[R-meta] Obtaining study-level effect size and sampling variance through robust variance models

[Mufan Luo]

Dear meta-analysists,
Hope this email finds you well.
I am conducting a meta-analysis using robust variance model. To create forest plot for each study, I’d like to obtain mean effect size and sampling variance for each study.
I decided to use forest function in metafor to create the forest plots.
Since the forest function only accepts rma file, I am trying to fit a rma model (rather than rma.uni) that produces the same coefficient, 95% CI and p-value as the robu model.
For example, below is my robu model,
run.anxiety <- robu(formula = Fisher.s.Z ~ 1,
                    var.eff.size = Fisher_var,
                    data = anxiety,
                    studynum = Study,
                    modelweights = "CORR")
According to prior discussion about converting robu to rma.uni in this mail list, I also calculated the number of studies k in cluster j, average of sampling variance Vbar, and tau square.

tau_sq_robu_anx <- as.numeric(run.anxiety$mod_info$tau.sq)
anxiety$k <- with(anxiety, table(Study)[Study])
anxiety$Vbar <- with(anxiety, tapply(Fisher_var, Study, mean)[Study])

I am trying to get the weight and plug it into the following model,

rma(yi = weightedES, vi = ??, data = weighted)

However, I am not sure if the correct calculation is

anxiety$Vnew <- with(anxiety, as.numeric(Vbar + tau_sq_robu_anx)

Thank you so much for our attention.
Best,
Mufan
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