Abstract
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).
Highlights
Meta-analysis is the synthesis of quantitative information from related studies to produce summary results to help answer clinically relevant questions, such as whether a treatment is effective
The approach generalises how percentage weights are calculated in a traditional single parameter meta-analysis, and allows percentage weights to be derived for more complex models including meta-regression, one-stage individual participant data (IPD) analyses and multivariate and network metaanalysis
Though focus will usually be on deriving percentage study weights toward summary effects and interactions, our approach is applicable for any parameter that is specified within a meta-analysis model that can be expressed as a general or generalised linear mixed model
Summary
Meta-analysis is the synthesis of quantitative information from related studies to produce summary (pooled) results to help answer clinically relevant questions, such as whether a treatment is effective. Statistical models for meta-analysis often use aggregate data (such as a treatment effect estimate and its variance) from each study, but increasingly they utilise individual participant data (IPD).. Regardless of the approach taken, forest plots are an important way to disseminate results to a clinical audience as they quickly summarise the size and spread of individual study results alongside the summary meta-analysis result. It is preferable to include, for each study, the numerical group-specific summary data, the effect size and confidence interval, and the percentage weight’.3. Percentage study weights aim to break down the summary meta-analysis result into the relative contribution of each individual study, and are interpretable by non-statisticians In relation to forest plots, the PRISMA Statement recommends that ‘. . . it is preferable to include, for each study, the numerical group-specific summary data, the effect size and confidence interval, and the percentage weight’.3 Percentage study weights aim to break down the summary meta-analysis result into the relative contribution of each individual study, and are interpretable by non-statisticians
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