# Alternative funnel plot, without using standard error (SE)

Before submission of my meta-analysis I want to make a funnel plot to test for heterogeneity and publication bias. I have the pooled effect size and the effect sizes from each study, that take values from -1 to +1. I have the sample sizes n1, n2 for patients and controls from each study. As I cannot calculate the standard error (SE), I cannot perform Egger's regression. I cannot use SE or precision=1/SE on the vertical axis.

### Questions

• Can I still make a funnel plot with effect size on the horizontal axon and total sample size n (n=n1+n2) on the vertical axis?
• How should such a funnel plot be interpreted?

Some published papers presented such funnel plot with total sample size on the vertical axis (Pubmed PMIDs: 10990474, 10456970). Also, wikipedia funnel plot wiki agree on this. But, most importantly, Mathhias Egger's paper on BMJ 1999 (PubMed PMID: 9451274) shows such a funnel plot, with no SE but only sample size on the vertical axis.

### More Questions

• Is such a plot acceptable when the standard error is not known?
• Is it the same as the classical funnel plot with SE or presicion=1/SE on the vertical axon?
• Is its interpretation different?
• How should I set the lines to make the equilateral triangle?
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 what percent of your studies lack an estimate of SE? Have you considered using any of these transformations? stats.stackexchange.com/q/2917/1381 – David Feb 22 '11 at 2:53 @David All included studies lack an estimate of SE, SD, means, CI due to the nature of the analysis. See stats.stackexchange.com/questions/7426/eggers-test-in-spss for the description of the problem. Thanks for the suggested transformations. – Staty Despair Feb 23 '11 at 2:08

Q: Can I still make a funnel plot with effect size on the horizontal axon and total sample size n (n=n1+n2) on the vertical axis?
A: Yes

Q: How should such a funnel plot be interpreted?
A: It is still a funnel plot. However, funnel plots should be interpreted with caution. For example, if you have only 5-10 effect sizes, a funnel plot is useless. Furthermore, although funnel plots are a helpful visualization technique, their interpretation can be misleading. The presence of an asymmetry does not proof the existence of publication bias. Egger et al. (1997: 632f.) mention a number of reasons that can result in funnel plot asymmetries, e.g. true heterogeneity, data irregularities like methodologically poorly designed small studies or fraud. So, funnel plots can be helpful in identifying possible publication bias, however, they should always be combined with a statistical test.

Q: Is such a plot acceptable when the standard error is not known?
A: Yes

Q: Is it the same as the classical funnel plot with SE or presicion=1/SE on the vertical axon?
A: No, the shape of the 'funnel' can be different.

Q: Is its interpretation different?
A: Yes, see above

Q: How should I set the lines to make the equilateral triangle?
A: What do you mean by "lines to make the equilateral triangle"? Do you mean the 95%-CI lines? You will need the standard errors...

You also might be interested in:

They propose a statistical test which focuses on sample size instead of standard errors.

By the way, do you know the book "Publication Bias in Meta-Analysis: Prevention, Assessment and Adjustments"? It will answer a lot of your questions.

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+1 This answer is a good read due to its clarity, authority, and consistently helpful focus on responding to the questions. – whuber Feb 22 '11 at 14:53
Thanks for the clear answer. I am going to start a new thread on Peters et al 2006, JAMA paper. – Staty Despair Feb 23 '11 at 3:02