[R-meta] publication bias on BLUPs

[Yefeng Yang]

Hi experts,

I am writing to you with utmost gratitude for the incredible support I received during my recent query about BLUPs on this platform. The explanations provided by experts like James, Wolfgang, and others were truly invaluable, and their selfless dedication to helping countless individuals like myself without any financial support is truly commendable.

Over the past few weeks, my fascination with BLUPs has only grown. Some knowledge might be fairly easy for experts, but they are new to me. Now I come across two new questions about BLUPs in the context of meta-analysis.

My questions are two-fold: (1) whether there is a way to test whether publication bias has an impact on the estimates of BLUPs, (2) if yes, how to get the bias-adjusted BLUPs.

Let's use the dataset in metafor as an example:
# calculate es and var
dat <- escalc(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat.egger2001, subset=-16)
# fit RE model
res <- rma(yi, vi, data=dat)
# use the Egger test to test publication bias, assuming funnel asymmetry is the proxy of publication bias
regtest(res, model="lm")  # we see there is a correlation between mean and se
#  we use a correction method. There are quite a few, such as precision-based method (i.e., intercept from Egger's test) and trim-and-fill . Here we use trim-and-fill
trimfill(res) # we get the bias-adjusted effect

So how to answer my two questions? If no readily available solution, any comments or inspiration? Very much appreciated.

Best,
Yefeng

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