[R-meta] Multivariate meta regression and predict for robust estimates

[Ivan Jukic]

Dear all,

Let's say that one wants to perform a multivariate random-effects meta regression where the data structure can be described as follows: 1) There are 2 outcomes; 2) there is a continious moderator of interest; 3) all studies reported on both outcomes; and 4) most of the studies reported multiple effect sizes for at least one of the outcomes. This means that some participants, from certain groups and for a given outcome, provided data multiple times. 

Following the examples below (where 1 is extremely relevant)

1. https://www.jepusto.com/imputing-covariance-matrices-for-multi-variate-meta-analysis/ 
2. http://www.metafor-project.org/doku.php/analyses:berkey1998
3. https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2017-August/000097.html

I would specify the model as follows: 

res <- rma.mv(yi = yi,
                  V = V,
                  data = dat,
                  random = ~ outcome | study,
                  method = "REML",
                  test = "t",
                  slab = study, 
                  struct = "UN",
                  mods = ~ mod1*outcome)

A) I'm wondering if this would account for the fact that there are multiple effect sizes coming from the same study for a given outcome? In a "regular" multilevel model, I would typically have study/es_id.

B) In addition, is anyone aware of the predict function that could be used with robust estimates (e.g., after using coef_test from clubSandwich package)? Predict.rma.mv works wonderfuly in combination with robust from metafor, but I would like to take the advantage of clubSandwich's "CR2" that should in principle lead to more accurate results in small samples.

There is something similar that apparently works with robu package. 
https://rdrr.io/github/zackfisher/robumeta/src/R/predict.robu.R

Thank you for your time,
Ivan