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      Automated generation of node‐splitting models for assessment of inconsistency in network meta‐analysis

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          Abstract

          Network meta‐analysis enables the simultaneous synthesis of a network of clinical trials comparing any number of treatments. Potential inconsistencies between estimates of relative treatment effects are an important concern, and several methods to detect inconsistency have been proposed. This paper is concerned with the node‐splitting approach, which is particularly attractive because of its straightforward interpretation, contrasting estimates from both direct and indirect evidence. However, node‐splitting analyses are labour‐intensive because each comparison of interest requires a separate model. It would be advantageous if node‐splitting models could be estimated automatically for all comparisons of interest.

          We present an unambiguous decision rule to choose which comparisons to split, and prove that it selects only comparisons in potentially inconsistent loops in the network, and that all potentially inconsistent loops in the network are investigated. Moreover, the decision rule circumvents problems with the parameterisation of multi‐arm trials, ensuring that model generation is trivial in all cases. Thus, our methods eliminate most of the manual work involved in using the node‐splitting approach, enabling the analyst to focus on interpreting the results. © 2015 The Authors Research Synthesis Methods Published by John Wiley & Sons Ltd.

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          Most cited references 8

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          The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials.

          When little or no data directly comparing two treatments are available, investigators often rely on indirect comparisons from studies testing the treatments against a control or placebo. One approach to indirect comparison is to pool findings from the active treatment arms of the original controlled trials. This approach offers no advantage over a comparison of observational study data and is prone to bias. We present an alternative model that evaluates the differences between treatment and placebo in two sets of clinical trials, and preserves the randomization of the originally assigned patient groups. We apply the method to data on sulphamethoxazole-trimethoprim or dapsone/pyrimethamine as prophylaxis against Pneumocystis carinii in HIV infected patients. The indirect comparison showed substantial increased benefit from the former (odds ratio 0.37, 95% CI 0.21 to 0.65), while direct comparisons from randomized trials suggests a much smaller difference (risk ratio 0.64, 95% CI 0.45 to 0.90; p-value for difference of effect = 0.11). Direct comparisons of treatments should be sought. When direct comparisons are unavailable, indirect comparison meta-analysis should evaluate the magnitude of treatment effects across studies, recognizing the limited strength of inference.
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            Validity of indirect comparison for estimating efficacy of competing interventions: empirical evidence from published meta-analyses.

            To determine the validity of adjusted indirect comparisons by using data from published meta-analyses of randomised trials. Direct comparison of different interventions in randomised trials and adjusted indirect comparison in which two interventions were compared through their relative effect versus a common comparator. The discrepancy between the direct and adjusted indirect comparison was measured by the difference between the two estimates. Database of abstracts of reviews of effectiveness (1994-8), the Cochrane database of systematic reviews, Medline, and references of retrieved articles. 44 published meta-analyses (from 28 systematic reviews) provided sufficient data. In most cases, results of adjusted indirect comparisons were not significantly different from those of direct comparisons. A significant discrepancy (P<0.05) was observed in three of the 44 comparisons between the direct and the adjusted indirect estimates. There was a moderate agreement between the statistical conclusions from the direct and adjusted indirect comparisons (kappa 0.51). The direction of discrepancy between the two estimates was inconsistent. Adjusted indirect comparisons usually but not always agree with the results of head to head randomised trials. When there is no or insufficient direct evidence from randomised trials, the adjusted indirect comparison may provide useful or supplementary information on the relative efficacy of competing interventions. The validity of the adjusted indirect comparisons depends on the internal validity and similarity of the included trials.
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              Evidence Synthesis for Decision Making 4

              Inconsistency can be thought of as a conflict between “direct” evidence on a comparison between treatments B and C and “indirect” evidence gained from AC and AB trials. Like heterogeneity, inconsistency is caused by effect modifiers and specifically by an imbalance in the distribution of effect modifiers in the direct and indirect evidence. Defining inconsistency as a property of loops of evidence, the relation between inconsistency and heterogeneity and the difficulties created by multiarm trials are described. We set out an approach to assessing consistency in 3-treatment triangular networks and in larger circuit structures, its extension to certain special structures in which independent tests for inconsistencies can be created, and describe methods suitable for more complex networks. Sample WinBUGS code is given in an appendix. Steps that can be taken to minimize the risk of drawing incorrect conclusions from indirect comparisons and network meta-analysis are the same steps that will minimize heterogeneity in pairwise meta-analysis. Empirical indicators that can provide reassurance and the question of how to respond to inconsistency are also discussed.
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                Author and article information

                Journal
                Res Synth Methods
                Res Synth Methods
                10.1002/(ISSN)1759-2887
                JRSM
                Research Synthesis Methods
                John Wiley and Sons Inc. (Hoboken )
                1759-2879
                1759-2887
                13 October 2015
                March 2016
                : 7
                : 1 ( doiID: 10.1002/jrsm.v7.1 )
                : 80-93
                Affiliations
                [ 1 ] Department of EpidemiologyUniversity of Groningen, University Medical Center Groningen GroningenThe Netherlands
                [ 2 ] School of Social and Community MedicineUniversity of Bristol BristolUK
                Author notes
                [* ] Correspondence to: Gert van Valkenhoef, Department of Epidemiology, University of Groningen, University Medical Center Groningen, Groningen, The Netherlands.

                E‐mail: g.h.m.van.valkenhoef@ 123456rug.nl

                Article
                JRSM1167 RSM-03-2014-0012.R3
                10.1002/jrsm.1167
                5057346
                26461181
                © 2015 The Authors Research Synthesis Methods Published by John Wiley & Sons Ltd.

                This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

                Page count
                Pages: 14
                Product
                Categories
                Original Article
                Original Articles
                Custom metadata
                2.0
                jrsm1167
                March 2016
                Converter:WILEY_ML3GV2_TO_NLMPMC version:4.9.4 mode:remove_FC converted:12.10.2016

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