[R-meta] BLUPs revisit

Hi Yefang,

I think you've posed questions that are quite challenging to answer via a listserv discussion. They're essentially methodological research questions, and answering them properly would likely require running simulations and perhaps doing mathematical derivations. Thus, it's unlikely that people would have ready responses to questions like this.

James

On Tue, Jan 30, 2024 at 1:16?AM Yefeng Yang via R-sig-meta-analysis <r-sig-meta-analysis at r-project.org<mailto:r-sig-meta-analysis at r-project.org>> wrote:
Hi all,

Would someone like to provide some comments on my question? I would be grateful, if could help me out, especially the MA experts like Wolfgang and James.

Best,
Yefeng

________________________________
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org<mailto:r-sig-meta-analysis-bounces at r-project.org>> on behalf of Yefeng Yang via R-sig-meta-analysis <r-sig-meta-analysis at r-project.org<mailto:r-sig-meta-analysis at r-project.org>>
Sent: 26 January 2024 11:41
To: r-sig-meta-analysis at r-project.org<mailto:r-sig-meta-analysis at r-project.org> <r-sig-meta-analysis at r-project.org<mailto:r-sig-meta-analysis at r-project.org>>
Cc: Yefeng Yang <yefeng.yang1 at unsw.edu.au<mailto:yefeng.yang1 at unsw.edu.au>>
Subject: [R-meta] BLUPs revisit

Dear the community,

Hope you are all doing well in the new year.

I am very interested in BLUPs in meta-analysis. I have asked relevant questions before; something like whether sd of the BLUPs is equal to the tau. I got an excellent answer from the community.

Now I have a new one. I am considering whether we can use BLUPs to assess the statistical properties of the studies included in a meta-analysis. Very much appreciated in advance.

I would like to use a numerical example to present my question. Let's calculate the BLUPs with:
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
res <- rma(yi, vi, data=dat)
study_es <- blup(res)

The value `prep` in ` blup(res)` or object `study_es ` is actually the study-specific effect, which accounts for the sampling errors.

If I use `prep` to divide by `se` (another value in ` blup(res)` or object `study_es `), I will get the so-called signal-noise-ratio (SNR), which is different from the test statistic of each effect: yi/sqrt(vi). Next, assuming there is no publication bias, I can use SNR to calculate the power for each study: Phi(-1.96 - SNR) + 1 - Phi(1.96 - SNR). The advantage of this method is that we do not need to assume the meta-analytic effect size estimate (overall mean) is the true effect for each study.  I have two specific questions:
(1) ?Does this sound reasonable? I feel something wrong with using the `se` as the standard error of the study-specific true effect - not quite sure we should use `se` or sqrt(vi),
(2) Some literature criticizes that empirical BLUPs have large uncertainty. S to properly use them, one needs to account for the uncertainty. If this is the case, how to account for it?

Best,
Yefeng





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