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To assess the characteristics and core statistical methodology specific to network meta-analyses (NMAs) in clinical research articles. We searched MEDLINE, EMBASE, and the Cochrane Database of Systematic Reviews from inception until April 14, 2015, for NMAs of randomized controlled trials including at least four different interventions. Two reviewers independently screened potential studies, whereas data abstraction was performed by a single reviewer and verified by a second. A total of 456 NMAs, which included a median (interquartile range) of 21 (13–40) studies and 7 (5–9) treatment nodes, were assessed. A total of 125 NMAs (27%) were star networks; this proportion declined from 100% in 2005 to 19% in 2015 (P = 0.01 by test of trend). An increasing number of NMAs discussed transitivity or inconsistency (0% in 2005, 86% in 2015, P < 0.01) and 150 (45%) used appropriate methods to test for inconsistency (14% in 2006, 74% in 2015, P < 0.01). Heterogeneity was explored in 256 NMAs (56%), with no change over time (P = 0.10). All pairwise effects were reported in 234 NMAs (51%), with some increase over time (P = 0.02). The hierarchy of treatments was presented in 195 NMAs (43%), the probability of being best was most commonly reported (137 NMAs, 70%), but use of surface under the cumulative ranking curves increased steeply (0% in 2005, 33% in 2015, P < 0.01). Many NMAs published in the medical literature have significant limitations in both the conduct and reporting of the statistical analysis and numerical results. The situation has, however, improved in recent years, in particular with respect to the evaluation of the underlying assumptions, but considerable room for further improvements remains.

The number of systematic reviews that aim to compare multiple interventions using network meta-analysis is increasing. In this study, we highlight aspects of a standard systematic review protocol that may need modification when multiple interventions are to be compared. We take the protocol format suggested by Cochrane for a standard systematic review as our reference and compare the considerations for a pairwise review with those required for a valid comparison of multiple interventions. We suggest new sections for protocols of systematic reviews including network meta-analyses with a focus on how to evaluate their assumptions. We provide example text from published protocols to exemplify the considerations. Standard systematic review protocols for pairwise meta-analyses need extensions to accommodate the increased complexity of network meta-analysis. Our suggested modifications are widely applicable to both Cochrane and non-Cochrane systematic reviews involving network meta-analyses.

To present some simple graphical and quantitative ways to assist interpretation and improve presentation of results from multiple-treatment meta-analysis (MTM). We reanalyze a published network of trials comparing various antiplatelet interventions regarding the incidence of serious vascular events using Bayesian approaches for random effects MTM, and we explore the advantages and drawbacks of various traditional and new forms of quantitative displays and graphical presentations of results. We present the results under various forms, conventionally based on the mean of the distribution of the effect sizes; based on predictions; based on ranking probabilities; and finally, based on probabilities to be within an acceptable range from a reference. We show how to obtain and present results on ranking of all treatments and how to appraise the overall ranks. Bayesian methodology offers a multitude of ways to present results from MTM models, as it enables a natural and easy estimation of all measures based on probabilities, ranks, or predictions.

ObjectiveTo provide a framework for quantifying the robustness of treatment ranks based on Surface Under the Cumulative RAnking curve (SUCRA) in network meta-analysis (NMA) and investigating potential factors associated with lack of robustness.MethodsWe propose the use of Cohen’s kappa to quantify the agreement between SUCRA-based treatment ranks estimated through NMA of a complete data set and a subset of it. We illustrate our approach using five published NMA data sets, where robustness was assessed by removing studies one at a time.ResultsOverall, SUCRA-based treatment ranks were robust to individual studies in the five data sets we considered. We observed more incidences of disagreement between ranks in the networks with larger numbers of treatments. Most treatments moved only one or two ranks up or down. The lowest quadratic weighted kappa estimate observed across all networks was in the network with the smallest number of treatments (4), where weighted kappa=40%. In the network with the largest number of treatments (12), the lowest observed quadratic weighted kappa=89%, reflecting a small shift in this network's treatment ranks overall. Preliminary observations suggest that a study’s size, the number of studies making a treatment comparison, and the agreement of a study’s estimated treatment effect(s) with those estimated by other studies making the same comparison(s) may explain the overall robustness of treatment ranks to studies.ConclusionsInvestigating robustness or sensitivity in an NMA may reveal outlying rank changes that are clinically or policy-relevant. Cohen’s kappa is a useful measure that permits investigation into study characteristics that may explain varying sensitivity to individual studies. However, this study presents a framework as a proof of concept and further investigation is required to identify potential factors associated with the robustness of treatment ranks using more extensive empirical evaluations.

