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Research article
Gerta Rücker
Universitatsklinikum Freiburg
Corresponding Author
ORCiD: https://orcid.org/0000-0002-2192-2560
License:
This work is licensed under a CC BY 4.0 License. Read Full License
Background: 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.
Methods: 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.
Results: 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.
Conclusions: 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.
Keywords
Network meta-analysis, Study weight, Study contribution, Study importance
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CURRENT STATUS: Published
View the published article at BMC Medical Research Methodology.
Version 4
Posted 08 Jul, 2020
No community comments so far
Submission checks complete
On 07 Jul, 2020
Editorial decision: Accept
On 06 Jul, 2020
No comments provided
Editorial decision: Minor revision
On 24 Jun, 2020
Review #1 received
Received 23 Jun, 2020
Reviewer #1 agreed
On 09 Jun, 2020
Reviewers invited
Invitations sent on 08 Jun, 2020
Editor assigned
On 07 Jun, 2020
Submission checks complete
On 06 Jun, 2020
Editor invited
On 06 Jun, 2020
No comments provided
Editorial decision: Major revision
On 21 May, 2020
Review #2 received
Received 20 May, 2020
Review #1 received
Received 18 May, 2020
Reviewer #1 agreed
On 30 Apr, 2020
Reviewer #2 agreed
On 30 Apr, 2020
Reviewers invited
Invitations sent on 29 Apr, 2020
Editor assigned
On 28 Apr, 2020
Editor invited
On 27 Apr, 2020
Submission checks complete
On 30 Sep, 2019
No comments provided
Editorial decision: Major revision
On 13 Mar, 2020
Review #2 received
Received 08 Mar, 2020
Reviewer #2 agreed
On 20 Feb, 2020
Review #1 received
Received 11 Nov, 2019
Reviewer #1 agreed
On 29 Oct, 2019
Reviewers invited
Invitations sent on 25 Oct, 2019
Submission checks complete
On 30 Sep, 2019
Editor assigned
On 19 Sep, 2019
Editor invited
On 18 Sep, 2019
First submitted
On 13 Sep, 2019
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HTML Views: ...
Subject Areas
Health Economics & Outcomes Research
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See the published version of this preprint at BMC Medical Research Methodology.
This is a preprint, a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research article
Gerta Rücker
Universitatsklinikum Freiburg
Corresponding Author
ORCiD: https://orcid.org/0000-0002-2192-2560
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Published
View the published article at BMC Medical Research Methodology.
Version 4
Posted 08 Jul, 2020
No community comments so far
Submission checks complete
On 07 Jul, 2020
Editorial decision: Accept
On 06 Jul, 2020
No comments provided
Editorial decision: Minor revision
On 24 Jun, 2020
Review #1 received
Received 23 Jun, 2020
Reviewer #1 agreed
On 09 Jun, 2020
Reviewers invited
Invitations sent on 08 Jun, 2020
Editor assigned
On 07 Jun, 2020
Submission checks complete
On 06 Jun, 2020
Editor invited
On 06 Jun, 2020
No comments provided
Editorial decision: Major revision
On 21 May, 2020
Review #2 received
Received 20 May, 2020
Review #1 received
Received 18 May, 2020
Reviewer #1 agreed
On 30 Apr, 2020
Reviewer #2 agreed
On 30 Apr, 2020
Reviewers invited
Invitations sent on 29 Apr, 2020
Editor assigned
On 28 Apr, 2020
Editor invited
On 27 Apr, 2020
Submission checks complete
On 30 Sep, 2019
No comments provided
Editorial decision: Major revision
On 13 Mar, 2020
Review #2 received
Received 08 Mar, 2020
Reviewer #2 agreed
On 20 Feb, 2020
Review #1 received
Received 11 Nov, 2019
Reviewer #1 agreed
On 29 Oct, 2019
Reviewers invited
Invitations sent on 25 Oct, 2019
Submission checks complete
On 30 Sep, 2019
Editor assigned
On 19 Sep, 2019
Editor invited
On 18 Sep, 2019
First submitted
On 13 Sep, 2019
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Health Economics & Outcomes Research
License:
This work is licensed under a CC BY 4.0 License. Read Full License
View the published article at BMC Medical Research Methodology.
Background: 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.
Methods: 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.
Results: 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.
Conclusions: 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.
Figure 1
Figure 2
Figure 3
Figure 4
This is a list of supplementary files associated with this preprint. Click to download.
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