List of Tables

List of Figures

Acknowledgements

Preface

Web Site

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 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

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

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 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)

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

Nomenclature

Worked Examples

16

Identifying and Quantifying Heterogeneity

Introduction

Isolating the Variation in True Effects

Computing Q

Estimating r²

The I² Statistic

Comparing the Measures of Heterogeneity

Confidence Intervals for r²

Confidence Intervals (or Uncertainty Intervals) for I²

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 r²

Random Effects with Pooled Estimate of r²

The Proportion of Variance Explained

Mixed-Effects 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

Summary Points

21

Notes on Subgroup Analyses and Meta-Regression

Introduction

Computational Model

Multiple Comparisons

Software

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

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

Summary 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 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

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

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, Web Sites and Professional Organizations

Books on Systematic Review Methods

Books on Meta-Analysis

Web Sites

References

Index