Abstract
In a quantitative synthesis of studies via meta-analysis, it is possible that some studies provide a markedly different relative treatment effect or have a large impact on the summary estimate and/or heterogeneity. Extreme study effects (outliers) can be detected visually with forest/funnel plots and by using statistical outlying detection methods. A forward search (FS) algorithm is a common outlying diagnostic tool recently extended to meta-analysis. FS starts by fitting the assumed model to a subset of the data which is gradually incremented by adding the remaining studies according to their closeness to the postulated data-generating model. At each step of the algorithm, parameter estimates, measures of fit (residuals, likelihood contributions), and test statistics are being monitored and their sharp changes are used as an indication for outliers. In this article, we extend the FS algorithm to network meta-analysis (NMA). In NMA, visualization of outliers is more challenging due to the multivariate nature of the data and the fact that studies contribute both directly and indirectly to the network estimates. Outliers are expected to contribute not only to heterogeneity but also to inconsistency, compromising the NMA results. The FS algorithm was applied to real and artificial networks of interventions that include outliers. We developed an R package (NMAoutlier) to allow replication and dissemination of the proposed method. We conclude that the FS algorithm is a visual diagnostic tool that helps to identify studies that are a potential source of heterogeneity and inconsistency.
Highlights
In most healthcare conditions, we have to evaluate several competing interventions
Network meta-analysis (NMA) is an extension of pairwise meta-analysis that allows for multiple treatment comparisons by synthesizing direct and indirect evidence.[1,2,3,4,5]
The article is organized as follows: Section 2 discusses motivating examples; Section 3 discusses the random effects NMA model using graph-theoretical methods as introduced by Rücker[31]; Section 4 outlines the methodological extension of the forward search (FS) algorithm to the NMA model; Section 5 presents an application of the proposed methodology in published NMAs and simulated datasets; Section 6 discusses the main findings and provides directions for using the proposed diagnostic methodology for NMA; and Section 7 contains our conclusion
Summary
We have to evaluate several competing interventions. Network meta-analysis (NMA) is an extension of pairwise meta-analysis that allows for multiple treatment comparisons by synthesizing direct and indirect evidence.[1,2,3,4,5] Transitivity is a fundamental assumption in NMA, stating that the distribution of effect modifiers is similar across treatment comparisons.[1]. Several statistical methods have been suggested to accommodate the results from outliers within a meta-analysis by allowing for flexible distributions of the random effects. The FS algorithm was initially developed as an outlier detection tool for the estimation of covariance matrices[23] and regression models.[24,25] It was subsequently extended to standard multivariate methods,[26] factor analysis,[27] and item response theory models[28] and was recently applied in meta-regression.[29] FS starts by fitting the hypothesized data generating model to a subset of the data which is gradually incremented by adding the remaining studies according to their closeness to the postulated model. The article is organized as follows: Section 2 discusses motivating examples; Section 3 discusses the random effects NMA model using graph-theoretical methods as introduced by Rücker[31]; Section 4 outlines the methodological extension of the FS algorithm to the NMA model; Section 5 presents an application of the proposed methodology in published NMAs and simulated datasets; Section 6 discusses the main findings and provides directions for using the proposed diagnostic methodology for NMA; and Section 7 contains our conclusion
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