Rucker, G, Nikolakopoulou, A, Papakonstantinou, T, Salanti, G, Riley, R and Schwarzer, G (2020) The statistical importance of a study for a network meta-analysis estimate. BMC Medical Research Methodology, 20 (1). ISSN 1471-2288

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In pairwise meta-analysis, the contribution of each study to the pooled estimate is given by its weight, which is based on the inverse variance of the estimate from that study. For network meta-analysis (NMA), the contribution of direct (and indirect) evidence is easily obtained from the diagonal elements of a hat matrix. It is, however, not fully clear how to generalize this to the percentage contribution of each study to a NMA estimate.

We define the importance of each study for a NMA estimate by the reduction of the estimate’s variance when adding the given study to the others. An equivalent interpretation is the relative loss in precision when the study is left out. Importances are values between 0 and 1. An importance of 1 means that the study is an essential link of the pathway in the network connecting one of the treatments with another.

Importances can be defined for two-stage and one-stage NMA. These numbers in general do not add to one and thus cannot be interpreted as ‘percentage contributions’. After briefly discussing other available approaches, we question whether it is possible to obtain unique percentage contributions for NMA.

Importances generalize the concept of weights in pairwise meta-analysis in a natural way. Moreover, they are uniquely defined, easily calculated, and have an intuitive interpretation. We give some real examples for illustration.

Item Type: Article
Additional Information: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated in a credit line to the data.
Uncontrolled Keywords: Network meta-analysis; Study weight; Study contribution; Study importance
Subjects: R Medicine > R Medicine (General)
R Medicine > R Medicine (General) > R735 Medical education. Medical schools. Research
Divisions: Faculty of Medicine and Health Sciences > School of Primary, Community and Social Care
Depositing User: Symplectic
Date Deposited: 21 Jul 2020 10:43
Last Modified: 17 Aug 2020 13:38

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