Extending DerSimonian and Laird's methodology to perform network meta‐analyses with random inconsistency effects

Network meta‐analysis is becoming more popular as a way to compare multiple treatments simultaneously. Here, we develop a new estimation method for fitting models for network meta‐analysis with random inconsistency effects. This method is an extension of the procedure originally proposed by DerSimonian and Laird. Our methodology allows for inconsistency within the network. The proposed procedure is semi‐parametric, non‐iterative, fast and highly accessible to applied researchers. The methodology is found to perform satisfactorily in a simulation study provided that the sample size is large enough and the extent of the inconsistency is not very severe. We apply our approach to two real examples. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

[1]  N. Laird,et al.  Meta-analysis in clinical trials. , 1986, Controlled clinical trials.

[2]  Nicky J Welton,et al.  Linear inference for mixed treatment comparison meta‐analysis: a two‐stage approach , 2012, Research Synthesis Methods.

[3]  Georgia Salanti,et al.  Evaluation of networks of randomized trials , 2008, Statistical methods in medical research.

[4]  Dan Jackson,et al.  Consistency and inconsistency in network meta-analysis: model estimation using multivariate meta-regression‡ , 2012, Research synthesis methods.

[5]  Bradley P Carlin,et al.  Network meta-analysis of randomized clinical trials: Reporting the proper summaries , 2014, Clinical trials.

[6]  Richard D Riley,et al.  A matrix-based method of moments for fitting the multivariate random effects model for meta-analysis and meta-regression , 2013, Biometrical journal. Biometrische Zeitschrift.

[7]  Spyros Konstantopoulos,et al.  Fixed effects and variance components estimation in three‐level meta‐analysis , 2011, Research synthesis methods.

[8]  C. Gamble,et al.  Topical antibiotics without steroids for chronically discharging ears with underlying eardrum perforations. , 2005, The Cochrane database of systematic reviews.

[9]  Sarah E Brockwell,et al.  A simple method for inference on an overall effect in meta‐analysis , 2007, Statistics in medicine.

[10]  A E Ades,et al.  Accounting for correlation in network meta‐analysis with multi‐arm trials , 2012, Research synthesis methods.

[11]  Dan Jackson,et al.  Extending DerSimonian and Laird's methodology to perform multivariate random effects meta‐analyses , 2009, Statistics in medicine.

[12]  S Dias,et al.  Checking consistency in mixed treatment comparison meta‐analysis , 2010, Statistics in medicine.

[13]  Daniel Jackson,et al.  A refined method for multivariate meta-analysis and meta-regression , 2013, Statistics in medicine.

[14]  Ian R. White,et al.  Network Meta-analysis , 2015 .

[15]  Wolfgang Viechtbauer,et al.  Confidence intervals for the amount of heterogeneity in meta‐analysis , 2007, Statistics in medicine.

[16]  Bradley P Carlin,et al.  Bayesian hierarchical models for network meta-analysis incorporating nonignorable missingness , 2017, Statistical methods in medical research.

[17]  Tianjing Li,et al.  Network meta-analysis-highly attractive but more methodological research is needed , 2011, BMC medicine.

[18]  I. White,et al.  Quantifying the impact of between-study heterogeneity in multivariate meta-analyses , 2012, Statistics in medicine.

[19]  Andrea Cipriani,et al.  Conceptual and Technical Challenges in Network Meta-analysis , 2013, Annals of Internal Medicine.

[20]  Bradley P Carlin,et al.  Detecting outlying trials in network meta‐analysis , 2015, Statistics in medicine.

[21]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[22]  Gerta Rücker,et al.  Reduce dimension or reduce weights? Comparing two approaches to multi‐arm studies in network meta‐analysis , 2014, Statistics in medicine.

[23]  AE Ades,et al.  Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies‡ , 2012, Research synthesis methods.

[24]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[25]  Douglas G Altman,et al.  Methodological problems in the use of indirect comparisons for evaluating healthcare interventions: survey of published systematic reviews , 2009, BMJ : British Medical Journal.

[26]  Wolfgang Viechtbauer,et al.  Methods for calculating confidence and credible intervals for the residual between-study variance in random effects meta-regression models , 2014, BMC Medical Research Methodology.

[27]  Dan Jackson,et al.  A design-by-treatment interaction model for network meta-analysis with random inconsistency effects , 2014, Statistics in medicine.

[28]  Julian P T Higgins,et al.  Evaluation of inconsistency in networks of interventions. , 2013, International journal of epidemiology.

[29]  Ian R. White,et al.  Multivariate Random-effects Meta-regression: Updates to Mvmeta , 2011 .

[30]  G. Lu,et al.  Assessing Evidence Inconsistency in Mixed Treatment Comparisons , 2006 .

[31]  Christopher H. Schmid,et al.  Characteristics of Networks of Interventions: A Description of a Database of 186 Published Networks , 2014, PloS one.

[32]  Georgia Salanti,et al.  Indirect and mixed‐treatment comparison, network, or multiple‐treatments meta‐analysis: many names, many benefits, many concerns for the next generation evidence synthesis tool , 2012, Research synthesis methods.

[33]  Harald Binder,et al.  Visualizing the flow of evidence in network meta‐analysis and characterizing mixed treatment comparisons , 2013, Statistics in medicine.

[34]  Tatyana Shamliyan,et al.  A Bayesian Missing Data Framework for Multiple Continuous Outcome Mixed Treatment Comparisons , 2013 .

[35]  P. Onghena,et al.  Parametric and nonparametric bootstrap methods for meta-analysis , 2005, Behavior research methods.

[36]  Dan Jackson,et al.  Confidence intervals for the between‐study variance in random effects meta‐analysis using generalised Cochran heterogeneity statistics , 2013, Research synthesis methods.

[37]  T. Lumley.  Network meta‐analysis for indirect treatment comparisons , 2002, Statistics in medicine.

[38]  Harald Binder,et al.  A graphical tool for locating inconsistency in network meta-analyses , 2013, BMC Medical Research Methodology.

[39]  A Gasparrini,et al.  Multivariate meta-analysis for non-linear and other multi-parameter associations , 2012, Statistics in medicine.

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