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Methods for MetaAnalysis in Medical Research 

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Comment from the Stata technical groupMetaanalysis as a statistical and scientific tool has grown immensely in popularity over the last decade as a way to systematically present new research results in the proper context, given all previous related work. This text covers much of the statistical methodology used by metaanalysts, from the most basic to the advanced, and is ideal for selfstudy as it requires little background knowledge of statistics. The authors do a good job of presenting their concepts free of mathematical theory, which is of little use to the practicing researcher. The book begins in part A with some basic metaanalysis terminology and biostatistical terms, such as odds, odds ratios, and relative risks. Part A then continuous with a discussion of heterogeneity, the application of fixedeffects and randomeffects methods for combining study estimates, publication bias, sensitivity analysis, and graphical techniques. Part B covers Bayesian methods (which fit naturally with the concept of metaanalysis), the metaanalysis of individual patient data, missing data, the metaanalysis of nonstandard data types, multiple and correlated outcome measures, observational studies, survival data, and miscellaneous topics. 

Table of contentsView table of contents >> Preface
Acknowledgments
Part A: MetaAnalysis Methodology: The Basics
1 Introduction—Metaanalysis: Its Development and Uses
1.1 Evidencebased health care
1.2 Evidencebased everything! 1.3 Pulling together the evidence—systematic reviews 1.4 Why metaanalysis? 1.5 Aim of this book 1.6 Concluding remarks References 2 Defining Outcome Measures used for Combining via Metaanalysis
2.1 Introduction
2.2 Noncomparative binary outcomes
2.2.1 Odds
2.3 Comparative binary outcomes2.2.2 Incidence rates
2.3.1 The Odds ratio
2.4 Continuous data2.3.2 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?
2.4.1 Outcomes defined on their original metric (mean difference)
2.5 Ordinal outcomes2.4.2 Outcomes defined using standardized mean differences 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
3.3 Graphical informal tests/explorations of heterogeneity3.2.2 Extensions/alternative tests 3.2.3 Example: Testing for heterogeneity in the cholesterol lowering trial dataset
3.3.1 Plot of normalized (z) scores
3.4 Possible causes of heterogeneity3.3.2 Forest plot 3.3.3 Radial plot (Galbraith diagram) 3.3.4 L'Abbé plot
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
3.6 The validity of pooling studies with heterogeneous outcomes3.5.2 Include covariates in a regression model (metaregression) 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 mixedeffect models 3.7 Summary/Discussion References 4 Fixed Effects Methods for Combining Study Estimates
4.1 Introduction
4.2 General fixed effect model — the inverse varianceweighted method
4.2.1 Example: Combining odds ratios using the inverse varianceweighted method
4.3 Specific methods for combining odds ratios4.2.2 Example: Combining standardized mean differences using a continuous outcome scale
4.3.1 Mantel–Haenszel method for combining odds ratios
4.4 Summary/Discussion4.3.2 Peto's method for combining odds ratios 4.3.3 Combining odds ratios via maximumlikelihood techniques 4.3.4 Exact methods of interval estimation 4.3.5 Discussion of the relative merits of each method 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
5.7 Comparison of random with fixed effect models5.6.2 Exact approach to random effects metaanalysis of binary data 5.6.3 Miscellaneous extensions to the random effects model 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
6.3 Regression models for metaanalysis6.2.2 Example: Stratification by patient characteristics
6.3.1 Metaregression models (fixedeffects regression)
6.4 Summary/Discussion6.3.2 Metaregression example: a metaanalysis of Bacillus CalmetteGuérin (BCG) vaccine for the prevention of tuberculosis (TB) 6.3.3 Mixed effect models (randomeffects regression) 6.3.4 Mixed model example: A reanalysis of Bacillus CalmetteGuérin (BCG) vaccine for the prevention of tuberculosis (TB) trials 6.3.5 Mixed modelling extensions References 7 Publication Bias
7.1 Introduction
7.2 Evidence of publication and related bias
7.2.1 Survey of authors
7.3 The seriousness and consequences of publication bias for metaanalysis7.2.2 Published versus registered trials in a metaanalysis 7.2.3 Followup of cohorts of registered studies 7.2.4 Nonempirical evidence 7.2.5 Evidence of language bias 7.4 Predictors of publication bias (factors effecting the probability a study will get published) 7.5 Identifying publication bias in a metaanalysis
7.5.1 The funnel plot
7.6 Taking into account publication bias or adjusting the results of a metaanalysis in the presence of publication bias7.5.2 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
7.6.1 Analysing only the largest studies
7.7 Broader perspective solutions to publication bias7.6.2 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
7.7.1 Prospective registration of trials
7.8 Including unpublished information7.7.2 Changes in publication process and journals 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
8.3 Incorporating study quality into a metaanalysis8.2.2 Observational Studies
8.3.1 Graphical plot
8.4 Practical implementation8.3.2 Cumulative methods 8.3.3 Regression model 8.3.4 Weighting 8.3.5 Excluding studies 8.3.6 Sensitivity analysis 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 metaanalytic methods
9.3.1 Assessing the impact of choice of study weighting
