Preface

Acknowledgments

Part A: Meta-Analysis Methodology: The Basics

1 Introduction—Meta-analysis: Its Development and Uses

1.1 Evidence-based health care

1.2 Evidence-based everything!

1.3 Pulling together the evidence—systematic reviews

1.4 Why meta-analysis?

1.5 Aim of this book

1.6 Concluding remarks

References

2 Defining Outcome Measures used for Combining via Meta-analysis

2.1 Introduction

2.2 Non-comparative binary outcomes

2.2.1 Odds

2.2.2 Incidence rates

2.3 Comparative binary outcomes

2.3.1 The Odds ratio

2.3.2 Relative risk (or rate ratio/relative rate)

2.3.3 Risk differences between proportions (or the absolute risk reduction)

2.3.4 The number needed to treat

2.3.5 Comparisons of rates

2.3.6 Other scales of measurement used in summarizing binary data

2.3.7 Which scale to use?

2.4 Continuous data

2.4.1 Outcomes defined on their original metric (mean difference)

2.4.2 Outcomes defined using standardized mean differences

2.5 Ordinal outcomes

2.6 Summary/Discussion

References

3 Assessing Between Study Heterogeneity

3.1 Introduction

3.2 Hypothesis tests for presence of heterogeneity

3.2.1 Standard *x*^{2} test

3.2.2 Extensions/alternative tests

3.2.3 Example: Testing for heterogeneity in the cholesterol lowering trial dataset

3.3 Graphical informal tests/explorations of heterogeneity

3.3.1 Plot of normalized (*z*) scores

3.3.2 Forest plot

3.3.3 Radial plot (Galbraith diagram)

3.3.4 L'Abbé plot

3.4 Possible causes of heterogeneity

3.4.1 Specific factors that may cause heterogeneity in RCTs

3.5 Methods for investigating and dealing with sources of heterogeneity

3.5.1 Change scale of outcome variable

3.5.2 Include covariates in a regression model (*meta-regression*)

3.5.3 Exclude studies

3.5.4 Analyse groups of studies separately

3.5.5 Use of random effects models

3.5.6 Use of mixed-effect models

3.6 The validity of pooling studies with heterogeneous outcomes

3.7 Summary/Discussion

References

4 Fixed Effects Methods for Combining Study Estimates

4.1 Introduction

4.2 General fixed effect model — the inverse variance-weighted method

4.2.1 Example: Combining odds ratios using the inverse variance-weighted method

4.2.2 Example: Combining standardized mean differences using a continuous outcome scale

4.3 Specific methods for combining odds ratios

4.3.1 Mantel–Haenszel method for combining odds ratios

4.3.2 Peto's method for combining odds ratios

4.3.3 Combining odds ratios via maximum-likelihood techniques

4.3.4 Exact methods of interval estimation

4.3.5 Discussion of the relative merits of each method

4.4 Summary/Discussion

References

5 Random Effects Models for Combining Study Estimates

5.1 Introduction

5.2 Algebraic derivation for random effects models by the weighted method

5.3 Maximum likelihood and restricted maximum likelihood estimate solutions

5.4 Comparison of estimation method

5.5 Example: Combining the cholesterol lowering trials using a random effects model

5.6 Extensions to the random effects model

5.6.1 Including uncertainty induced by estimating the between study variance

5.6.2 Exact approach to random effects meta-analysis of binary data

5.6.3 Miscellaneous extensions to the random effects model

5.7 Comparison of random with fixed effect models

5.8 Summary/Discussion

References

6 Exploring Between Study Heterogeneity

6.1 Introduction

6.2 Subgroup analyses

6.2.1 Example: Stratification by study characteristics

6.2.2 Example: Stratification by patient characteristics

6.3 Regression models for meta-analysis

6.3.1 Meta-regression models (fixed-effects regression)

6.3.2 Meta-regression example: a meta-analysis of Bacillus Calmette-Guérin (BCG) vaccine for the prevention of tuberculosis (TB)

6.3.3 Mixed effect models (random-effects regression)

6.3.4 Mixed model example: A re-analysis of Bacillus Calmette-Guérin (BCG) vaccine for the prevention of tuberculosis (TB) trials

