The statistical importance of a study for a network meta-analysis estimate
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.
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Posted 08 Jul, 2020
On 16 Jul, 2020
On 07 Jul, 2020
On 06 Jul, 2020
On 24 Jun, 2020
Received 23 Jun, 2020
On 09 Jun, 2020
Invitations sent on 08 Jun, 2020
On 07 Jun, 2020
On 06 Jun, 2020
On 06 Jun, 2020
On 21 May, 2020
Received 20 May, 2020
Received 18 May, 2020
On 30 Apr, 2020
On 30 Apr, 2020
Invitations sent on 29 Apr, 2020
On 28 Apr, 2020
On 27 Apr, 2020
On 30 Sep, 2019
On 13 Mar, 2020
Received 08 Mar, 2020
On 20 Feb, 2020
Received 11 Nov, 2019
On 29 Oct, 2019
Invitations sent on 25 Oct, 2019
On 30 Sep, 2019
On 19 Sep, 2019
On 18 Sep, 2019
On 13 Sep, 2019
The statistical importance of a study for a network meta-analysis estimate
Posted 08 Jul, 2020
On 16 Jul, 2020
On 07 Jul, 2020
On 06 Jul, 2020
On 24 Jun, 2020
Received 23 Jun, 2020
On 09 Jun, 2020
Invitations sent on 08 Jun, 2020
On 07 Jun, 2020
On 06 Jun, 2020
On 06 Jun, 2020
On 21 May, 2020
Received 20 May, 2020
Received 18 May, 2020
On 30 Apr, 2020
On 30 Apr, 2020
Invitations sent on 29 Apr, 2020
On 28 Apr, 2020
On 27 Apr, 2020
On 30 Sep, 2019
On 13 Mar, 2020
Received 08 Mar, 2020
On 20 Feb, 2020
Received 11 Nov, 2019
On 29 Oct, 2019
Invitations sent on 25 Oct, 2019
On 30 Sep, 2019
On 19 Sep, 2019
On 18 Sep, 2019
On 13 Sep, 2019
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.