[R-meta] Calculating the covariance structure for multilevel meta-analysis using the raw mean

[Akifumi Yanagisawa]

Dear all,

I am currently conducting a multilevel meta-analysis with the metafor package using the raw mean. 
The following is sample data which describes the characteristics of my data. Please note the actual data set includes more studies.

## data structure ##
dat <- data.frame(
  id = c(1,2,3,4,5, 6, 7),
  study = c("study1","study1", "study2", "study2", "study3", "study3", "study4"),
  treatment = c("treatment1","treatment1", "treatment2", "treatment3", "treatment3", "treatment4", "treatment4"),
  mi = c(5.3, 5.1, 2.2, 3.4, 2.5, 5.1, 3.3),
  sdi = c(1.2, 1.3, 0.5, 3.1, 0.7, 2.1, 0.8),
  ni = c(28, 30, 20, 20, 42, 43, 120))
require(metafor)
dat <- escalc(data = dat, measure = "MN", mi = mi, sdi = sdi, ni = ni)
dat

As you can see in the above data, some studies examined only one type of treatment. I am trying to specify the model using the the following code.

res <- rma.mv (yi, vi, mods = ~ treatment - 1, random = ~treatment | study, struct = "DIAG", data = dat)

However, I cannot figure out how to calculate the covariance structure for this case, i.e., some studies include only one treatment. I am thinking that I probably cannot use the same approach as network meta-analysis. I would appreciate it if I could learn how to calculate the covariance matrix for this case.

Also, some of the studies measured the outcome using two types of measurements. None of these studies reported a correlation between measurement 1 and measurement 2. Would it be possible for me to include this type of measurement as a factor while somehow specifying the covariance matrix for this as well? Or, should I just analyze the data separately for each type of measurement?

## data structure 2 ##
dat <- data.frame(
  id = c(1,2,3,4,5, 6, 7),
  study = c("study1","study1", "study2", "study2", "study3", "study3", "study4"),
  treatment = c("treatment1","treatment1", "treatment2", "treatment3", "treatment3", "treatment4", "treatment4"),
  measurement = c("measurement1","measurement2", "measurement1", "measurement1", "measurement2", "measurement2", "measurement1"),
  mi = c(5.3, 5.1, 2.2, 3.4, 2.5, 5.1, 3.3),
  sdi = c(1.2, 1.3, 0.5, 3.1, 0.7, 2.1, 0.8),
  ni = c(28, 30, 20, 20, 42, 43, 120))
dat <- escalc(data = dat, measure = "MN", mi = mi, sdi = sdi, ni = ni)
res <- rma.mv(data = dat ,yi, vi, mods = ~ treatment + measurement -1, random = ~treatment|study, struct = "DIAG”)


Thank you very much for your help,
Aki