9.4 Summary/DiscussionReferences 10 Reporting the Results of a Metaanalysis
10.1 Introduction
10.2 Overview and structure of a report 10.3 Graphical displays used for reporting the findings of a metaanalysis
10.3.1 Forest plots
10.4 Summary/Discussion10.3.2 Radial plots 10.3.3 Funnel plots 10.3.4 Displaying the distribution of effect size estimates 10.3.5 Graphs investigating length of followup References Part B: Advanced and Specialized Metaanalysis Topics
11 Bayesian Methods in Metaanalysis
11.1 Introduction
11.2 Bayesian methods in health research
11.2.1 General introduction
11.3 Bayesian metaanalysis of normally distributed data 11.2.2 General advantages/disadvantages of Bayesian methods 11.2.3 Example: Bayesian analysis of a single trial using a normal conjugate model
11.3.1 Example: Combining trials with continuous outcome measures using Bayesian methods
11.4 Bayesian metaanalysis of binary data
11.4.1 Example: Combining binary outcome measures using Bayesian methods
11.5 Empirical Bayes methods in metaanalysis11.6 Advantages/disadvantages of Bayesian methods in metanalysis
11.6.1 Advantages
11.7 Extensions and specific areas of application11.6.2 Disadvantages
11.7.1 Incorporating study quality
11.8 Summary/Discussion11.7.2 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 References 12 Metaanalysis of Individual Patient Data
12.1 Introduction
12.2 Procedural methodology
12.2.1 Data collection
12.3 Issues involved in carrying out IPD metaanalyses12.2.2 Checking data 12.4 Comparing metaanalysis 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 metaanalysis context
13.5 Bayesian methods for missing data13.4.2 Missing data methods specific to metaanalysis 13.4.3 Example: Dealing with missing standard deviations of estimated in a metaanalysis 13.6 Summary/Discussion References 14 Metaanalysis 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
14.4 Metaanalysis of diagnostic test accuracy14.3.2 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 Nonparametric method of combining different data type effect measures
14.4.1 Combining binary test results
14.5 Metaanalysis using surrogate markers14.4.2 Combining ordered categorical test results 14.4.3 Combining continuous test results 14.6 Combining a number of crossover trials using the patient preference outcome 14.7 Votecounting methods 14.8 Combining pvalues/significance levels
14.8.1 Minimum p method
14.9 Novel applications of metaanalysis using nonstandard methods or data14.8.2 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 pvalues 14.10 Summary/Discussion References 15 Metaanalysis of Multiple and Correlated Outcome Measures
15.1 Introduction
15.2 Combining multiple pvalues 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.
15.5 Summary/Discussion15.4.2 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 References 16 Metaanalysis 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
16.3 Analysis of summary data16.2.2 Data manipulation for data extraction 16.2.3 Methods for transforming and adjusting reported results
16.3.1 Heterogeneity of observational studies
16.4 Reporting the results of metaanalysis of observational studies16.3.2 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 16.5 Use of sensitivity and influence analysis 16.6 Study quality considerations for observational studies 16.7 Other issues concerning metaanalysis of observational studies
16.7.1 Analysing individual patient data from observational studies
16.8 Unresolved issues concerning the metaanalysis of observational studies16.7.2 Combining doseresponse data 16.7.3 Metaanalysis of single case research 16.9 Summary/Discussion References 17 Generalized Synthesis of Evidence—Combining Different Sources of Evidence
17.1 Introduction
17.2 Incorporating singlearm studies: models for incorporating historical controls
17.2.1 Example
17.3 Combining matched and unmatched data17.4 Approaches for combining studies containing multiple and/or different treatment arms
17.4.1 Approach of Gleser and Olkin
17.5 The confidence profile method17.4.2 Models of Berkey et al. 17.4.3 Method of Higgins 17.4.4 Mixed model of DuMouchel 17.6 Crossdesign synthesis
17.6.1 Beginnings
17.7 Summary/Discussion17.6.2 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 References 18 Metaanalysis of Survival Data
18.1 Introduction
18.2 Inferring/estimating and combining (log) hazard ratios 18.3 Calculation of the ‘logrank’ odds ratio 18.4 Calculation of pooled survival rates 18.5 Method of Hunink and Wong 18.6 Iterative generalized least squares for metaanalysis of survival data at multiple times
18.6.1 Application of the model
18.7 Identifying prognostic factors using a log (relative risk) measure18.8 Combining quality of life adjusted survival data 18.9 Metaanalysis 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
18.10 Summary/Discussion18.9.2 Is obtaining and using survival data necessary? References 19 Cumulative Metaanalysis
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 approaches19.5 Issues regarding uses of cumulative metaanalysis 19.6 Summary/Discussion References 20 Miscellaneous and Developing Areas of Application in Metaanalysis
20.1 Introduction
20.2 Alternatives to conventional metaanalysis
20.2.1 Estimating and extrapolating a response surface
20.3 Developing areas20.2.2 Odd man out method 20.2.3 Best evidence synthesis
20.3.1 Prospective metaanalysis
References 20.3.2 Economic evaluation through metaanalysis 20.3.3 Combining metaanalysis and decision analysis 20.3.4 Net benefit model synthesizing disparate sources of information Appendix I: Software Used for the Examples in this Book
Subject Index

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