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      A design-by-treatment interaction model for network meta-analysis with random inconsistency effects

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          Abstract

          Network meta-analysis is becoming more popular as a way to analyse multiple treatments simultaneously and, in the right circumstances, rank treatments. A difficulty in practice is the possibility of ‘inconsistency’ or ‘incoherence’, where direct evidence and indirect evidence are not in agreement. Here, we develop a random-effects implementation of the recently proposed design-by-treatment interaction model, using these random effects to model inconsistency and estimate the parameters of primary interest. Our proposal is a generalisation of the model proposed by Lumley and allows trials with three or more arms to be included in the analysis. Our methods also facilitate the ranking of treatments under inconsistency. We derive R and I 2 statistics to quantify the impact of the between-study heterogeneity and the inconsistency. We apply our model to two examples. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

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          The interpretation of random-effects meta-analysis in decision models.

          A Ades, G. Lu, J. P. T. Higgins (2005)
          This article shows that the interpretation of the random-effects models used in meta-analysis to summarize heterogeneous treatment effects can have a marked effect on the results from decision models. Sources of variation in meta-analysis include the following: random variation in outcome definition (amounting to a form of measurement error), variation between the patient groups in different trials, variation between protocols, and variation in the way a given protocol is implemented. Each of these alternatives leads to a different model for how the heterogeneity in the effect sizes previously observed might relate to the effect size(s) in a future implementation. Furthermore, these alternative models require different computations and, when the net benefits are nonlinear in the efficacy parameters, result in different expected net benefits. The authors' analysis suggests that the mean treatment effect from a random-effects meta-analysis will only seldom be an appropriate representation of the efficacy expected in a future implementation. Instead, modelers should consider either the predictive distribution of a future treatment effect, or they should assume that the future implementation will result in a distribution of treatment effects. A worked example, in a probabilistic, Bayesian posterior framework, is used to illustrate the alternative computations and to show how parameter uncertainty can be combined with variation between individuals and heterogeneity in meta-analysis.
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            Evidence Synthesis for Decision Making 4

            Sofia Dias, Nicky Welton, Alex J Sutton … (2013)
            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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              Undue reliance on I2 in assessing heterogeneity may mislead

              Gerta Rücker, Guido Schwarzer, James R Carpenter … (2008)
              Background The heterogeneity statistic I 2, interpreted as the percentage of variability due to heterogeneity between studies rather than sampling error, depends on precision, that is, the size of the studies included. Methods Based on a real meta-analysis, we simulate artificially 'inflating' the sample size under the random effects model. For a given inflation factor M = 1, 2, 3,... and for each trial i, we create a M-inflated trial by drawing a treatment effect estimate from the random effects model, using s i 2 /M as within-trial sampling variance. Results As precision increases, while estimates of the heterogeneity variance τ 2 remain unchanged on average, estimates of I 2 increase rapidly to nearly 100%. A similar phenomenon is apparent in a sample of 157 meta-analyses. Conclusion When deciding whether or not to pool treatment estimates in a meta-analysis, the yard-stick should be the clinical relevance of any heterogeneity present. τ 2, rather than I 2, is the appropriate measure for this purpose.
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                Author and article information

                Journal
                Journal ID (nlm-ta): Stat Med
                Journal ID (iso-abbrev): Stat Med
                Journal ID (publisher-id): sim
                Title: Statistics in Medicine
                Publisher: BlackWell Publishing Ltd (Oxford, UK )
                ISSN (Print): 0277-6715
                ISSN (Electronic): 1097-0258
                Publication date (Print): 20 September 2014
                Publication date (Electronic): 29 April 2014
                Volume: 33
                Issue: 21
                Pages: 3639-3654
                Affiliations
                [a ]MRC Biostatistics Unit Cambridge, U.K.
                [b ]Centre for Reviews and Dissemination, University of York U.K.
                [c ]University of Bristol U.K.
                Author notes
                *Correspondence to: Dan Jackson, MRC Biostatistics Unit, Institute of Public Health, Cambridge, U.K.
                [†]

                E-mail: daniel.jackson@ 123456mrc-bsu.cam.ac.uk

                Article
                DOI: 10.1002/sim.6188
                PMC ID: 4285290
                PubMed ID: 24777711
                SO-VID: f935e02e-2b12-449f-9f40-3ba1010dbb22
                Copyright © © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.
                License:

                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.

                History
                Date received : 17 December 2012
                Date revision received : 03 April 2014
                Date accepted : 06 April 2014
                Categories
                Subject: Research Articles

                ScienceOpen disciplines: Biostatistics
                Keywords: inconsistency,mixed treatment comparisons,multiple treatments meta-analysis,network meta-analysis,sensitivity analysis
                Data availability:
                ScienceOpen disciplines: Biostatistics
                Keywords: inconsistency, mixed treatment comparisons, multiple treatments meta-analysis, network meta-analysis, sensitivity analysis

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