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Abstract
BackgroundIn network meta-analysis, several alternative treatments can be compared by pooling the evidence of all randomised comparisons made in different studies. Incorporated indirect conclusions require a consistent network of treatment effects. An assessment of this assumption and of the influence of deviations is fundamental for the validity evaluation.MethodsWe show that network estimates for single pairwise treatment comparisons can be approximated by the evidence of a subnet that is decomposable into independent paths. Path-based estimates and the estimate of the residual evidence can be used with their contribution to the network estimate to set up a forest plot for the consistency assessment. Using a network meta-analysis of twelve antidepressants and controlled perturbations in the real and constructed consistent data, we discuss the consistency assessment by the independent path decomposition in contrast to an approach using a recently presented graphical tool, the net heat plot. In addition, we define influence functions that describe how changes in study effects are translated into network estimates.ResultsWhile the consistency assessment by the net heat plot comprises all network estimates, an independent path decomposition and visualisation in a forest plot is tailored to one specific treatment comparison. It allows for the recognition as to whether inconsistencies between different paths of evidence and outlier effects do affect the considered treatment comparison.ConclusionsThe approximation of the network estimate for a single comparison by the evidence of a subnet and the visualisation of the decomposition into independent paths provide the applicability of a graphical validation instrument that is known from classical meta-analysis.
Highlights
In network meta-analysis, several alternative treatments can be compared by pooling the evidence of all randomised comparisons made in different studies
In the following, we briefly present a fixed effects model for network meta-analysis that has already been explained in more detail by Krahn et al [10] and in this context analyse how changes in study effects are translated into network estimates
Characterising each study by the investigated set of treatments, it has been demonstrated that the generalised least squares estimation for a fixed effect model can be partitioned into two steps [10]: Firstly, the evidence is pooled for each design d (d = 1, . . . , D) to get an aggregated treatment effect θddir
Summary
In network meta-analysis, several alternative treatments can be compared by pooling the evidence of all randomised comparisons made in different studies. Incorporated indirect conclusions require a consistent network of treatment effects. An assessment of this assumption and of the influence of deviations is fundamental for the validity evaluation. Salanti et al [5] graphically analysed consistency using a forest plot of the differences between direct and indirect evidence in single network loops. In a forest plot, estimates based on direct, indirect (obtained by backcalculation or node-splitting [6]), and combined evidence for one treatment comparison can be compared [1,2] without reflecting detailed sources of potential inconsistencies. Krahn et al [10] proposed a matrix visualisation, called net heat plot, that highlights hot spots of inconsistency between specific direct evidence in the whole network and renders possible drivers transparent
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