The galaxy plot: A new visualization tool for bivariate meta-analysis studies

Chuan Hong, Rui Duan, Lingzhen Zeng, Rebecca A. Hubbard, Thomas Lumley, Richard D. Riley, Haitao Chu, Stephen E. Kimmel, Yong Chen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 2-dimensional space. We illustrate the use of the galaxy plot with 2 case studies, including a meta-analysis of hypertension trials with studies from 1979-1991 (Hypertension. 2005;45(5):907-913) and a meta-analysis of structured telephone support or noninvasive telemonitoring with studies from 1966-2015 (Heart. 2017;103(4):255-257). The galaxy plot is an intuitive visualization tool that can aid in interpreting 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.

Original languageEnglish (US)
Pages (from-to)861-869
Number of pages9
JournalAmerican journal of epidemiology
Issue number8
StatePublished - Aug 1 2020

Bibliographical note

Funding Information:
The work of R.D., Y.C., and H.C. was supported in part by National Institutes of Health grants 1R01LM012607 (R.D., Y.C.), 1R01AI130460 (R.D., Y.C.), and R01LM012982A1 (H.C.). Conflict of interest: none declared.

Publisher Copyright:
© The Author(s) 2020. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail:


  • Barycenter
  • Bivariate meta-analysis
  • Funnel plots
  • Small-study effects
  • Visualization tools


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