[R-meta] publication bias on BLUPs

[James Pustejovsky]

Hi Yefeng,

As far as I know, this is a wide open methodological question.

My entirely speculative first guess would be to use something like a
Vevea-Hedges selection model (e.g., metafor::selmodel()) to estimate the
mean and variance of the effect size distribution, and then calculate the
BLUPs as precision-weighted averages of the study-specific point estimates
and the overall average effect estimate. But like I said, this is nothing
more than speculation, with no supporting theory or evidence that it's
valid.

You could perhaps do something similar with regression-based corrections or
with trim-and-fill, but those methods involve very rough approximations
that aren't based on generative models for the data. I'm therefore less
keen on using them for this sort of bias correction.

James

On Tue, Jul 4, 2023 at 11:21 PM Yefeng Yang via R-sig-meta-analysis <
r-sig-meta-analysis using r-project.org> wrote:

> 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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