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      Ranking treatments in frequentist network meta-analysis works without resampling methods

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          Abstract

          Background

          Network meta-analysis is used to compare three or more treatments for the same condition. Within a Bayesian framework, for each treatment the probability of being best, or, more general, the probability that it has a certain rank can be derived from the posterior distributions of all treatments. The treatments can then be ranked by the surface under the cumulative ranking curve (SUCRA). For comparing treatments in a network meta-analysis, we propose a frequentist analogue to SUCRA which we call P-score that works without resampling.

          Methods

          P-scores are based solely on the point estimates and standard errors of the frequentist network meta-analysis estimates under normality assumption and can easily be calculated as means of one-sided p-values. They measure the mean extent of certainty that a treatment is better than the competing treatments.

          Results

          Using case studies of network meta-analysis in diabetes and depression, we demonstrate that the numerical values of SUCRA and P-Score are nearly identical.

          Conclusions

          Ranking treatments in frequentist network meta-analysis works without resampling. Like the SUCRA values, P-scores induce a ranking of all treatments that mostly follows that of the point estimates, but takes precision into account. However, neither SUCRA nor P-score offer a major advantage compared to looking at credible or confidence intervals.

          Electronic supplementary material

          The online version of this article (doi:10.1186/s12874-015-0060-8) contains supplementary material, which is available to authorized users.

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          Most cited references12

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          Indirect treatment comparison/network meta-analysis study questionnaire to assess relevance and credibility to inform health care decision making: an ISPOR-AMCP-NPC Good Practice Task Force report.

          Despite the great realized or potential value of network meta-analysis of randomized controlled trial evidence to inform health care decision making, many decision makers might not be familiar with these techniques. The Task Force developed a consensus-based 26-item questionnaire to help decision makers assess the relevance and credibility of indirect treatment comparisons and network meta-analysis to help inform health care decision making. The relevance domain of the questionnaire (4 questions) calls for assessments about the applicability of network meta-analysis results to the setting of interest to the decision maker. The remaining 22 questions belong to an overall credibility domain and pertain to assessments about whether the network meta-analysis results provide a valid answer to the question they are designed to answer by examining 1) the used evidence base, 2) analysis methods, 3) reporting quality and transparency, 4) interpretation of findings, and 5) conflicts of interest. The questionnaire aims to help readers of network meta-analysis opine about their confidence in the credibility and applicability of the results of a network meta-analysis, and help make decision makers aware of the subtleties involved in the analysis of networks of randomized trial evidence. It is anticipated that user feedback will permit periodic evaluation and modification of the questionnaire. Copyright © 2014 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.
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            Efficacy and acceptability of pharmacological treatments for depressive disorders in primary care: systematic review and network meta-analysis.

            The purpose of this study was to investigate whether antidepressants are more effective than placebo in the primary care setting, and whether there are differences between substance classes regarding efficacy and acceptability. We conducted literature searches in MEDLINE, Embase, Cochrane Central Register of Controlled Trials (CENTRAL), and PsycINFO up to December 2013. Randomized trials in depressed adults treated by primary care physicians were included in the review. We performed both conventional pairwise meta-analysis and network meta-analysis combining direct and indirect evidence. Main outcome measures were response and study discontinuation due to adverse effects. A total of 66 studies with 15,161 patients met the inclusion criteria. In network meta-analysis, tricyclic and tetracyclic antidepressants (TCAs), selective serotonin reuptake inhibitors (SSRIs), a serotonin-noradrenaline reuptake inhibitor (SNRI; venlafaxine), a low-dose serotonin antagonist and reuptake inhibitor (SARI; trazodone) and hypericum extracts were found to be significantly superior to placebo, with estimated odds ratios between 1.69 and 2.03. There were no statistically significant differences between these drug classes. Reversible inhibitors of monoaminoxidase A (rMAO-As) and hypericum extracts were associated with significantly fewer dropouts because of adverse effects compared with TCAs, SSRIs, the SNRI, a noradrenaline reuptake inhibitor (NRI), and noradrenergic and specific serotonergic antidepressant agents (NaSSAs). Compared with other drugs, TCAs and SSRIs have the most solid evidence base for being effective in the primary care setting, but the effect size compared with placebo is relatively small. Further agents (hypericum, rMAO-As, SNRI, NRI, NaSSAs, SARI) showed some positive results, but limitations of the currently available evidence makes a clear recommendation on their place in clinical practice difficult. © 2015 Annals of Family Medicine, Inc.
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              Analysis of the systematic reviews process in reports of network meta-analyses: methodological systematic review

              Objective To examine whether network meta-analyses, increasingly used to assess comparative effectiveness of healthcare interventions, follow the key methodological recommendations for reporting and conduct of systematic reviews. Design Methodological systematic review of reports of network meta-analyses. Data sources Cochrane Database of Systematic Reviews, Database of Abstracts of Reviews of Effects, Medline, and Embase, searched from inception to 12 July 2012. Review methods All network meta-analyses comparing clinical efficacy of three or more interventions based on randomised controlled trials, excluding meta-analyses with an open loop network of three interventions. We assessed the reporting of general characteristics and key methodological components of the systematic review process using two composite outcomes. For some components, if reporting was adequate, we assessed their conduct quality. Results Of 121 network meta-analyses covering a wide range of medical areas, 100 (83%) assessed pharmacological interventions and 11 (9%) non-pharmacological interventions; 56 (46%) were published in journals with a high impact factor. The electronic search strategy for each database was not reported in 88 (73%) network meta-analyses; for 36 (30%), the primary outcome was not clearly identified. Overall, 61 (50%) network meta-analyses did not report any information regarding the assessment of risk of bias of individual studies, and 103 (85%) did not report any methods to assess the likelihood of publication bias. Overall, 87 (72%) network meta-analyses did not report the literature search, searched only one database, did not search other sources, or did not report an assessment of risk of bias of individual studies. These methodological components did not differ by publication in a general or specialty journal or by public or private funding. Conclusions Essential methodological components of the systematic review process—conducting a literature search and assessing risk of bias of individual studies—are frequently lacking in reports of network meta-analyses, even when published in journals with high impact factors.
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                Author and article information

                Contributors
                ruecker@imbi.uni-freiburg.de
                sc@imbi.uni-freiburg.de
                Journal
                BMC Med Res Methodol
                BMC Med Res Methodol
                BMC Medical Research Methodology
                BioMed Central (London )
                1471-2288
                31 July 2015
                31 July 2015
                2015
                : 15
                : 58
                Affiliations
                Institute for Medical Biometry and Statistics, Medical Center – University of Freiburg, Stefan-Meier-Strasse 26, Freiburg, 79104 Germany
                Article
                60
                10.1186/s12874-015-0060-8
                4521472
                26227148
                cc5038d7-dedf-466c-b566-aaffbbe5b804
                © Rücker and Schwarzer. 2015

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

                History
                : 6 May 2015
                : 23 July 2015
                Categories
                Research Article
                Custom metadata
                © The Author(s) 2015

                Medicine
                network meta-analysis,ranking,‘probability of being best’-statistic,surface under the cumulative ranking,sucra,p-value,auc

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