Paper detail

On the physical interpretation of a meta-analysis in the presence of heterogeneity and bias: from clinical trials to Mendelian randomization

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 used this analogy, with some success, to explain the concepts of weighing evidence and of biased evidence to a young audience at the Cambridge Science Festival, without recourse to precise definitions or statistical formulae. In this paper we aim to formalise this analogy at a more technical level using the estimating equation framework: firstly, to help elucidate some of the basic statistical models employed in a meta-analysis and secondly, to forge new connections between bias adjustment in the evidence synthesis and causal inference literatures.