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Introduction to Meta-Analysis

Michael Borenstein, Larry Hedges, Julian P.T. Higgins, and Hannah R. Rothstein
Publisher: Wiley
Copyright: 2009
ISBN-13: 978-0-470-05724-7
Pages: 450; hardcover
Price: $52.25

Comment from the Stata technical group

Meta-analysis has gained increasing popularity since the early 1990s as a way to synthesize the results from separate studies. It is widely used in the medical sciences, education, and business. This text is both complete and current, and is ideal for researchers wanting a conceptual treatment of the methodology. A chapter on statistical software for performing meta-analysis (including how to do so in Stata) is also included.

Table of contents

List of Tables
List of Figures
Part 1: Introduction
1 How a meta-analysis works
Individual studies
The summary effect
Heterogeneity of effect sizes
Summary points
2 Why perform a meta-analysis
The streptokinase 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 of effect size computations
4 Effect sizes based on means
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)
Risk ratio
Odds ratio
Risk difference
Choosing an effect size index
Summary points
6 Effect sizes based on correlations
Computing r
Other approaches
Summary points
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
Summary points
8 Factors that affect precision
Factors that affect precision
Sample size
Study design
Summary points
9 Concluding remarks
Part 3: Fixed-effect versus random-effects models
10 Overview
11 Fixed-effect model
The true effect size
Impact of sampling error
Performing a fixed-effect meta-analysis
Summary points
12 Random-effects model
The true effect sizes
Impact of sampling error
Performing a random-effects meta-analysis
Summary points
13 Fixed-effect versus random-effects models
Definition of a summary effect
Estimating the summary effect
Extreme effect size in a large study or a small 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)
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
Worked examples
16 Identifying and quantifying heterogeneity
Isolating the variation in true effects
Computing Q
Estimating τ2
The I2 statistic
Comparing the measures of heterogeneity
Confidence intervals for τ2
Confidence intervals (or uncertainty intervals) for I2
Summary points
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
Summary points
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)
Summary points
19 Subgroup analyses
Fixed-effect model within subgroups
Computational models
Random effects with separate estimates of τ2
Random effects with pooled estimate of τ2
The proportion of variance explained
Mixed-effects model
Obtaining an overall effect in the presence of subgroups
Summary points
20 Meta-regression
Fixed-effect model
Fixed or random effects for unexplained heterogeneity
Random-effects model
Summary points
21 Notes on subgroup analyses and meta-regression
Computational model
Multiple comparisons
Analyses of subgroups and regression analyses 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
Combining across subgroups
Comparing subgroups
Summary points
24 Multiple outcomes or time-points within a study
Combining across outcomes or time-points
Comparing outcomes or time-points within a study
Summary points
25 Multiple comparisons within a study
Combining across multiple comparisons within a study
Differences between treatments
Summary points
26 Notes on complex data structures
Summary effect
Differences in effect
Part 6: Other issues
27 Overview
28 Vote counting—A new name for an old problem
Why vote counting is wrong
Vote counting is a pervasive problem
Summary points
29 Power analysis for meta-analysis
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
The problem of missing studies
Methods for addressing bias
Illustrative example
The model
Getting a sense of the data
Is there evidence of any bias?
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
Some important caveats
Small-study effects
Concluding remarks
Summary points
Part 7: Issues related to effect size
31 Overview
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
Summary points
33 Simpson’s paradox
Circumcision and risk of HIV infection
An example of the paradox
Summary points
34 Generality of the basic inverse-variance method
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
Vote counting
The sign test
Combining p-values
Summary points
37 Further methods for dichotomous data
Mantel–Haenszel method
One-step (Peto) formula for odds ratio
Summary points
38 Psychometric meta-analysis
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?
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
The computational model
Forest plots
Sensitivity analysis
Summary points
42 Cumulative meta-analysis
Why perform a cumulative meta-analysis?
Summary points
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?
Concluding remarks
Summary points
Part 10: Resources and software
44 Software
The software
Three examples of meta-analysis software
Comprehensive Meta-Analysis (CMA) 2.0
RevMan 5.0
Stata macros with Stata 10.0
Summary points
45 Books, websites and professional organizations
Books on systematic review methods
Books on meta-analysis
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