Quantitative assessment of inconsistency in meta-analysis using decision thresholds with two new indices

Objectives: In evidence synthesis, inconsistency is typically assessed visually and with the I² and the Q statistics. However, these measures have important limitations (i) if there are few primary studies of small sample sizes or (ii) if there are multiple studies with precise estimates. In addition, with the increasing use of decision thresholds (DT), for example in Grading of Recommendations Assessment, Development and Evaluation evidence to decision (EtD) frameworks, inconsistency judgments can be anchored around DTs. In this article, we developed quantitative measures to assess inconsistency based on DTs. Study Design and Setting: We developed two measures to quantify inconsistency based on DTs – the decision inconsistency (DI) and the across-studies inconsistency (ASI) indices. The DI and the ASI are based on the distribution of the posterior samples studies’ effect sizes (ES) across interpretation categories defined by DTs. We developed these indices for the Bayesian context, followed by a frequentist extension. Results: The DI informs on the overall inconsistency of ESs across interpretation categories, while the ASI quantifies how different studies are compared to each other (in relation to interpretation categories) based on absolute effects. A DI ≥ 50% and an ASI ≥ 25% are suggestive of important inconsistency. We provide an R package (metainc) and a web tool (https://metainc.med.up.pt/) to support the computation of the DI and ASI, including in the context of sensitivity analyses assessing the impact of potential uncertainty in inconsistency. Conclusion: The DI and the ASI can contribute to quantitatively assess inconsistency, particularly as DTs are gaining recognition in evidence synthesis and health decision-making.