Methods for Meta-analysis in Medical Research

Transcription

1 Methods for Meta-analysis in Medical Research Alex J. Sutton University of Leicester, UK Keith R. Abrams University of Leicester, UK David R. Jones University of Leicester, UK Trevor A. Sheldon University of York, UK Fujian Song University of York, UK JOHN WILEY & SONS, LTD Chichester New York Weinheim Brisbane Singapore Toronto

2 Contents Preface Acknowledgements Part A: Meta-Analysis Methodology: The Basics 1. Introduction - Meta-analysis: Its Development and Uses. 1 Evidence-based health care.2 Evidence-based everything!.3 Pulling together the evidence - systematic reviews.4 Why meta-analysis?.5 Aim of this book.6 Concluding remarks References XV xvii Deflning Outcome Measures used for Combining via Meta-analysis Introduction 2.2 Non-comparative binary outcomes Odds Incidence rates 2.3 Comparative binary outcomes The Odds ratio Relative risk (or rate ratio/relative rate) Risk differences between proportions (or the absolute risk reduction) The number needed to treat Comparisons of rates Other scales of measurement used in summarizing binary data Which scale to use?

3 vi CONTENTS 2.4 Continuous data Outcomes defined on their original metric (mean difference) Outcomes defined using standardized mean differences Ordinal outcomes Summary/Discussion 33 References Assessing Between Study Heterogeneity Introduction Hypothesis tests for presence of heterogeneity Standard x 2 test Extensions/alternative tests Example: Testing for heterogeneity in the cholesterol lowering trial dataset Graphical informal tests/explorations of heterogeneity Plot of normalized (z) scores Forest plot Radial plot (Galbraith diagram) VAbbe plot Possible causes of heterogeneity Specific factors that may cause heterogeneity in RCTs Methods for investigating and dealing with sources of heterogeneity Change scale of outcome variable Include covariates in a regression model (meta-regression) Exclude studies Analyse groups of studies separately Use of random effects models Use of mixed-effect models The validity of pooling studies with heterogeneous outcomes Summary/Discussion 53 References Fixed Effects Methods for Combining Study Estimates Introduction General fixed effect model - the inverse variance-weighted method Example: Combining odds ratios using the inverse variance-weighted method Example: Combining standardized mean differences using a continuous outcome scale 62

4 CONTENTS vii 4.3 Specific methods for combining odds ratios Mantel-Haenszel method for combining odds ratios Peto's method for combining odds ratios Combining odds ratios via maximum-likelihood techniques Exact methods of interval estimation Discussion of the relative merits of each method Summary/Discussion 70 References Random Effects Models for Combining Study Estimates Introduction Algebraic derivation for random effects models by the weighted method Maximum likelihood and restricted maximum likelihood estimate solutions Comparison of estimation methods Example: Combining the cholesterol lowering trials using a random effects model Extensions to the random effects model Including uncertainty induced by estimating the between study variance Exact approach to random effects meta-analysis of binary data Miscellaneous extensions to the random effects model Comparison of random with fixed effect models Summary/Discussion 84 References Exploring Between Study Heterogeneity Introduction Subgroup analyses Example: Stratification by study characteristics Example: Stratification by patient characteristics Regression models for meta-analysis Meta-regression models (fixed-effects regression) Meta-regression example: a meta-analysis of Bacillus Calmette-Guerin (BCG) vaccine for the prevention of tuberculosis (TB) Mixed effect models (random-effects regression) Mixed model example: A re-analysis of Bacillus Calmette-Guerin (BCG) vaccine for the prevention of tuberculosis (TB) trials 99

5 viii CONTENTS Mixed modelling extensions Summary/Discussion 104 References Publication Bias Introduction Evidence of publication and related bias Survey of authors Published versus registered trials in a meta-analysis Follow-up of cohorts of registered studies Non-empirical evidence Evidence of language bias The seriousness and consequences of publication bias for meta-analysis Predictors of publication bias (factors effecting the probability a study will get published) Identifying publication bias in a meta-analysis The funnel plot Rank correlation test Linear regression test Other methods to detect publication bias Practical advice on methods for detecting publication bias' Taking into account publication bias or adjusting the results of a meta-analysis in the presence of publication bias Analysing only the largest studies Rosenthal's 'file drawer' method Models which estimate the number of unpublished studies, but do not adjust Selection models using weighted distribution theory The'Trim and Fill'method The sensitivity approach of Copas Broader perspective solutions to publication bias Prospective registration of trials Changes in publication process and journals Including unpublished information Summary/Discussion 127 References Study Quality Introduction Methodological factors that may affect the quality of studies Experimental studies 135

6 CONTENTS ix Observational Studies Incorporating study quality into a meta-analysis Graphical plot Cumulative methods Regression model Weighting Excluding studies Sensitivity analysis Practical implementation Summary/Discussion 144 References Sensitivity Analysis Introduction Sensitivity of results to inclusion criteria Sensitivity of results to meta-analytic methods Assessing the impact of choice of study weighting Summary/Discussion 151 References Reporting the Results of a Meta-analysis Introduction Overview and structure of a report Graphical displays used for reporting the findings of a meta-analysis Forest plots Radial plots Funnel plots Displaying the distribution of effect size estimates Graphs investigating length of follow-up Summary/Discussion 158 References 158 Part B: Advanced and Specialized Meta-analysis Topics Bayesian Methods in Meta-analysis Introduction Bayesian methods in health research General introduction General advantages/disadvantages of Bayesian methods Example: Bayesian analysis of a single trial using a normal conjugate model 167

