Introduction to Meta-Analysis
Books
- Published: 13 March 2009
- ISBN: 0470057246
- Author(s): Michael Borenstein, Larry V. Hedges, Julian P. T. Higgins, Hannah R. Rothstein
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- 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
List of FiguresList 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
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