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Am J Epidemiol. 2020 Jan 13. pii: kwz286. doi: 10.1093/aje/kwz286. [Epub ahead of print]

Galaxy Plot: A New Visualization Tool of Bivariate Meta-Analysis Studies.

Author information

Department of Biomedical Informatics, Harvard Medical School, Boston, Massachusetts.
Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts.
Department of Statistics, University of Auckland, Auckland, New Zealand.
Research Institute of Primary Care and Health Sciences, Keele University, Staffordshire, UK.
Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, Minnesota.
Department of Medicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania.


Funnel plots have been widely used to detect small study effects in the results of univariate meta-analyses. However, there is no existing visualization tool that is the counterpart of the funnel plot in the multivariate setting. We propose a new visualization method, the galaxy plot, which can simultaneously present the effect sizes of bivariate outcomes and their standard errors in a two-dimensional space. We illustrate the use of galaxy plot by two case studies, including a meta-analysis of hypertension trials with studies from 1979 to 1991, and a meta-analysis of structured telephone support or non-invasive telemonitoring with studies from 1966 to 2015. The galaxy plot is an intuitive visualization tool that can aid in interpretation of results of multivariate meta-analysis. It preserves all of the information presented by separate funnel plots for each outcome while elucidating more complex features that may only be revealed by examining the joint distribution of the bivariate outcomes.


Bivariate Meta-Analysis; Funnel Plot; Small Study Effects; Visualization Tool


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