[R-meta] quick question about covariances

[Andrew Guerin]

Hi, I am running an analysis in which I need to generate a variance-covariance matrix for data with shared controls ('multiple treatments dependence').
I have done this before with standardised mean differences, raw mean differences, and lnVR - calculating the covariances using formulas on the metafor website and graciously provided by James Pustejovsky.

This time my effect size data are log mean ratios / response ratios, and I was hoping someone could check my logic.

Given that the sampling variance for the effect size  - obtained using escalc(measure="ROM", vtype="LS"...) - seems to be based on the formula (from Hedges 1999)

v = (sdc ^ 2  / (nc * mc ^ 2)) + (sde ^ 2  / (ne * me ^ 2)) 

sdc, nc , mc  are sd, n and mean for the control treatment
sde, ne, me are the same for the experimental samples

then does it follow that the covariance for samples which share the same control will simply be

Cov = sdc ^ 2  / (nc * mc ^ 2) ?

Out of curiosity, if I were to use vtype="HO" instead, where the formula for the sampling variance is

v =  (sdp ^ 2)   *    (1  / (nc * mc ^ 2)) + (1  / (ne * me ^ 2))

sdp = pooled standard deviation.

Then presumably it is more complicated to calculate the covariance since sdp is already calculated using nc, sdc, ne, and sde, so would be different for every control-treatment pair.

Thanks,
Andrew