[R-meta] Publication Bias

[Guido Schwarzer]

Laura,

It took me some time to have a closer look.

As already mentioned by Wolfgang, our work (Rücker et al., 2008) on 
tests for funnel plot asymmetry focused on meta-analysis with binary 
outcomes comparing two groups. I am not sure whether (all of) our 
simulation results apply one-to-one to meta-analysis of single proportions.

Methods for funnel plot asymmetry in meta-analysis of single proportions 
have been evaluated in Hunter et al. (2014). According to the authors, 
it is "the first study to formally assess the utility of funnel plots 
for [...] meta-analyses of non-comparative, proportion studies". Based 
on simulation studies, they argue that sample size instead of the 
standard error of logit transformed proportions is the preferred measure 
of precision (which corresponds to use the Peters test, e.g., 
metabias(..., method = "peters") in R package *meta*). However, this 
paper does not consider arcsine or double arcsine transformed 
proportions. Using arcsine or double arcsine transformed proportions and 
corresponding standard errors should be okay as the SEs only depend on 
the sample sizes: sqrt(0.25 * (1 / n) and sqrt(1 / (4 * n + 2)), 
respectively.

Note, the use of funnel plots for single proportions has been discussed 
before in the context of public health surveillance (Spiegelhalter, 
2005; Dover & Schopflocher, 2012). In these publications, funnel plots 
are based on untransformed proportions and sample size.

I will write a separate email regarding the very different results using 
regtest() with argument model = "lm" or "rma" in *metafor* (and the 
relation to R function metabias() in *meta*).

Best wishes,
Guido


References:

Dover DC, Schopflocher DP, 2011, Using funnel plots in public health 
surveillance, Population Health Metrics, 9(1), p. 58

Hunter JP et al., 2014, In meta-analyses of proportion studies, funnel 
plots were found to be an inaccurate method of assessing publication 
bias, Journal of Clinical Epidemiology, 67(8), pp. 897-903

Rücker G et al., 2008, Arcsine test for publication bias in 
meta-analyses with binary outcomes, Statistics in Medicine, 27(5), pp. 746-6

Spiegelhalter DJ, 2005, Funnel plots for comparing institutional 
performance, Statistics in Medicine, 24(8), pp. 1185-202

-- 
Dr. Guido Schwarzer (sc at imbi.uni-freiburg.de)
Institute of Medical Biometry and Statistics
Stefan-Meier-Str. 26, D-79104 Freiburg | Phone: +49 (0)761 203 6668
http://www.imbi.uni-freiburg.de        | Fax:   +49 (0)761 203 6680


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