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      Is network meta-analysis as valid as standard pairwise meta-analysis? It all depends on the distribution of effect modifiers

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          Abstract

          Background

          In the last decade, network meta-analysis of randomized controlled trials has been introduced as an extension of pairwise meta-analysis. The advantage of network meta-analysis over standard pairwise meta-analysis is that it facilitates indirect comparisons of multiple interventions that have not been studied in a head-to-head fashion. Although assumptions underlying pairwise meta-analyses are well understood, those concerning network meta-analyses are perceived to be more complex and prone to misinterpretation.

          Discussion

          In this paper, we aim to provide a basic explanation when network meta-analysis is as valid as pairwise meta-analysis. We focus on the primary role of effect modifiers, which are study and patient characteristics associated with treatment effects. Because network meta-analysis includes different trials comparing different interventions, the distribution of effect modifiers cannot only vary across studies for a particular comparison (as with standard pairwise meta-analysis, causing heterogeneity), but also between comparisons (causing inconsistency). If there is an imbalance in the distribution of effect modifiers between different types of direct comparisons, the related indirect comparisons will be biased. If it can be assumed that this is not the case, network meta-analysis is as valid as pairwise meta-analysis.

          Summary

          The validity of network meta-analysis is based on the underlying assumption that there is no imbalance in the distribution of effect modifiers across the different types of direct treatment comparisons, regardless of the structure of the evidence network.

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          Most cited references 21

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          Quantifying heterogeneity in a meta-analysis.

          The extent of heterogeneity in a meta-analysis partly determines the difficulty in drawing overall conclusions. This extent may be measured by estimating a between-study variance, but interpretation is then specific to a particular treatment effect metric. A test for the existence of heterogeneity exists, but depends on the number of studies in the meta-analysis. We develop measures of the impact of heterogeneity on a meta-analysis, from mathematical criteria, that are independent of the number of studies and the treatment effect metric. We derive and propose three suitable statistics: H is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom; R is the ratio of the standard error of the underlying mean from a random effects meta-analysis to the standard error of a fixed effect meta-analytic estimate, and I2 is a transformation of (H) that describes the proportion of total variation in study estimates that is due to heterogeneity. We discuss interpretation, interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity. We conclude that H and I2, which can usually be calculated for published meta-analyses, are particularly useful summaries of the impact of heterogeneity. One or both should be presented in published meta-analyses in preference to the test for heterogeneity. Copyright 2002 John Wiley & Sons, Ltd.
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            How should meta-regression analyses be undertaken and interpreted?

            Appropriate methods for meta-regression applied to a set of clinical trials, and the limitations and pitfalls in interpretation, are insufficiently recognized. Here we summarize recent research focusing on these issues, and consider three published examples of meta-regression in the light of this work. One principal methodological issue is that meta-regression should be weighted to take account of both within-trial variances of treatment effects and the residual between-trial heterogeneity (that is, heterogeneity not explained by the covariates in the regression). This corresponds to random effects meta-regression. The associations derived from meta-regressions are observational, and have a weaker interpretation than the causal relationships derived from randomized comparisons. This applies particularly when averages of patient characteristics in each trial are used as covariates in the regression. Data dredging is the main pitfall in reaching reliable conclusions from meta-regression. It can only be avoided by prespecification of covariates that will be investigated as potential sources of heterogeneity. However, in practice this is not always easy to achieve. The examples considered in this paper show the tension between the scientific rationale for using meta-regression and the difficult interpretative problems to which such analyses are prone. Copyright 2002 John Wiley & Sons, Ltd.
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              Combination of direct and indirect evidence in mixed treatment comparisons.

              Mixed treatment comparison (MTC) meta-analysis is a generalization of standard pairwise meta-analysis for A vs B trials, to data structures that include, for example, A vs B, B vs C, and A vs C trials. There are two roles for MTC: one is to strengthen inference concerning the relative efficacy of two treatments, by including both 'direct' and 'indirect' comparisons. The other is to facilitate simultaneous inference regarding all treatments, in order for example to select the best treatment. In this paper, we present a range of Bayesian hierarchical models using the Markov chain Monte Carlo software WinBUGS. These are multivariate random effects models that allow for variation in true treatment effects across trials. We consider models where the between-trials variance is homogeneous across treatment comparisons as well as heterogeneous variance models. We also compare models with fixed (unconstrained) baseline study effects with models with random baselines drawn from a common distribution. These models are applied to an illustrative data set and posterior parameter distributions are compared. We discuss model critique and model selection, illustrating the role of Bayesian deviance analysis, and node-based model criticism. The assumptions underlying the MTC models and their parameterization are also discussed. Copyright 2004 John Wiley & Sons, Ltd.
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                Author and article information

                Contributors
                Journal
                BMC Med
                BMC Med
                BMC Medicine
                BioMed Central
                1741-7015
                2013
                4 July 2013
                : 11
                : 159
                Affiliations
                [1 ]Mapi, 180 Canal Street, Suite 503, Boston, MA 02114, USA
                [2 ]Tufts University School of Medicine, 145 Harrison Avenue, Boston, MA 02111, USA
                [3 ]LSE Health & Social Care, London School of Economics & Political Science, Cowdray House, 20 Houghton Street, London WC2A 2AE, UK
                1741-7015-11-159
                10.1186/1741-7015-11-159
                3707819
                23826681
                Copyright © 2013 Jansen and Naci; licensee BioMed Central Ltd.

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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