sets and the program code may be downloaded from G.K.'s website at http: //www . statistik .uni-dortmund. de/"knapp. Given that the possible application areas of meta-analysis are fairly broad, we have limited ourselves to a selected few applications depending on our own interest and expertise.

Financial support from the Dortmund University of Technology, Dortmund, Ger- many, and University of Maryland, Baltimore County, Maryland, are thankfully ac- knowledged. We are also grateful to Professors Leon Glaser, Satish Iyenger, and Neil Timm from the University of Pittsburgh for providing us with reprints of their papers on many aspects of multivariate meta-analysis. We are thankful to Professor Anirban Dasgupta of Purdue University for giving us his kind permission to include his work on combination ofpolls in this book. This certainly adds a new dimension! This book grew out of many lectures delivered on some of the topics of statistical meta-analysis at the University of Hong Kong (B.K.S.), Tunghai University (B.K.S.) (Taichung, Taiwan), University of South Australia (B.K.S), University of Tampere, Finland (G.K. and B.K.S.), University of Turku, Finland (G.K. and B.K.S.), United States Environmental Protection Agency (G.K. and B.K.S.) and the U.S. National Center for Health Statistics (G.K. and B.K.S.), and, of course, at our host institutions

PREFACE XV

(B.K.S. at the University of Maryland, Baltimore County, J.H. and G.K. at Dortmund University of Technology).

We mention with great pleasure the invitations received from all these places and the many comments we received from the audience, including our own students, which helped us to improve the contents and the presentations. We very much appreciate the excellent academic atmosphere at Dortmund University of Technology and University of Maryland, Baltimore County, where most of the book was written.

Last but not least, we express our sincere thanks to our understanding family mem- bers who occasionally had to put up with our changing moods due to the tremendous pressure in writing this book with as much information and accuracy as possible.

JOACHIM HARTUNG GUIDO KKAPP

BIMAL K. SINHA Dortmund, Germany Baltimore, Maryland June 2008