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Statistical Meta-Analysis with Applications



Statistical Meta-Analysis with Applications

Joachim Hartung, Guido Knapp, Bimal K. Sinha

ISBN: 978-1-118-21096-3 September 2011 248 Pages

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An accessible introduction to performing meta-analysis across various areas of research

The practice of meta-analysis allows researchers to obtain findings from various studies and compile them to verify and form one overall conclusion. Statistical Meta-Analysis with Applications presents the necessary statistical methodologies that allow readers to tackle the four main stages of meta-analysis: problem formulation, data collection, data evaluation, and data analysis and interpretation. Combining the authors' expertise on the topic with a wealth of up-to-date information, this book successfully introduces the essential statistical practices for making thorough and accurate discoveries across a wide array of diverse fields, such as business, public health, biostatistics, and environmental studies.

Two main types of statistical analysis serve as the foundation of the methods and techniques: combining tests of effect size and combining estimates of effect size. Additional topics covered include:

  • Meta-analysis regression procedures
  • Multiple-endpoint and multiple-treatment studies

  • The Bayesian approach to meta-analysis

  • Publication bias

  • Vote counting procedures

  • Methods for combining individual tests and combining individual estimates

  • Using meta-analysis to analyze binary and ordinal categorical data

Numerous worked-out examples in each chapter provide the reader with a step-by-step understanding of the presented methods. All exercises can be computed using the R and SAS software packages, which are both available via the book's related Web site. Extensive references are also included, outlining additional sources for further study.

Requiring only a working knowledge of statistics, Statistical Meta-Analysis with Applications is a valuable supplement for courses in biostatistics, business, public health, and social research at the upper-undergraduate and graduate levels. It is also an excellent reference for applied statisticians working in industry, academia, and government.


1. Introduction.

2. Various Measures of Effect Size.

2.1 Effect Size based on Means.

2.2 Effect Size based on Proportions.

2.3 Effect Size based on - Coefficient and Odds Ratio.

2.4 Effect Size based on Correlation.

3. Combining Independent Tests.

3.1 Introduction.

3.2 Description of Combined Tests.

4. Methods of Combining Effect Sizes.

5. Inference about a Common Mean of Several Univariate Normal Populations.

5.1 Results on Common Mean Estimation.

5.2 Asymptotic Comparison of Some Estimates of Common Mean for k = 2 Populations.

5.3 Confidence Intervals for the Common Mean.

5.4 Applications.

5.5 Appendix: Theory of Fisher’s Method.

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 Introduction.

7.2 Homogeneous Error Variances.

7.3 Heterogeneous Error Variances.

8. Combining Controlled Trials with Normal Outcomes.

8.1 Difference of Means.

8.2 Standardized Difference of Means.

8.3 Ratio of Means.

9. Combining Controlled Trials with Discrete Outcomes.

9.1 Binary Data.

9.2 Ordinal Data.

10. Meta-Regression.

10.1 Model with One Covariate.

10.2 Model with More Than One Covariate.

10.3 Further Extensions and Applications.

11. Multivariate Meta-Analysis.

11.1 Combining Multiple Dependent Variables from a Single Study.

11.2 Modeling Multivariate Effect Sizes.

12. Bayesian Meta-Analysis.

12.1 A General Bayesian Model for Meta-Analysis under Normality.

12.2 Further Examples of Bayesian Analyses.

12.3 A Unified Bayesian Approach to Meta-Analysis.

12.4 Further Results on Bayesian Meta-Analysis.

13. Publication Bias.

14. Recovery of Inter-Block Information.

14.1 Notations and Test Statistics.

14.2 BIBD with Fixed Treatment Effects.

15. Combination of Polls.

15.1 Formulation of the Problem.

15.2 Meta-Analysis of Polls.

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.

18. Data Sets.

18.1 Validity Studies.

18.2 Effects of Teacher Expectance on Pupil IQ.

18.3 Dentifrice Data.

18.4 Effectiveness of Amlodipine on Work Capacity.

18.5 Effectiveness of Cisapride on the Treatment of Nonulcer Dyspepsia.

18.6 Secondhand Smoking.

18.7 Effectiveness of Misoprostol in Preventing Gastrointestinal Damage.

18.8 Prevention of Tuberculosis.



"The strength of this book is certainly the detailed development and presentation of inference for normal fixed and random effects models as applied in meta-analysis and similar studies, such as inter-laboratory studies. A particularly well done part of the book centers on homogeneity testing and on confidence interval estimation of the so-called heterogeneity parameter in the standard random effects model." (Journal of Biopharmaceutical Statistics, January 2010)

"The authors have written a good guide to a broad section of the methods available for statistical meta-analysis." (Mathematical Reviews, 2009)

"[The authors], active researchers themselves, have done a commendable job in writing this introductory book noted for its clarity and style of presentation and coverage of some totally new topics." (Choice, April 2009)