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

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          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.


          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.


          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.


          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 references 28

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          Statistical significance for genomewide studies.

          With the increase in genomewide experiments and the sequencing of multiple genomes, the analysis of large data sets has become commonplace in biology. It is often the case that thousands of features in a genomewide data set are tested against some null hypothesis, where a number of features are expected to be significant. Here we propose an approach to measuring statistical significance in these genomewide studies based on the concept of the false discovery rate. This approach offers a sensible balance between the number of true and false positives that is automatically calibrated and easily interpreted. In doing so, a measure of statistical significance called the q value is associated with each tested feature. The q value is similar to the well known p value, except it is a measure of significance in terms of the false discovery rate rather than the false positive rate. Our approach avoids a flood of false positive results, while offering a more liberal criterion than what has been used in genome scans for linkage.
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            Computational Many-Particle Physics

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              Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial.

              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. Copyright © 2011 Elsevier Inc. All rights reserved.

                Author and article information

                BMC Med Res Methodol
                BMC Med Res Methodol
                BMC Medical Research Methodology
                BioMed Central (London )
                31 July 2015
                31 July 2015
                : 15
                Institute for Medical Biometry and Statistics, Medical Center – University of Freiburg, Stefan-Meier-Strasse 26, Freiburg, 79104 Germany
                © Rücker and Schwarzer. 2015

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.

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                © The Author(s) 2015


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