6.3.5 Mixed modelling extensions

6.4 Summary/Discussion

References

7 Publication Bias

7.1 Introduction

7.2 Evidence of publication and related bias

7.2.1 Survey of authors

7.2.2 Published versus registered trials in a meta-analysis

7.2.3 Follow-up of cohorts of registered studies

7.2.4 Non-empirical evidence

7.2.5 Evidence of language bias

7.3 The seriousness and consequences of publication bias for meta-analysis

7.4 Predictors of publication bias (factors effecting the probability a study will get published)

7.5 Identifying publication bias in a meta-analysis

7.5.1 The funnel plot

7.5.2 Rank correlation test

7.5.3 Linear regression test

7.5.4 Other methods to detect publication bias

7.5.5 Practical advice on methods for detecting publication bias

7.6 Taking into account publication bias or adjusting the results of a meta-analysis in the presence of publication bias

7.6.1 Analysing only the largest studies

7.6.2 Rosenthal's ‘file drawer’ method

7.6.3 Models which estimate the number of unpublished studies, but do not adjust

7.6.4 Selection models using weighted distribution theory

7.6.5 The ‘Trim and Fill’ method

7.6.6 The sensitivity approach of Copas

7.7 Broader perspective solutions to publication bias

7.7.1 Prospective registration of trials

7.7.2 Changes in publication process and journals

7.8 Including unpublished information

7.9 Summary/Discussion

References

8 Study Quality

8.1 Introduction

8.2 Methodological factors that may affect the quality of studies

8.2.1 Experimental studies

8.2.2 Observational Studies

8.3 Incorporating study quality into a meta-analysis

8.3.1 Graphical plot

8.3.2 Cumulative methods

8.3.3 Regression model

8.3.4 Weighting

8.3.5 Excluding studies

8.3.6 Sensitivity analysis

8.4 Practical implementation

8.5 Summary/Discussion

References

9 Sensitivity Analysis

9.1 Introduction

9.2 Sensitivity of results to inclusion criteria

9.3 Sensitivity of results to meta-analytic methods

9.3.1 Assessing the impact of choice of study weighting

9.4 Summary/Discussion

References

10 Reporting the Results of a Meta-analysis

10.1 Introduction

10.2 Overview and structure of a report

10.3 Graphical displays used for reporting the findings of a meta-analysis

10.3.1 Forest plots

10.3.2 Radial plots

10.3.3 Funnel plots

10.3.4 Displaying the distribution of effect size estimates

10.3.5 Graphs investigating length of follow-up

10.4 Summary/Discussion

References

Part B: Advanced and Specialized Meta-analysis Topics

11 Bayesian Methods in Meta-analysis

11.1 Introduction

11.2 Bayesian methods in health research

11.2.1 General introduction

11.2.2 General advantages/disadvantages of Bayesian methods

11.2.3 Example: Bayesian analysis of a single trial using a normal conjugate model

11.3 Bayesian meta-analysis of normally distributed data

11.3.1 Example: Combining trials with continuous outcome measures using Bayesian methods

11.4 Bayesian meta-analysis of binary data

11.4.1 Example: Combining binary outcome measures using Bayesian methods

11.5 Empirical Bayes methods in meta-analysis

11.6 Advantages/disadvantages of Bayesian methods in met-analysis

11.6.1 Advantages

11.6.2 Disadvantages

11.7 Extensions and specific areas of application

11.7.1 Incorporating study quality

11.7.2 Inclusion of covariates

11.7.3 Model selection

11.7.4 Hierarchical models

11.7.5 Sensitivity analysis

11.7.6 Comprehensive modelling

11.7.7 Other developments

11.8 Summary/Discussion

References

12 Meta-analysis of Individual Patient Data

12.1 Introduction

12.2 Procedural methodology

12.2.1 Data collection

12.2.2 Checking data

12.3 Issues involved in carrying out IPD meta-analyses

12.4 Comparing meta-analysis using IPD or summary data?

12.5 Combining individual patient and summary data

12.6 Summary/Discussion

References

13 Missing Data

13.1 Introduction

13.2 Reasons for missing data

13.3 Categories of missing data at the study level

13.4 Analytic methods for dealing with missing data

13.4.1 General missing data methods which can be applied in the meta-analysis context

13.4.2 Missing data methods specific to meta-analysis

13.4.3 Example: Dealing with missing standard deviations of estimated in a meta-analysis

13.5 Bayesian methods for missing data

13.6 Summary/Discussion

References

14 Meta-analysis of Different Types of Data

14.1 Introduction

14.2 Combining ordinal data

14.3 Issues concerning scales of measurement when combining data

14.3.1 Transforming scales, maintaining same data type

14.3.2 Binary outcome data reported on different scales

14.3.3 Combining studies whose outcomes are reported using different data types

14.3.4 Combining summaries of binary outcomes with those of continuous outcomes

14.3.5 Non-parametric method of combining different data type effect measures

14.4 Meta-analysis of diagnostic test accuracy

14.4.1 Combining binary test results

14.4.2 Combining ordered categorical test results

14.4.3 Combining continuous test results

