[R-meta] publication bias on BLUPs

[Yefeng Yang]

Dear James,

I appreciate your comments. Your idea of using the selection model looks very inspiring. Given that Wolfgang already developed the selection model function metafor::selmodel(), it might be worth trying it. If you happen to come across literature relevant to the bias-correction to BLUPs, I would be grateful if you would like to share it here.

Best,
Yefeng
________________________________
From: James Pustejovsky <jepusto using gmail.com>
Sent: Thursday, 6 July 2023 1:19
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Yefeng Yang <yefeng.yang1 using unsw.edu.au>
Subject: Re: [R-meta] publication bias on BLUPs

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<mailto: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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