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 x2 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
