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# Introduction to Meta-Analysis

## byMichael Borenstein, Larry V. Hedges, Julian P. T. Higgins

### Hardcover | April 13, 2009

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*Introduction to Meta-Analysis*:

- Outlines the role of meta-analysis in the research process
- Shows how to compute effects sizes and treatment effects
- Explains the fixed-effect and random-effects models for synthesizing data
- Demonstrates how to assess and interpret variation in effect size across studies
- Clarifies concepts using text and figures, followed by formulas and examples
- Explains how to avoid common mistakes in meta-analysis
- Discusses controversies in meta-analysis
- Features a web site with additional material and exercises

*A superb combination of lucid prose and informative graphics, written by four of the world’s* *leading experts on all aspects of meta-analysis. Borenstein, Hedges, Higgins, and Rothstein* *provide a refreshing departure from cookbook approaches with their clear explanations of* *the what and why of meta-analysis. The book is ideal as a course textbook or for self-study.* *My students, who used pre-publication versions of some of the chapters, raved about the* *clarity of the explanations and examples.* David Rindskopf, Distinguished Professor of Educational Psychology, City University of New York, Graduate School and University Center, & Editor of the Journal of Educational and Behavioral Statistics*.*

*The approach taken by* Introduction to Meta-analysis *is intended to be primarily conceptual,* *and it is amazingly successful at achieving that goal. The reader can comfortably skip the* *formulas and still understand their application and underlying motivation. For the more* *statistically sophisticated reader, the relevant formulas and worked examples provide a superb* *practical guide to performing a meta-analysis. The book provides an eclectic mix of examples* *from education, social science, biomedical studies, and even ecology. For anyone considering* *leading a course in meta-analysis, or pursuing self-directed study, Introduction to* *Meta-analysis would be a clear first choice.* Jesse A. Berlin, ScD

Introduction to Meta-Analysis *is an excellent resource for novices and experts alike. The book* *provides a clear and comprehensive presentation of all basic and most advanced approaches* *to meta-analysis. This book will be referenced for decades.* Michael A. McDaniel, Professor of Human Resources and Organizational Behavior, Virginia Commonwealth University

### Details & Specs

The following ISBNs are associated with this title:

ISBN - 10:0470057246

ISBN - 13:9780470057247

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### Extra Content

Table of Contents

List of Tables

Acknowledgements

Preface

PART 1: INTRODUCTION

1 HOW A META-ANALYSIS WORKS

Introduction

Individual studies

The summary effect

Heterogeneity of effect sizes

Summary points

2 WHY PERFORM A META-ANALYSIS

Introduction

The SKIV meta-analysis

Statistical significance

Clinical importance of the effect

Consistency of effects

Summary points

PART 2: EFFECT SIZE AND PRECISION

3 OVERVIEW

Treatment effects and effect sizes

Parameters and estimates

Outline

4 EFFECT SIZES BASED ON MEANS

Introduction

Raw (unstandardized) mean difference D

Standardized mean difference, D and G

Response ratios

Summary points

5 EFFECT SIZES BASED ON BINARY DATA (2×2 TABLES)

Introduction

Risk ratio

Odds ratio

Risk difference

Choosing an effect size index

Summary points

6 EFFECT SIZES BASED ON CORRELATIONS

Introduction

Computing R

Other approaches

Summary points

7 CONVERTING AMONG EFFECT SIZES

Introduction

Converting from the log odds ratio to D

Converting from D to the log odds ratio

Converting from R to D

Converting from D to R

Summary points

8 FACTORS THAT AFFECT PRECISION

Introduction

Factors that affect precision

Sample size

Study design

Summary points

9 CONCLUDING REMARKS

Further reading

PART 3: FIXED-EFFECT VERSUS RANDOM-EFFECTS MODELS

10 OVERVIEW

Introduction

Nomenclature

11 FIXED-EFFECT MODEL

Introduction

The true effect size

Impact of sampling error

Performing a fixed-effect meta-analysis

Summary points

12 RANDOM-EFFECTS MODEL

Introduction

The true effect sizes

Impact of sampling error

Performing a random-effects meta-analysis

Summary points

13 FIXED EFFECT VERSUS RANDOM-EFFECTS MODELS

Introduction

Definition of a summary effect

Estimating the summary effect

Extreme effect size in large study

Confidence interval

The null hypothesis

Which model should we use?

Model should not be based on the test for heterogeneity

Concluding remarks

Summary points

14 WORKED EXAMPLES (PART 1)

Introduction

Worked example for continuous data (Part 1)

Worked example for binary data (Part 1)

Worked example for correlational data (Part 1)

Summary points

PART 4: HETEROGENEITY

15 OVERVIEW

Introduction

16 IDENTIFYING AND QUANTIFYING HETEROGENEITY

Introduction

Isolating the variation in true effects

Computing Q

Estimating tau-squared

The I 2 statistic

Comparing the measures of heterogeneity

Confidence intervals for T 2

Confidence intervals (or uncertainty intervals) for I 2

Summary points

17 PREDICTION INTERVALS

Introduction

Prediction intervals in primary studies

Prediction intervals in meta-analysis

Confidence intervals and prediction intervals

Comparing the confidence interval with the prediction interval

Summary points

18 WORKED EXAMPLES (PART 2)

Introduction

Worked example for continuous data (Part 2)

