[R-meta] BLUPs revisit

[Yefeng Yang]

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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