Visualizing inconsistency in network meta-analysis by independent path decomposition

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.

We 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.

While 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.

The 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.