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Abstract:
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The funnel plot is a graphical visualisation of summary data estimates from a meta-analysis, and is a useful tool for detecting departures from the standard modelling assumptions. Although perhaps not widely appreciated, a simple extension of the funnel plot can help to facilitate an intuitive interpretation of the mathematics underlying a meta-analysis at a more fundamental level, by equating it to determining the centre of mass of a physical system. We exploit this fact to forge new connections between statistical inference and bias adjustment in the evidence synthesis and causal inference literatures. An on-line web application (named the `Meta-Analyzer') is introduced to further facilitate this physical analogy. Finally, we demonstrate the utility of the Meta-Analyzer as a tool for detecting and adjusting for invalid instruments within the context of Mendelian randomization.
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