Estimating the contribution of studies in network meta-analysis: paths, flows and streams.

Papakonstantinou, Theodoros; Nikolakopoulou, Adriani; Rücker, Gerta; Chaimani, Anna; Schwarzer, Guido; Egger, Matthias; Salanti, Georgia (2018). Estimating the contribution of studies in network meta-analysis: paths, flows and streams. F1000Research, 7, p. 610. F1000 Research Ltd 10.12688/f1000research.14770.2

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In network meta-analysis, it is important to assess the influence of the limitations or other characteristics of individual studies on the estimates obtained from the network. The percentage contribution matrix, which shows how much each direct treatment effect contributes to each treatment effect estimate from network meta-analysis, is crucial in this context. We use ideas from graph theory to derive the percentage that is contributed by each direct treatment effect. We start with the 'projection' matrix in a two-step network meta-analysis model, called the matrix, which is analogous to the hat matrix in a linear regression model. We develop a method to translate entries to percentage contributions based on the observation that the rows of  can be interpreted as flow networks, where a stream is defined as the composition of a path and its associated flow. We present an algorithm that identifies the flow of evidence in each path and decomposes it into direct comparisons. To illustrate the methodology, we use two published networks of interventions. The first compares no treatment, quinolone antibiotics, non-quinolone antibiotics and antiseptics for underlying eardrum perforations and the second compares 14 antimanic drugs. We believe that this approach is a useful and novel addition to network meta-analysis methodology, which allows the consistent derivation of the percentage contributions of direct evidence from individual studies to network treatment effects.

Item Type:

Journal Article (Original Article)


04 Faculty of Medicine > Pre-clinic Human Medicine > Institute of Social and Preventive Medicine (ISPM)

UniBE Contributor:

Papakonstantinou, Theodoros; Nikolakopoulou, Adriani; Egger, Matthias and Salanti, Georgia


600 Technology > 610 Medicine & health
300 Social sciences, sociology & anthropology > 360 Social problems & social services




F1000 Research Ltd




Tanya Karrer

Date Deposited:

25 Oct 2018 12:35

Last Modified:

22 Oct 2019 17:31

Publisher DOI:


PubMed ID:


Additional Information:

Papkonstantinou and Nikolakopoulou contributed equally to this work

Uncontrolled Keywords:

flow networks indirect evidence percentage contributions projection matrix




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