Graphical displays for meta‐analysis: An overview with suggestions for practice

Meta-analyses are fundamental tools for collating and synthesizing large amounts of information, and graphical displays have become the principal tool for presenting the results of multiple studies of the same research question. We review standard and proposed graphical displays for presentation of meta-analytic data, and offer our recommendations on how they might be presented to provide the most useful and user-friendly illustrations. We concentrate on graphs that specifically aim to present similar sorts of univariate results from multiple studies. We start with forest plots and funnel plots, and proceed to Galbraith (or radial) plots, L'Abbé (and related) plots, further plots useful for investigating heterogeneity, plots useful for model diagnostics and plots for illustrating likelihoods and Bayesian meta-analyses. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  F. Mosteller,et al.  A comparison of results of meta-analyses of randomized control trials and recommendations of clinical experts. Treatments for myocardial infarction. , 1992, JAMA.

[2]  I Olkin,et al.  Diagnostic statistical procedures in medical meta-analyses. , 1999, Statistics in medicine.

[3]  R. Myers,et al.  Raindrop Plots , 2003 .

[4]  Considerations and recommendations for figures in Cochrane reviews : graphs of statistical data , 2008 .

[5]  J. L. Tang,et al.  Misleading funnel plot for detection of bias in meta-analysis. , 2000, Journal of clinical epidemiology.

[6]  G. Smith,et al.  Bias in meta-analysis detected by a simple, graphical test , 1997, BMJ.

[7]  D J Spiegelhalter,et al.  Bayesian approaches to random-effects meta-analysis: a comparative study. , 1995, Statistics in medicine.

[8]  Alex J Sutton,et al.  Contour-enhanced meta-analysis funnel plots help distinguish publication bias from other causes of asymmetry. , 2008, Journal of clinical epidemiology.

[9]  S. Brophy,et al.  Interventions for latent autoimmune diabetes (LADA) in adults. , 2011, The Cochrane database of systematic reviews.

[10]  David Moher,et al.  Addressing Reporting Biases , 2008 .

[11]  Issei Fujishiro,et al.  The elements of graphing data , 2005, The Visual Computer.

[12]  Harukazu Tsuruta,et al.  Development and validation of MIX: comprehensive free software for meta-analysis of causal research data , 2006, BMC medical research methodology.

[13]  G L Delclos,et al.  Controversy of oral contraceptives and risk of rheumatoid arthritis: meta-analysis of conflicting studies and review of conflicting meta-analyses with special emphasis on analysis of heterogeneity. , 1996, American journal of epidemiology.

[14]  J. Ioannidis,et al.  Recursive cumulative meta-analysis: a diagnostic for the evolution of total randomized evidence from group and individual patient data. , 1999, Journal of clinical epidemiology.

[15]  S. Thompson,et al.  How should meta‐regression analyses be undertaken and interpreted? , 2002, Statistics in medicine.

[16]  C H Schmid,et al.  Cumulative meta-analysis of clinical trials builds evidence for exemplary medical care. , 1995, Journal of clinical epidemiology.

[17]  Eliseo Guallar,et al.  A graphical display useful for meta-analysis , 1997 .

[18]  William DuMouchel,et al.  Computer-modeling and Graphical Strategies for Meta-analysis , 2000 .

[19]  Bertrand Baujat,et al.  A graphical method for exploring heterogeneity in meta‐analyses: application to a meta‐analysis of 65 trials , 2002, Statistics in medicine.

[20]  David J Spiegelhalter,et al.  A re-evaluation of random-effects meta-analysis , 2009, Journal of the Royal Statistical Society. Series A,.

[21]  H C Van Houwelingen,et al.  A bivariate approach to meta-analysis. , 1993, Statistics in medicine.

[22]  C P Langlotz,et al.  Meta-analysis of diagnostic procedures: a brief overview. , 1998, Academic radiology.

[23]  Konrad Jamrozik.  Age-specific relevance of usual blood pressure to vascular mortality: a meta-analysis of individual data for one million adults in 61 prospective studies , 2002 .

[24]  David Moher,et al.  Forest plots in reports of systematic reviews: a cross-sectional study reviewing current practice. , 2010, International journal of epidemiology.

[25]  Jonathan J Deeks,et al.  Issues in the selection of a summary statistic for meta‐analysis of clinical trials with binary outcomes , 2002, Statistics in medicine.

[26]  Christopher H Schmid,et al.  Summing up evidence: one answer is not always enough , 1998, The Lancet.

[27]  Steff Lewis,et al.  Forest plots: trying to see the wood and the trees , 2001, BMJ : British Medical Journal.

[28]  George Davey Smith,et al.  Meta-analysis: Principles and procedures , 1997, BMJ.

[29]  John B. Willett,et al.  The visual presentation and interpretation of meta-analyses. , 1994 .

[30]  Karin Ried,et al.  Interpreting and understanding meta-analysis graphs--a practical guide. , 2006, Australian family physician.

[31]  Marcus R. Munafò,et al.  Assessing publication bias in genetic association studies: evidence from a recent meta-analysis , 2004, Psychiatry Research.

[32]  R. Ferrer,et al.  Graphical methods for detecting bias in meta-analysis. , 1998, Family medicine.

[33]  S G Thompson,et al.  A likelihood approach to meta-analysis with random effects. , 1996, Statistics in medicine.

[34]  Jonathan A C Sterne,et al.  Systematic reviews in health care: Investigating and dealing with publication and other biases in meta-analysis. , 2001, BMJ.

[35]  J. Copas,et al.  Meta-analysis, funnel plots and sensitivity analysis. , 2000, Biostatistics.

