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:
Peters, Jaime L., Alex J. Sutton, David R. Jones, Keith R. Abrams, and Lesly Rushton. 2006. Comparison of two methods to detect publication bias in meta-analysis. Journal of the American Medical Association 295, no. 6: 676--80. (see "An Alternative to Egger’s
Regression Test")
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.
Best Answer
With such a small number of analyzed trials, all the methods for possible detection of publication bias are underpowered. Therefore instead of claiming that you conducted any of the analyses and did not detect evidence of publication bias, you should state that:
Methods section: "We intended to assess publication bias using funnel plot techniques, Begg’s rank test and Egger’s regression test, as appropriate given the known limitations of these methods.
Results section: "Publication bias was not assessed as there were inadequate numbers of included trials to properly assess a funnel plot or more advanced regression-based assessments."
This is a standard statement I use for Cochrane reviews and teach my students.
Hope this helps.
Ahmed