[R-meta] Which method to compute 95% confidence intervals around individual effect sizes (standardized mean differences) ?

Dakis-Yaoba OUEDRAOGO d@k|@-y@ob@@ouedr@ogo @end|ng |rom mnhn@|r
Tue May 18 16:59:53 CEST 2021

Dear all, 

I am gathering studies about effects of various chemicals on corals, and for every concentration of a chemical I computed the standardized mean differences for several outcomes. My final goal is to know for which maximal concentration of a chemical no significant effect is observed, and for which minimal concentration of a chemical a significant effect is observed. 
To get this I computed the 95% confidence intervals around the standardized mean differences to identify the effect sizes that are significantly/non significantly different from zero. 

I am quite confused about how to properly compute these condidence intervals. I could see 3 different types of CI :

1/ 95% CI assuming a normal distribution 
data$cilow <- data$yi - sqrt(data$vi)*qnorm(0.05/2, lower.tail = FALSE) 
data$ciup <- data$yi + sqrt(data$vi)*qnorm(0.05/2, lower.tail = FALSE) 

2/ 95% Wald-type confidence intervals
These are computed using the summary.escalc() function in metafor

3/ The confidence intervals computed from a multi-level model rma.mv where a variance-covariance matrix V is specified to take into account that I have several concentrations compared to the same control (Correction of Gleser & Olkin, I followed the tutorial in 
to compute V)

mod <- rma.mv(yi=yi, V=V, mods= ~1, random= ~1 | ID_case, data=data, method="REML")

With forest(mod) I can see the individual study 95%CI on the plot and I can get them with
mod$yi - sqrt(mod$vi)*qnorm(0.05/2, lower.tail = FALSE)
mod$yi + sqrt(mod$vi)*qnorm(0.05/2, lower.tail = FALSE)

Because the method chosen to compute the 95% CI around the individual standardized mean differences will greatly influence the conclusions about the problematic chemical concentrations, I will greatly appreciate any help, comment or advise on my issue.

Best wishes,

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