[36]  J. Sterne,et al.  Funnel plots for detecting bias in meta-analysis: guidelines on choice of axis. , 2001, Journal of clinical epidemiology.

[37]  S. Yusuf,et al.  Overcoming the limitations of current meta-analysis of randomised controlled trials , 1998, The Lancet.

[38]  J. Carlin.  Meta-analysis for 2 x 2 tables: a Bayesian approach. , 1992, Statistics in medicine.

[39]  R. Galbraith,et al.  Some Applications of Radial Plots , 1994 .

[40]  I. Olkin,et al.  The case of the misleading funnel plot , 2006, BMJ : British Medical Journal.

[41]  Theo Stijnen,et al.  Advanced methods in meta‐analysis: multivariate approach and meta‐regression , 2002, Statistics in medicine.

[42]  Jonathan A C Sterne,et al.  Investigating and Dealing with Publication and Other Biases , 2008 .

[43]  S Duval,et al.  Trim and Fill: A Simple Funnel‐Plot–Based Method of Testing and Adjusting for Publication Bias in Meta‐Analysis , 2000, Biometrics.

[44]  S L Rifat.  Graphic representations of effect estimates: an example from a meta-analytic review. , 1990, Journal of clinical epidemiology.

[45]  D. Altman,et al.  Assessing Risk of Bias in Included Studies , 2008 .

[46]  A. M. Walker,et al.  Odd man out: a graphical approach to meta-analysis. , 1988, American journal of public health.

[47]  T C Chalmers,et al.  Cumulative meta-analysis of therapeutic trials for myocardial infarction. , 1992, The New England journal of medicine.

[48]  Karel G M Moons,et al.  More than numbers: the power of graphs in meta-analysis. , 2008, American journal of epidemiology.

[49]  M. Zwahlen,et al.  Body-mass index and incidence of cancer: a systematic review and meta-analysis of prospective observational studies , 2008, The Lancet.

[50]  R Elvik,et al.  Evaluating the statistical conclusion validity of weighted mean results in meta-analysis by analysing funnel graph diagrams. , 1998, Accident; analysis and prevention.

[51]  K A L'Abbé,et al.  Meta-analysis in clinical research. , 1987, Annals of internal medicine.

[52]  John B. Copas,et al.  The radial plot in meta‐analysis: approximations and applications , 2009 .

[53]  Harald Breivik,et al.  Meta-analysis of epidural analgesia versus parenteral opioid analgesia after colorectal surgery , 2007 .

[54]  Brad J. Bushman,et al.  Using the normal quantile plot to explore meta-analytic data sets. , 1998 .

[55]  C S Berkey,et al.  A random-effects regression model for meta-analysis. , 1995, Statistics in medicine.

[56]  Michele Tarsilla.  Cochrane Handbook for Systematic Reviews of Interventions , 2010, Journal of MultiDisciplinary Evaluation.

[57]  R F Galbraith,et al.  A note on graphical presentation of estimated odds ratios from several clinical trials. , 1988, Statistics in medicine.

[58]  John Danesh,et al.  Seven haemostatic gene polymorphisms in coronary disease: meta-analysis of 66 155 cases and 91 307 controls , 2006, The Lancet.

[59]  A Whitehead,et al.  A general parametric approach to the meta-analysis of randomized clinical trials. , 1991, Statistics in medicine.

[60]  S. Thompson,et al.  Detecting and describing heterogeneity in meta-analysis. , 1998, Statistics in medicine.

[61]  Karin Ried,et al.  Interpreting and understanding meta-analysis graphs , 2006 .

[62]  Raghu Kacker,et al.  Random-effects model for meta-analysis of clinical trials: an update. , 2007, Contemporary clinical trials.

[63]  S. Thompson,et al.  Quantifying heterogeneity in a meta‐analysis , 2002, Statistics in medicine.

[64]  Geoffrey D. Borman,et al.  Visual and narrative interpretation , 2009 .

[65]  F. Bonnet,et al.  Meta‐analysis of epidural analgesia versus parenteral opioid analgesia after colorectal surgery , 2007, The British journal of surgery.

[66]  S Greenland,et al.  Quantitative methods in the review of epidemiologic literature. , 1987, Epidemiologic reviews.

[67]  P Glasziou,et al.  Meta-analytic methods for diagnostic test accuracy. , 1995, Journal of clinical epidemiology.

[68]  M. Pittler.  Systematic Reviews in Health Care: Meta‐analysis in Context , 2010 .

[69]  Simon G Thompson,et al.  Why and how Sources of Heterogeneity Should be Investigated , 2008 .

[70]  S G Thompson,et al.  Controversies in meta-analysis: the case of the trials of serum cholesterol reduction , 1993, Statistical methods in medical research.

[71]  Chandler Stolp,et al.  Summing Up: The Science of Reviewing Research , 1984 .

[72]  A Liberati,et al.  Understanding systematic reviews: the meta-analysis graph (also called ‘forest plot’) , 2007, Internal and emergency medicine.

[73]  L. Hedges,et al.  Introduction to Meta‐Analysis , 2009, International Coaching Psychology Review.

[74]  K R Abrams,et al.  Bayesian methods in meta-analysis and evidence synthesis. , 2001, Statistical methods in medical research.

[75]  J C Bailar,et al.  The practice of meta-analysis. , 1995, Journal of clinical epidemiology.

[76]  Christopher H Schmid,et al.  In an empirical evaluation of the funnel plot, researchers could not visually identify publication bias. , 2005, Journal of clinical epidemiology.