Statistical Meta-Analysis with Applications

This book combines the authors' experiences on the topic and brings out a wealth of new information relevant to the study of meta-analysis. Applications ranging from business to education to environment to health sciences in both univariate and multivariate cases are presented alongside and subservient to theory. The treatment of the common mean of univariate normal populations, tests of homogeneity, one-way random effects model, categorical data, recovery of inter-block information, and combination of polls is entirely new. A special feature includes the incorporation of detailed discussions on the computational aspects and related software to carry out statistical meta-analysis in practice. Most of the methods described can be understood and applied with a solid master's level background in statistics. Practitioners will benefit from the book owing to a host of worked-out examples from numerous and various contexts.

JOACHIM HARTUNG, PhD, is Professor in the Department of Statistics at the Dortmund University of Technology, Germany. He has published several books and two dozen journal articles in the field of statistics. GUIDO KNAPP, PhD, is Assistant Professor in the Department of Statistics at the Dortmund University of Technology, Germany. Dr. Knapp's areas of research interest include variance component models, error components regression models, meta-analysis, and flexible design in clinical trials. BIMAL K. SINHA, PhD, is Presidential Research Professor of Statistics in the Department of Mathematics and Statistics at the University of Maryland at Baltimore County (UMBC). A Fellow of both the Institute of Mathematical Statistics and the American Statistical Association, Dr. Sinha's research specializes in the areas of multivariate analysis, mixed linear models, decision theory, robustness, and environmental statistics.

Preface	p. xiii
Introduction	p. 1
Various Measures of Effect Size	p. 13
Effect Size Based on Means	p. 13
Effect Size Based on Proportions	p. 17
Effect Size Based on [open phi] Coefficient and Odds Ratio	p. 19
Effect Size Based on Correlation	p. 22
Combining Independent Tests	p. 25
Introduction	p. 25
Description of Combined Tests	p. 27
Methods of Combining Effect Sizes	p. 35
Inference about a Common Mean of Several Univariate Normal Populations	p. 43
Results on Common Mean Estimation	p. 45
Small-Sample Comparison of [mu subscript GD] with Other Estimators	p. 45
Properties of [mu subscript GD]	p. 48
Asymptotic Comparison of Some Estimates of Common Mean for [kappa] = 2 Populations	p. 52
Confidence Intervals for the Common Mean	p. 54
Approximate Confidence Intervals	p. 55
Exact Confidence Intervals	p. 56
Applications	p. 59
Theory of Fisher's Method	p. 60
Tests of Homogeneity in Meta-Analysis	p. 63
Model and Test Statistics	p. 64
An Exact Test of Homogeneity	p. 67
Applications	p. 68
One-Way Random Effects Model	p. 73
Introduction	p. 73
Homogeneous Error Variances	p. 76
Test for [sigma subscript a superscript 2] = 0	p. 76
Approximate Tests for H[subscript 0]: [sigma subscript a superscript 2] = [delta] > 0 and Confidence Intervals for [sigma subscript a superscript 2]	p. 77
Exact Test and Confidence Interval for [sigma subscript a superscript 2] Based on a Generalized P-value Approach	p. 81
Tests and Confidence Intervals for [mu]	p. 85
Heterogeneous Error Variances	p. 85
Tests for H[subscript 0]: [sigma subscript a superscript 2] = 0	p. 85
Tests for H[subscript 0]: [sigma subscript a superscript 2] = [delta] > 0	p. 85
Nonnegative Estimation of [sigma subscript a superscript 2] and Confidence Intervals	p. 87
Inference about [mu]	p. 93
Combining Controlled Trials with Normal Outcomes	p. 97
Difference of Means	p. 98
Approximate Confidence Intervals for the Common Mean Difference	p. 100
Exact Confidence Intervals for the Common Mean Difference	p. 100
Testing Homogeneity	p. 102
Analysis in the Random Effects Model	p. 103
Standardized Difference of Means	p. 107
Ratio of Means	p. 110
Combining Controlled Trials with Discrete Outcomes	p. 113
Binary Data	p. 116
Effect Size Estimates	p. 116
Homogeneity Tests	p. 118
Binomial-Normal Hierarchical Models in Meta-Analysis	p. 118
An Example for Combining Results from Controlled Clinical Trials	p. 120
An Example for Combining Results from Observational Studies	p. 121
Ordinal Data	p. 122
Proportional Odds Model	p. 123
Agresti's [alpha]	p. 124
An Example of Combining Results from Controlled Clinical Trials	p. 124
Meta-Regression	p. 127
Model with One Covariate	p. 128
Model with More Than One Covariate	p. 132
Further Extensions and Applications	p. 136
Multivariate Meta-Analysis	p. 139
Combining Multiple Dependent Variables from a Single Study	p. 141
Modeling Multivariate Effect Sizes	p. 143
Multiple-Endpoint Studies	p. 144
Multiple-Treatment studies	p. 149
Bayesian Meta-Analysis	p. 155
A General Bayesian Model for Meta-Analysis under Normality	p. 156
Further Examples of Bayesian Analyses	p. 159
A Unified Bayesian Approach to Meta-Analysis	p. 164
Further Results on Bayesian Meta-Analysis	p. 167
Publication Bias	p. 171
Recovery of Interblock Information	p. 179
Notation and Test Statistics	p. 180
BIBD with Fixed Treatment Effects	p. 183
Combined Tests When b > v	p. 184
Combined Tests When b = v	p. 187
A Numerical Example	p. 188
Combination of Polls	p. 191
Formulation of the Problem	p. 192
Meta-Analysis of Polls	p. 196
Estimation of [theta]	p. 196
Confidence Interval for [theta]	p. 198
Hypothesis Testing for [theta]	p. 200
Vote Counting Procedures	p. 203
Computational Aspects	p. 213
Extracting Summary Statistics	p. 213
Combining Tests	p. 214
Generalized P-values	p. 215
Combining Effect Sizes	p. 217
Graphics	p. 218
Sample Program in R	p. 218
Sample Program in SAS	p. 220
Data Sets	p. 225
Validity Studies	p. 225
Effects of Teacher Expectance on Pupil IQ	p. 226
Dentifrice Data	p. 227
Effectiveness of Amlodipine on Work Capacity	p. 228
Effectiveness of Cisapride on the Treatment of Nonulcer Dyspepsia	p. 229
Second-hand Smoking	p. 230
Effectiveness of Misoprostol in Preventing Gastrointestinal Damage	p. 230
Prevention of Tuberculosis	p. 230
References	p. 233
Index	p. 245
Table of Contents provided by Ingram. All Rights Reserved.

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Statistical Meta-Analysis with Applications

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