Worked example for binary data (Part 2)

Worked example for correlational data (Part 2)

Summary points

19 SUBGROUP ANALYSES

Introduction

Fixed-effect model within subgroups

Computational models

Random effects with separate estimates of T 2

Random effects with pooled estimate of T 2

The proportion of variance explained

Mixed-effect model

Obtaining an overall effect in the presence of subgroups

Summary points

20 META-REGRESSION

Introduction

Fixed-effect model

Fixed or random effects for unexplained heterogeneity

Random-effects model

Statistical power for regression

Summary points

21 NOTES ON SUBGROUP ANALYSES AND META-REGRESSION

Introduction

Computational model

Multiple comparisons

Software

Analysis of subgroups and regression are observational

Statistical power for subgroup analyses and meta-regression

Summary points

PART 5: COMPLEX DATA STRUCTURES

22 OVERVIEW

23 INDEPENDENT SUBGROUPS WITHIN A STUDY

Introduction

Combining across subgroups

Comparing subgroups

Summary points

24 MULTIPLE OUTCOMES OR TIME POINTS WITHIN A STUDY

Introduction

Combining across outcomes or time-points

Comparing outcomes or time-points within a study

Summary points

25 MULTIPLE COMPARISONS WITHIN A STUDY

Introduction

Combining across multiple comparisons within a study

Differences between treatments

Summary points

26 NOTES ON COMPLEX DATA STRUCTURES

Introduction

Combined effect

Differences in effect

PART 6: OTHER ISSUES

27 OVERVIEW

28 VOTE COUNTING – A NEW NAME FOR AN OLD PROBLEM

Introduction

Why vote counting is wrong

Vote-counting is a pervasive problem

Summary points

29 POWER ANALYSIS FOR META-ANALYSIS

Introduction

A conceptual approach

In context

When to use power analysis

Planning for precision rather than for power

Power analysis in primary studies

Power analysis for meta-analysis

Power analysis for a test of homogeneity

Summary points

30 PUBLICATION BIAS

Introduction

The problem of missing studies

Methods for addressing bias

Illustrative example

The model

Getting a sense of the data

Is the entire effect an artifact of bias

How much of an impact might the bias have?

Summary of the findings for the illustrative example

Small study effects

Concluding remarks

Summary points

PART 7: ISSUES RELATED TO EFFECT SIZE

31 OVERVIEW

32 EFFECT SIZES RATHER THAN P -VALUES

Introduction

Relationship between p-values and effect sizes

The distinction is important

The p-value is often misinterpreted

Narrative reviews vs. meta-analyses

Summary points

33 SIMPSON’S PARADOX

Introduction

Circumcision and risk of HIV infection

An example of the paradox

Summary points

34 GENERALITY OF THE BASIC INVERSE-VARIANCE METHOD

Introduction

Other effect sizes

Other methods for estimating effect sizes

Individual participant data meta-analyses

Bayesian approaches

Summary points

PART 8: FURTHER METHODS

35 OVERVIEW

36 META-ANALYSIS METHODS BASED ON DIRECTION AND P -VALUES

Introduction

Vote counting

The sign test

Combining p-values

Summary points

37 FURTHER METHODS FOR DICHOTOMOUS DATA

Introduction

Mantel-Haenszel method

One-step (Peto) formula for odds ratio

Summary points

38 PSYCHOMETRIC META-ANALYSIS

Introduction

The attenuating effects of artifacts

Meta-analysis methods

Example of psychometric meta-analysis

Comparison of artifact correction with meta-regression

Sources of information about artifact values

How heterogeneity is assessed

Reporting in psychometric meta-analysis

Concluding remarks

Summary points

PART 9: META-ANALYSIS IN CONTEXT

39 OVERVIEW

40 WHEN DOES IT MAKE SENSE TO PERFORM A META-ANALYSIS?

Introduction

Are the studies similar enough to combine?

Can I combine studies with different designs?

How many studies are enough to carry out a meta-analysis?

Summary points

41 REPORTING THE RESULTS OF A META-ANALYSIS

Introduction

The computational model

Forest plots

Sensitivity analysis

Summary points

42 CUMULATIVE META-ANALYSIS

Introduction

Why perform a cumulative meta-analysis?

Summary points

43 CRITICISMS OF META-ANALYSIS

Introduction

One number cannot summarize a research field

The file drawer problem invalidates meta-analysis

Mixing apples and oranges

Garbage in, garbage out

Important studies are ignored

Meta-analysis can disagree with randomized trials

Meta-analyses are performed poorly

Is a narrative review better?

Concluding remarks

Summary points

PART 10: RESOURCES AND SOFTWARE

44 SOFTWARE

Introduction

Three examples of meta-analysis software

The software

Comprehensive meta-analysis (CMA) 2.0

Revman 5.0

StataTM macros with Stata 10.0

Summary points

45 BOOKS, WEB SITES AND PROFESSIONAL ORGANIZATIONS

Books on systematic review methods

Books on meta-analysis

Web sites

INDEX