Evaluation of inconsistency in networks of interventions

BACKGROUND: The assumption of consistency, defined as agreement between direct and indirect sources of evidence, underlies the increasingly popular method of network meta-analysis. No evidence exists so far regarding the extent of inconsistency in full networks of interventions or the factors that control its statistical detection. METHODS: In this paper we assess the prevalence of inconsistency from data of 40 published networks of interventions involving 303 loops of evidence. Inconsistency is evaluated in each loop by contrasting direct and indirect estimates and by employing an omnibus test of consistency for the entire network. We explore whether different effect measures for dichotomous outcomes are associated with differences in inconsistency, and evaluate whether different ways to estimate heterogeneity affect the magnitude and detection of inconsistency. RESULTS: Inconsistency was detected in from 2% to 9% of the tested loops, depending on the effect measure and heterogeneity estimation method. Loops that included comparisons informed by a single study were more likely to show inconsistency. About one-eighth of the networks were found to be inconsistent. The proportions of inconsistent loops do not materially change when different effect measures are used. Important heterogeneity or the overestimation of heterogeneity was associated with a small decrease in the prevalence of statistical inconsistency. CONCLUSIONS: The study suggests that changing the effect measure might improve statistical consistency, and that an analysis of sensitivity to the assumptions and an estimator of heterogeneity might be needed before reaching a conclusion about the absence of statistical inconsistency, particularly in networks with few studies.