[R-meta] Vairance-Covariance Matrix with Shared Control Group

Arthur Albuquerque @rthurc@|r|o @end|ng |rom gm@||@com
Thu Mar 3 04:13:45 CET 2022

```Hi all,

I have a couple of questions about using metafor::vcalc() to create a variance-covariance matrix when many effect sizes reflect the difference between two conditions and there is a shared control group.

According to its documentation (https://wviechtb.github.io/metafor/reference/vcalc.html), in "Details", topic 5, "The degree of correlation between two contrast-type effect sizes that is induced by the use of a shared condition is a function of the size of the groups involved in the computation of the two effect sizes... By default, the group sizes (weights) are assumed to be identical across conditions, which implies a correlation of 0.5. If the group sizes (weights) are known, they can be specified via arguments w1 and w2.".

I would like to confirm:

1 - Is the actual correlation automatically calculated when arguments 'w1' and 'w2' are specified?

2 - Can one use the number of subjects in each condition for 'w1' and 'w2'?

While looking for these answers, I saw the last example in the documentation with metadat::dat.knapp2017. If I understood correctly, the correlation is pre-specified through 'rho' and, at the same time, 'w1' and 'w2' are also specified:

V <- vcalc(vi, cluster=study, grp1=group1, grp2=group2, w1=n_sz, w2=n_hc,

'n_sz' and 'n_hc' correspond to the numbers of patients in each group, which means that the answer to my second question above would be a "Yes". Is that it?

About my first question, if the answer is also "Yes", why were 'w1', 'w2', and 'rho’ specified at the same time? Instead, if the answer is "No", what am I missing here?

Thank you in advance!

Arthur M. Albuquerque

Medical student
Universidade Federal do Rio de Janeiro, Brazil

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