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.
Bibliographical noteFunding 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.
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- Bivariate meta-analysis
- Funnel plots
- Small-study effects
- Visualization tools