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.

Systematic reviews and meta-analyses of randomized trials have long been important synthesis tools for guiding evidence-based medicine. More recently, network meta-analyses, an extension of traditional meta-analyses enabling the comparison of multiple interventions, use new statistical methods to incorporate clinical evidence from both direct and indirect treatment comparisons in a network of treatments and associated trials. There is a need to provide education to ensure that core methodological considerations underlying network meta-analyses are well understood by readers and researchers to maximize their ability to appropriately interpret findings and appraise validity. Network meta-analyses are highly informative for assessing the comparative effects of multiple competing interventions in clinical practice and are a valuable tool for health technology assessment and comparative effectiveness research.

Systematic reviews that employ network meta-analysis are undertaken and published with increasing frequency while related statistical methodology is evolving. Future statistical developments and evaluation of the existing methodologies could be motivated by the characteristics of the networks of interventions published so far in order to tackle real rather than theoretical problems. Based on the recently formed network meta-analysis literature we aim to provide an insight into the characteristics of networks in healthcare research. We searched PubMed until end of 2012 for meta-analyses that used any form of indirect comparison. We collected data from networks that compared at least four treatments regarding their structural characteristics as well as characteristics of their analysis. We then conducted a descriptive analysis of the various network characteristics. We included 186 networks of which 35 (19%) were star-shaped (treatments were compared to a common comparator but not between themselves). The median number of studies per network was 21 and the median number of treatments compared was 6. The majority (85%) of the non-star shaped networks included at least one multi-arm study. Synthesis of data was primarily done via network meta-analysis fitted within a Bayesian framework (113 (61%) networks). We were unable to identify the exact method used to perform indirect comparison in a sizeable number of networks (18 (9%)). In 32% of the networks the investigators employed appropriate statistical methods to evaluate the consistency assumption; this percentage is larger among recently published articles. Our descriptive analysis provides useful information about the characteristics of networks of interventions published the last 16 years and the methods for their analysis. Although the validity of network meta-analysis results highly depends on some basic assumptions, most authors did not report and evaluate them adequately. Reviewers and editors need to be aware of these assumptions and insist on their reporting and accuracy.

Random-effects meta-analyses are very commonly used in medical statistics. Recent methodological developments include multivariate (multiple outcomes) and network (multiple treatments) meta-analysis. Here, we provide a new model and corresponding estimation procedure for multivariate network meta-analysis, so that multiple outcomes and treatments can be included in a single analysis. Our new multivariate model is a direct extension of a univariate model for network metaanalysis that has recently been proposed. We allow two types of unknown variance parameters in our model, which represent between-study heterogeneity and inconsistency. Inconsistency arises when different forms of direct and indirect evidence are not in agreement, even having taken between-study heterogeneity into account. However, the consistency assumption is often assumed in practice and so we also explain how to fit a reduced model which makes this assumption. Our estimation method extends several other commonly used methods for meta-analysis, including the method proposed by DerSimonian and Laird (1986). We investigate the use of our proposed methods in the context of both a simulation study and a real example.

To illustrate the potential and challenges of the simultaneous analysis of a network of trials, using as a case study the investigation of the relative effectiveness of four topical fluoride treatments and two control interventions (placebo and no treatment) in preventing dental caries in children. We performed multiple-treatments meta-analysis within a Bayesian framework by synthesizing six Cochrane reviews. We explored the compatibility between direct and indirect evidence and adjusted the results using a meta-regression model to take into account differences in the year of randomization across studies. The validity of our conclusions for the superiority of fluoride toothpaste as indicated from the initial network analysis using Bayesian methods was challenged when we adjusted for possible confounders. The network was dominated by studies comparing placebo with toothpaste, which were older and had been carried out in populations with higher baseline risk than studies involving other fluoride modalities. After adjusting for possible differences across studies, we did not find clear evidence that any topical fluoride modality is more effective than any other. Multiple-treatments meta-analysis methods allow for more detailed investigations than naïve methods in the analysis of indirect evidence on treatment effects.