14.5 Meta-analysis using surrogate markers

14.6 Combining a number of cross-over trials using the patient preference outcome

14.7 Vote-counting methods

14.8 Combining

*p*-values/significance levels

14.8.1 Minimum *p* method

14.8.2 Sum of *z*'s method

14.8.3 Sum of logs method

14.8.4 Logit method

14.8.5 Other methods of combining significance levels

14.8.6 Appraisal of the methods

14.8.7 Example of combining *p*-values

14.9 Novel applications of meta-analysis using non-standard methods or data

14.10 Summary/Discussion

References

15 Meta-analysis of Multiple and Correlated Outcome Measures

15.1 Introduction

15.2 Combining multiple

*p*-values

15.3 Method for reducing multiple outcomes to a single measure for each study

15.4 Development of a multivariate model

15.4.1 Model of Raudenbush *et al.*

15.4.2 Model of Gleser and Olkin

15.4.3 Multiple outcome model for clinical trials

15.4.4 Random effect multiple outcome regression model

15.4.5 DuMouchel's extended model for multiple outcomes

15.4.6 Illustration of the use of multiple outcome models

15.5 Summary/Discussion

References

16 Meta-analysis of Epidemiological and Other Observational Studies

16.1 Introduction

16.2 Extraction and derivation of study estimates

16.2.1 Scales of measurement used to report and combine observational studies

16.2.2 Data manipulation for data extraction

16.2.3 Methods for transforming and adjusting reported results

16.3 Analysis of summary data

16.3.1 Heterogeneity of observational studies

16.3.2 Fixed or random effects?

16.3.3 Weighting of observational studies

16.3.4 Methods for combining estimates of observations studies

16.3.5 Dealing with heterogeneity and combining the OC and breast cancer studies

16.4 Reporting the results of meta-analysis of observational studies

16.5 Use of sensitivity and influence analysis

16.6 Study quality considerations for observational studies

16.7 Other issues concerning meta-analysis of observational studies

16.7.1 Analysing individual patient data from observational studies

16.7.2 Combining dose-response data

16.7.3 Meta-analysis of single case research

16.8 Unresolved issues concerning the meta-analysis of observational studies

16.9 Summary/Discussion

References

17 Generalized Synthesis of Evidence—Combining Different Sources of Evidence

17.1 Introduction

17.2 Incorporating single-arm studies: models for incorporating historical controls

17.2.1 Example

17.3 Combining matched and unmatched data

17.4 Approaches for combining studies containing multiple and/or different treatment arms

17.4.1 Approach of Gleser and Olkin

17.4.2 Models of Berkey *et al.*

17.4.3 Method of Higgins

17.4.4 Mixed model of DuMouchel

17.5 The confidence profile method

17.6 Cross-design synthesis

17.6.1 Beginnings

17.6.2 Bayesian hierarchical models

17.6.3 Grouped random effects models of Larose and Dey

17.6.4 Synthesizing studies with disparate designs to assess the exposure effects on the incidence of a rare adverse event

17.6.5 Combining the results of cancer studies in humans and other species

17.6.6 Combining biochemical and epidemiological evidence

17.6.7 Combining information from disparate toxicological studies using stratified original regression

17.7 Summary/Discussion

References

18 Meta-analysis of Survival Data

18.1 Introduction

18.2 Inferring/estimating and combining (log) hazard ratios

18.3 Calculation of the ‘log-rank’ odds ratio

18.4 Calculation of pooled survival rates

18.5 Method of Hunink and Wong

18.6 Iterative generalized least squares for meta-analysis of survival data at multiple times

18.6.1 Application of the model

18.7 Identifying prognostic factors using a log (relative risk) measure

18.8 Combining quality of life adjusted survival data

18.9 Meta-analysis of survival data using individual patient data

18.9.1 Pooling independent samples of survival data to form an estimator of the common survival function

18.9.2 Is obtaining and using survival data necessary?

18.10 Summary/Discussion

References

19 Cumulative Meta-analysis

19.1 Introduction

19.2 Example: Ordering by date of publication

19.3 Using study characteristics other than date of publication

19.3.1 Example: Ordering the cholesterol trials by baseline risk in the control group

19.4 Bayesian approaches

19.5 Issues regarding uses of cumulative meta-analysis

19.6 Summary/Discussion

References

20 Miscellaneous and Developing Areas of Application in Meta-analysis

20.1 Introduction

20.2 Alternatives to conventional meta-analysis

20.2.1 Estimating and extrapolating a response surface

20.2.2 Odd man out method

20.2.3 Best evidence synthesis

20.3 Developing areas

20.3.1 Prospective meta-analysis

20.3.2 Economic evaluation through meta-analysis

20.3.3 Combining meta-analysis and decision analysis

20.3.4 Net benefit model synthesizing disparate sources of information

References

Appendix I: Software Used for the Examples in this Book

Subject Index