Introduction to Meta-Analysis
April 2009, ©2008
- 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 Tables
PART 1: INTRODUCTION
1 HOW A META-ANALYSIS WORKS
The summary effect
Heterogeneity of effect sizes
2 WHY PERFORM A META-ANALYSIS
The SKIV meta-analysis
Clinical importance of the effect
Consistency of effects
PART 2: EFFECT SIZE AND PRECISION
Treatment effects and effect sizes
Parameters and estimates
4 EFFECT SIZES BASED ON MEANS
Raw (unstandardized) mean difference D
Standardized mean difference, D and G
5 EFFECT SIZES BASED ON BINARY DATA (2×2 TABLES)
Choosing an effect size index
6 EFFECT SIZES BASED ON CORRELATIONS
7 CONVERTING AMONG EFFECT SIZES
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
8 FACTORS THAT AFFECT PRECISION
Factors that affect precision
9 CONCLUDING REMARKS
PART 3: FIXED-EFFECT VERSUS RANDOM-EFFECTS MODELS
11 FIXED-EFFECT MODEL
The true effect size
Impact of sampling error
Performing a fixed-effect meta-analysis
12 RANDOM-EFFECTS MODEL
The true effect sizes
Impact of sampling error
Performing a random-effects meta-analysis
13 FIXED EFFECT VERSUS RANDOM-EFFECTS MODELS
Definition of a summary effect
Estimating the summary effect
Extreme effect size in large study
The null hypothesis
Which model should we use?
Model should not be based on the test for heterogeneity
14 WORKED EXAMPLES (PART 1)
Worked example for continuous data (Part 1)
Worked example for binary data (Part 1)
Worked example for correlational data (Part 1)
PART 4: HETEROGENEITY
16 IDENTIFYING AND QUANTIFYING HETEROGENEITY
Isolating the variation in true effects
The I 2 statistic
Comparing the measures of heterogeneity
Confidence intervals for T 2
Confidence intervals (or uncertainty intervals) for I 2
17 PREDICTION INTERVALS
Prediction intervals in primary studies
Prediction intervals in meta-analysis
Confidence intervals and prediction intervals
Comparing the confidence interval with the prediction interval
18 WORKED EXAMPLES (PART 2)
Worked example for continuous data (Part 2)
Worked example for binary data (Part 2)
Worked example for correlational data (Part 2)
19 SUBGROUP ANALYSES
Fixed-effect model within subgroups
Random effects with separate estimates of T 2
Random effects with pooled estimate of T 2
The proportion of variance explained
Obtaining an overall effect in the presence of subgroups
Fixed or random effects for unexplained heterogeneity
Statistical power for regression
21 NOTES ON SUBGROUP ANALYSES AND META-REGRESSION
Analysis of subgroups and regression are observational
Statistical power for subgroup analyses and meta-regression
PART 5: COMPLEX DATA STRUCTURES
23 INDEPENDENT SUBGROUPS WITHIN A STUDY
Combining across subgroups
24 MULTIPLE OUTCOMES OR TIME POINTS WITHIN A STUDY
Combining across outcomes or time-points
Comparing outcomes or time-points within a study
25 MULTIPLE COMPARISONS WITHIN A STUDY
Combining across multiple comparisons within a study
Differences between treatments
26 NOTES ON COMPLEX DATA STRUCTURES
Differences in effect
PART 6: OTHER ISSUES
28 VOTE COUNTING – A NEW NAME FOR AN OLD PROBLEM
Why vote counting is wrong
Vote-counting is a pervasive problem
29 POWER ANALYSIS FOR META-ANALYSIS
A conceptual approach
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
30 PUBLICATION BIAS
The problem of missing studies
Methods for addressing bias
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
PART 7: ISSUES RELATED TO EFFECT SIZE
32 EFFECT SIZES RATHER THAN P -VALUES
Relationship between p-values and effect sizes
The distinction is important
The p-value is often misinterpreted
Narrative reviews vs. meta-analyses
33 SIMPSON’S PARADOX
Circumcision and risk of HIV infection
An example of the paradox
34 GENERALITY OF THE BASIC INVERSE-VARIANCE METHOD
Other effect sizes
Other methods for estimating effect sizes
Individual participant data meta-analyses
PART 8: FURTHER METHODS
36 META-ANALYSIS METHODS BASED ON DIRECTION AND P -VALUES
The sign test
37 FURTHER METHODS FOR DICHOTOMOUS DATA
One-step (Peto) formula for odds ratio
38 PSYCHOMETRIC META-ANALYSIS
The attenuating effects of artifacts
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
PART 9: META-ANALYSIS IN CONTEXT
40 WHEN DOES IT MAKE SENSE TO PERFORM A META-ANALYSIS?
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?
41 REPORTING THE RESULTS OF A META-ANALYSIS
The computational model
42 CUMULATIVE META-ANALYSIS
Why perform a cumulative meta-analysis?
43 CRITICISMS OF META-ANALYSIS
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?
PART 10: RESOURCES AND SOFTWARE
Three examples of meta-analysis software
Comprehensive meta-analysis (CMA) 2.0
StataTM macros with Stata 10.0
45 BOOKS, WEB SITES AND PROFESSIONAL ORGANIZATIONS
Books on systematic review methods
Books on meta-analysis
- Provides worked examples throughout, with visual explanations, using screenshots from Excel spreadsheets and computer programs such as Comprehensive Meta-Analysis (CMA) or Strata.
- Details instructions for performing the analyses shown in the screenshots, and manipulating the variables to fully master the techniques.
- Accompanied by a free download of an instructional version of comprehensive meta-analysis to enable the readers to perform all the exercises from the book.
- Authored by four of the leading names in meta-analysis research.
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