7 x CONTENTS 11.3 Bayesian meta-analysis of normally distributed data Example: Combining trials with continuous outcome measures using Bayesian methods Bayesian meta-analysis of binary data Example: Combining binary outcome measures using Bayesian methods Empirical Bayes methods in meta-analysis Advantages/disadvantages of Bayesian methods in meta-analysis Advantages Disadvantages Extensions and specific areas of application Incorporating study quality Inclusion of covariates Model selection Hierarchical models Sensitivity analysis Comprehensive modelling Other developments Summary/Discussion 183 References 183 / 12. Meta-analysis of Individual Patient Data Introduction Procedural methodology Data collection Checking data Issues involved in carrying out IPD meta-analyses Comparing meta-analysis using IPD or summary data? Combining individual patient and summary data Summary/Discussion 196 References Missing Data Introduction Reasons for missing data Categories of missing data at the study level Analytic methods for dealing with missing data General missing data methods which can be applied in the meta-analysis context Missing data methods specific to meta-analysis Example: Dealing with missing standard deviations of estimates in a meta-analysis 202

8 CONTENTS xi 13.5 Bayesian methods for missing data Summary/Discussion 203 References Meta-analysis of Different Types of Data Introduction Combining ordinal data Issues concerning scales of measurement when combining data Transforming scales, maintaining same data type Binary outcome data reported on different scales Combining studies whose outcomes are reported using different data types Combining summaries of binary outcomes with those of continuous outcomes Non-parametric method of combining different data type effect measures Meta-analysis of diagnostic test accuracy Combining binary test results Combining ordered categorical test results Combining continuous test results Meta-analysis using surrogate markers Combining a number of cross-over trials using the patient preference outcome Vote-counting methods Combining/7-values/significance levels Minimum p method Sum of z's method Sum of logs method Logit method Other methods of combining significance levels Appraisal of the methods Example of combining/7-values Novel applications of meta-analysis using non-standard methods or data Summary/Discussion 223 References Meta-analysis of Multiple and Correlated Outcome Measures Introduction Combining multiple/^-values Method for reducing multiple outcomes to a single measure for each study 231

9 xii CONTENTS 15.4 Development of a multivariate model Model of Raudenbush et al Model of Gleser and Olkin Multiple outcome model for clinical trials Random effect multiple outcome regression model DuMouchel's extended model for multiple outcomes Illustration of the use of multiple outcome models Summary/Discussion 236 References Meta-analysis of Epidemiological and Other Observational Studies Introduction Extraction and derivation of study estimates Scales of measurement used to report and combine observational studies Data manipulation for data extraction Methods for transforming and adjusting reported results Analysis of summary data Heterogeneity of observational studies Fixed or random effects? Weighting of observational studies Methods for combining estimates of observational studies Dealing with heterogeneity and combining the OC and breast cancer studies Reporting the results of meta-analysis of observational studies Use of sensitivity and influence analysis Study quality considerations for observational studies Other issues concerning meta-analysis of observational studies, Analysing individual patient data from observational studies Combining dose-response data Meta-analysis of single case research Unresolved issues concerning the meta-analysis of observational studies Summary/Discussion 255 References 255

10 CONTENTS xiii 17. Generalized Synthesis of Evidence - Combining Different Sources of Evidence Introduction Incorporating single-arm studies: models for incorporating historical controls Example Combining matched and unmatched data Approaches for combining studies containing multiple and/or different treatment arms Approach of Gleser and Olkin Models of Berkey et al Method of Higgins Mixed model of DuMouchel The confidence profile method Cross-design synthesis Beginnings Bayesian hierarchical models Grouped random effects models of Larose and Dey Synthesizing studies with disparate designs to assess the exposure effects on the incidence of a rare adverse event Combining the results of cancer studies in humans and other species Combining biochemical and epidemiological evidence Combining information from disparate toxicological studies using stratified ordinal regression Summary/Discussion 273 References Meta-analysis of Survival Data Introduction Inferring/estimating and combining (log) hazard ratios Calculation of the'log-rank'odds ratio Calculation of pooled survival rates Method of Hunink and Wong Iterative generalized least squares for meta-analysis of survival data at multiple times Application of the model Identifying prognostic factors using a log (relative risk) measure 282

11 xiv CONTENTS 18.8 Combining quality of life adjusted survival data Meta-analysis of survival data using individual patient data Pooling independent samples of survival data to form an estimator of the common survival function Is obtaining and using survival data necessary? Summary/Discussion 284 References Cumulative Meta-analysis Introduction Example: Ordering by date of publication Using study characteristics other than date of publication Example: Ordering the cholesterol trials by baseline risk in the control group Bayesian approaches Issues regarding uses of cumulative meta-analysis Summary/Discussion 292 References 292 / 20. Miscellaneous and Developing Areas of Application in Meta-analysis Introduction Alternatives to conventional meta-analysis Estimating and extrapolating a response surface Odd man out method Best evidence synthesis Developing areas Prospective meta-analysis Economic evaluation through meta-analysis ' Combining meta-analysis and decision analysis > Net benefit model synthesizing disparate sources of information 299 References 299 Appendix I: Software Used for the Examples in this Book 301 Subject index 309