[R-meta] Non-independence caused by repeated measurements over time and shared control

[Gabriele Midolo]

Dear all,

My research group is carrying out an ecological meta-analysis where primary
studies have multiple treatment (doses) compared to a single control group.
For this reason, we are fitting the model (res1), as follow:

calc.v <- function(x) {   v <- matrix((x$control_sd[1]^2 / (x$control_n[1]
* x$control_m[1]^2)) , nrow=nrow(x), ncol=nrow(x))
 diag(v) <- x$vi
 v }
get_V <- function(x) {   return(bldiag (lapply (split(x,
x$common_control_id), calc.v))) }
res1 <- rma.mv(yi, get_V(dat), random = ~ 1 | study/experiment/id,
data=dat)

where *common_control_id *is the variable identifying shared control group;
random object (~ 1 | *study/experiment/id*) reflects the nested structure
of our data where multiple experiments can be nested within each primary
study.

Our dataset nevertheless encompasses also multiple effect sizes as repeated
measurements over time (i.e. dat$time_hours) so that different treatment
doses can be compared to a single control at different time points within
each experiment. I can imagine that obtaining a variance-covariance matrix
dealing with non-independence caused by both shared control and time
measurements is going to be quite a challenge (is that even possible?).

Therefore, I was wondering to which extent it is appropriate to use inner
outer structure setting struct="AR" to deal with repeated measurements in
time, as follow (this does not account for the "study" and "id" level – I
learned that neglecting the latter is a mistake in multi-level modelling
though):

res2 <- rma.mv(yi, get_V(dat), random = ~ time_hours | experiment,
struct="AR", data=dat)

Alternatively, does it make sense using *time_hours *as a nested component
within the experiment as follow:
res3 <- rma.mv(yi, get_V(dat), random = ~ 1 |
study/experiment/time_hours/id, data=dat)

Thanks and best wishes,
Gabriele.

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