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Research article
The statistical importance of a study for a network meta-analysis estimate
Gerta Rücker
Universitatsklinikum Freiburg
Corresponding Author
ORCiD: https://orcid.org/0000-0002-2192-2560
License:
This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
View the published version 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.
Keywords
Network meta-analysis, Study weight, Study contribution, Study importance
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CURRENT STATUS: Under Review
Version 4
Posted 08 Jul, 2020
Published
On 16 Jul, 2020
No community comments so far
Submission checks complete
On 07 Jul, 2020
No comments provided
Editorial decision: Minor revision
On 23 Jun, 2020
Review #1 received
Received 22 Jun, 2020
Reviewer #1 agreed
On 08 Jun, 2020
Reviewers invited
Invitations sent on 07 Jun, 2020
Editor assigned
On 06 Jun, 2020
Submission checks complete
On 06 Jun, 2020
Editor invited
On 06 Jun, 2020
No comments provided
Editorial decision: Major revision
On 20 May, 2020
Review #2 received
Received 19 May, 2020
Review #1 received
Received 17 May, 2020
Reviewer #2 agreed
On 29 Apr, 2020
Reviewer #1 agreed
On 29 Apr, 2020
Reviewers invited
Invitations sent on 28 Apr, 2020
Editor assigned
On 27 Apr, 2020
Editor invited
On 27 Apr, 2020
Submission checks complete
On 29 Sep, 2019
No comments provided
Editorial decision: Major revision
On 12 Mar, 2020
Review #2 received
Received 07 Mar, 2020
Reviewer #2 agreed
On 19 Feb, 2020
Review #1 received
Received 10 Nov, 2019
Reviewer #1 agreed
On 28 Oct, 2019
Reviewers invited
Invitations sent on 24 Oct, 2019
Submission checks complete
On 29 Sep, 2019
Editor assigned
On 18 Sep, 2019
Editor invited
On 18 Sep, 2019
First submitted
On 12 Sep, 2019
Metrics
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PDF Downloads: ...
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Subject Areas
Health Economics & Outcomes Research
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This preprint is under consideration at BMC Medical Research Methodology. Preprints are preliminary reports that have not undergone peer review. They should not be considered conclusive, used to inform clinical practice, or referenced by the media as validated information.
Learn more about In Review
Research article
The statistical importance of a study for a network meta-analysis estimate
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: Under Review
Version 4
Posted 08 Jul, 2020
Published
On 16 Jul, 2020
No community comments so far
Submission checks complete
On 07 Jul, 2020
No comments provided
Editorial decision: Minor revision
On 23 Jun, 2020
Review #1 received
Received 22 Jun, 2020
Reviewer #1 agreed
On 08 Jun, 2020
Reviewers invited
Invitations sent on 07 Jun, 2020
Editor assigned
On 06 Jun, 2020
Submission checks complete
On 06 Jun, 2020
Editor invited
On 06 Jun, 2020
No comments provided
Editorial decision: Major revision
On 20 May, 2020
Review #2 received
Received 19 May, 2020
Review #1 received
Received 17 May, 2020
Reviewer #2 agreed
On 29 Apr, 2020
Reviewer #1 agreed
On 29 Apr, 2020
Reviewers invited
Invitations sent on 28 Apr, 2020
Editor assigned
On 27 Apr, 2020
Editor invited
On 27 Apr, 2020
Submission checks complete
On 29 Sep, 2019
No comments provided
Editorial decision: Major revision
On 12 Mar, 2020
Review #2 received
Received 07 Mar, 2020
Reviewer #2 agreed
On 19 Feb, 2020
Review #1 received
Received 10 Nov, 2019
Reviewer #1 agreed
On 28 Oct, 2019
Reviewers invited
Invitations sent on 24 Oct, 2019
Submission checks complete
On 29 Sep, 2019
Editor assigned
On 18 Sep, 2019
Editor invited
On 18 Sep, 2019
First submitted
On 12 Sep, 2019
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Health Economics & Outcomes Research
License:
This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
View the published version 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
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.