Riley, RD, Ensor, J, Jackson, D and Burke, DL (2017) Deriving percentage study weights in multi-parameter meta-analysis models: with application to meta-regression, network meta-analysis and one-stage individual participant data models. Stat Methods Med Res, 27 (10). pp. 2885-2905. ISSN 1477-0334

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Many meta-analysis models contain multiple parameters, for example due to multiple outcomes, multiple treatments or multiple regression coefficients. In particular, meta-regression models may contain multiple study-level covariates, and one-stage individual participant data meta-analysis models may contain multiple patient-level covariates and interactions. Here, we propose how to derive percentage study weights for such situations, in order to reveal the (otherwise hidden) contribution of each study toward the parameter estimates of interest. We assume that studies are independent, and utilise a decomposition of Fisher's information matrix to decompose the total variance matrix of parameter estimates into study-specific contributions, from which percentage weights are derived. This approach generalises how percentage weights are calculated in a traditional, single parameter meta-analysis model. Application is made to one- and two-stage individual participant data meta-analyses, meta-regression and network (multivariate) meta-analysis of multiple treatments. These reveal percentage study weights toward clinically important estimates, such as summary treatment effects and treatment-covariate interactions, and are especially useful when some studies are potential outliers or at high risk of bias. We also derive percentage study weights toward methodologically interesting measures, such as the magnitude of ecological bias (difference between within-study and across-study associations) and the amount of inconsistency (difference between direct and indirect evidence in a network meta-analysis).

Item Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution 3.0 License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (
Uncontrolled Keywords: percentage study weights; Fisher's information; individual patient data meta-analysis; meta-regression; network meta-analysis
Subjects: R Medicine > RA Public aspects of medicine
Divisions: Faculty of Medicine and Health Sciences > Primary Care Health Sciences
Related URLs:
Depositing User: Symplectic
Date Deposited: 02 Mar 2017 16:04
Last Modified: 08 Oct 2018 13:11

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