I am currently conducting a meta-analysis where we have several studies that report multiple outcomes from the same participants. We've been advised to use the
rma.mv function from the
metafor package in R. I have two questions about this:
1) We don't know the covariances between the different outcomes in the same studies (they're not reported in most papers). Until recently, I was thinking that the dependency among these outcomes would be accounted for by specifying a random effects structure like
random = ~ 1 | study. However, I've been reading that we should also be specifying the covariances between outcomes, and instead specify a random effects structure like
random = ~ outcome | study. What is the difference between these two approaches? Will simply specifying a random effect for study without knowing the covariances between outcomes within a study result in inaccurate estimates? Alternately, would it be possible/a good idea to specify a random effects structure like
random = ~ outcome | study without including the covariances between outcomes? Not all studies measure all outcomes in our meta-analysis.
2) I would like to calculate how much heterogeneity in effect sizes comes from between-study variance and how mcuh comes from within-study variance. Is there a statistic that
rma.mv can give me to tell me this? I understand that Cochran's Q is a test of heterogeneity, but can it be partialled into between- and within-study heterogeneity?