[R-meta] Can traditional publication bias modelling approaches work properly with meta-analyses of proportions?

Hi all,
I have a question about the use of publication bias modeling approaches in
meta-analyses of proportions.
The traditional approaches of assessing publication bias, such as the rank
correlation test, Egger?s regression model, and weight function approaches
have all assumed that the likelihood of a study getting published depends
on its sample size and statistical significance (Coburn and Vevea, 2015).
Although it has been confirmed by empirical research that statistical
significance plays a dominant role in publication (Preston et al., 2004),
this is not entirely the case. Cooper et al. (1997) have demonstrated that
the decision as to whether to publish a study is influenced by a variety of
criteria created by journal editors regardless of methodological quality
and significance, including but not limited to, the source of funding for
research, social preferences at the time when research is conducted, etc.
Obviously,the traditional methods fail to capture the full complexity of
the selection process.
In practice, authors of meta-analyses of proportions have employed these
methods in an attempt to detect publication bias. But, studies included in
meta-analyses of proportions are non-comparative, thus there are no
?negative? or ?undesirable? results or study characteristics like
significant levels that may have biased publications (Maulik et al., 2011).
Therefore, in my opinion, these traditional methods may not be able to
fully explain the asymmetric distribution of effect sizes on funnel plots.
It is also possible that they may fail to identify publication bias in
meta-analyses of proportions in that publication bias in non-comparative
studies may arise for reasons other than significance.
I'm not sure if my reasoning is correct. What do you think? Can the
traditional methods work properly with observational meta-analyses? If
someone could point me to some papers regarding this topic, that'd be
wonderful.
Thank you!

Naike

References:
Coburn, K. M., & Vevea, J. L. (2015). Publication bias as a function of
study characteristics. *Psychological methods*, *20*(3), 310.

Cooper, H., DeNeve, K., & Charlton, K. (1997). Finding the missing science:
The fate of studies submitted for review by a human subjects
committee. *Psychological
Methods*, *2*(4), 447.

Preston, C., Ashby, D., & Smyth, R. (2004). Adjusting for publication bias:
modelling the selection process. *Journal of Evaluation in Clinical
Practice*, *10*(2), 313-322.

Maulik, P. K., Mascarenhas, M. N., Mathers, C. D., Dua, T., & Saxena, S.
(2011). Prevalence of intellectual disability: a meta-analysis of
population-based studies. *Research in developmental disabilities*, *32*(2),
419-436.