### Table of Contents

## Funnel Plot Variations

### Description

A funnel plot shows the observed effect sizes or outcomes on the x-axis against some measure of precision of the observed effect sizes or outcomes on the y-axis. Based on Sterne and Egger (2001), the recommended choice for the y-axis is the standard error (in decreasing order) and this is also the default for the `funnel()`

function in the metafor package. In the absence of publication bias and heterogeneity, one would then expect to see the points forming a funnel shape, with the majority of the points falling inside of the pseudo-confidence region with bounds $\hat{\theta} \pm 1.96 SE$, where $\hat{\theta}$ is the estimated effect or outcome based on an equal-effects model and $SE$ is the standard error value from the y-axis. With other measures of precision for the y-axis, the expected shape of the funnel can be rather different. The plot below shows a variety of choices for the y-axis and how this impacts the shape of the funnel plot (and the form of the pseudo-confidence region).

### Plot

### Code

library(metafor) ### fit equal-effects model res <- rma(yi, vi, data=dat.hackshaw1998, measure="OR", method="EE") ### set up 2x2 array for plotting par(mfrow=c(2,2)) ### draw funnel plots funnel(res, main="Standard Error") funnel(res, yaxis="vi", main="Sampling Variance") funnel(res, yaxis="seinv", main="Inverse Standard Error") funnel(res, yaxis="vinv", main="Inverse Sampling Variance")

### References

Sterne, J. A. C., & Egger, M. (2001). Funnel plots for detecting bias in meta-analysis: Guidelines on choice of axis. *Journal of Clinical Epidemiology, 54*(10), 1046–1055.