Tipping point analysis for the between-arm correlation in an arm-based evidence synthesis

Systematic reviews and meta-analyses are essential tools in contemporary evidence-based medicine, synthesizing evidence from various sources to better inform clinical decision-making. However, the conclusions from different meta-analyses on the same topic can be discrepant, which has raised concerns about their reliability. One reason is that the result of a meta-analysis is sensitive to factors such as study inclusion/exclusion criteria and model assumptions. The arm-based meta-analysis model is growing in importance due to its advantage of including single-arm studies and historical controls with estimation efficiency and its flexibility in drawing conclusions with both marginal and conditional effect measures. Despite its benefits, the inference may heavily depend on the heterogeneity parameters that reflect design and model assumptions. This article aims to evaluate the robustness of meta-analyses using the arm-based model within a Bayesian framework. Specifically, we develop a tipping point analysis of the between-arm correlation parameter to assess the robustness of meta-analysis results. Additionally, we introduce some visualization tools to intuitively display its impact on meta-analysis results. We demonstrate the application of these tools in three real-world meta-analyses, one of which includes single-arm studies.