Meta‐analysis as a system of springs. (29th December 2020) - Papakonstantinou, Theodoros
Abstract: Meta‐analysis results are usually presented in forest plots, which show the individual study results and the summary effect along with their confidence intervals. In this paper, we propose a system of linear springs as a mechanical analogue of meta‐analysis that enables visualization and enhances intuition. The length of a spring corresponds to a study treatment effect and the stiffness of the spring corresponds to its inverse variance. To synthesize study springs we use two main operations: connection in parallel and connection in series. We show the equivalence between meta‐analysis and linear springs for fixed effect and random effects pairwise meta‐analysis and we also derive indirect treatment effects. We use examples to illustrate the different meta‐analytical schemes using the corresponding system of springs. The proposed visualization can serve as an educational tool, especially useful for researchers with no statistical background. The analogy between meta‐analysis and springs facilitates intuition for notions such as heterogeneity and the differences between fixed and random effects meta‐analysis.