[R-meta] Assessing selection bias / multivariate meta-analysis

[Pia-Magdalena Schmidt]

Dear all,
Although this topic has been discussed several times and I read the archives 
and referenced papers, I’m still not sure how to assess and possibly correct 
for selection bias in multivariate meta-analyses.


I used the metafor package and ran meta-analyses with SMCC as effect size 
(all studies used within-designs) and fitted rma.mv models as several 
studies report more than one effect size. Furthermore, I used cluster-robust 
methods to examine the robustness of the models.
For a subset of my data, I used meta-regressions with one continuous 
moderator.
All effect sizes are from published journal articles. The range of included 
studies is between 30 and 6 with a number of effect sizes between 45 and 10.


Since I want to take the dependencies into account, I would not use funnel 
plots or trim and fill. I wonder if using Egger's regression test adjusted 
for rma.mv as well as PET-PEESE and perhaps the sensitivity analysis 
suggested by Mathur & Vanderweele (2020) as well as 3PSM would be a 
reasonable way to go? Although the latter would only use one effect size per 
study or an aggregated effect size, right?


I would be very grateful for any recommendations!
Best,
Pia

Below is an excerpt from my code:
ES_all <- escalc(measure="SMCC", m1i= m1i, sd1i= sd1i, ni = ni, m2i= m2i, 
sd2i= sd2i, pi= pi, ri = ri, data= dat)
V <- vcalc(vi=ES_all$vi, cluster=id_database, obs = effect_id, rho =0.605, 
data=dat)
res <- rma.mv(yi=ES_all$yi, V, random = ~ 1 | id_database/effect_id, data = 
dat)
res.robust <- robust(res, cluster = id_database, clubSandwich = TRUE)

# subset
res_LOR <- rma.mv(yi=ES_LOR$yi, V, random = ~ 1 | id_database/effect_id, 
mods = ~ dose, data = dat)