[R-meta] How to conduct a meta-analysis on multiple-treatment studies with a repeated measure designs?

[Gabriele Midolo]

 Hi Koenraad,

I agree with what Michael put above.
Not sure this is what you are looking for, but I posted a similar question
some time ago and got a code from Wolfgang to build variance-covariance
matrix
based on Lajeunesse (2011) *Ecology*, 92(11), pp. 2049–2055:

calc.v <- function(x) {
   v <- matrix(x$SD_C[1]^2 / (x$N_C[1] * x$X_C[1]^2), nrow=nrow(x),
ncol=nrow(x))
   diag(v) <- x$vi
   v
}

V <- bldiag(lapply(split(dat, dat$common_ID), calc.v))
V

Where 'common_ID' is the column that codes groups of effect sizes that
share the mean ( 'X_C' ), standard deviation ( 'SD_C' ),and n ('N_C') of a
control group.
When calling rma.mv(), V is what you should then give as the second
argument instead of vi.

You should also be able to deal with repeated measure over time by adding a
nested element ( e.g. "sampling year") to the multi-level structure of your
model in rma.mv (something like "random = ~ Study / year / ID "), but I
could be wrong here...

Cheers,
Gabriele


On 14 May 2018 at 17:15, Koenraad van Meerbeek <
koenraad.vanmeerbeek at bios.au.dk> wrote:

> Dear all,
>
> We want to do a meta-analysis with the metafor package in R to study the
> effect of multiple experimental treatments on species diversity over time.
> First of all, we use data from multiple-treatment studies, in which the
> effect of different treatments are compared against a single control group.
> So far, this is the same as the Gleser & Olkin (2009) example on the
> metafor website. However, some of the studies also measured the effects of
> the treatments over time (repeated measures design).
>
> This is an example of how our data looks like (simplified). We also want
> to include magnitude of the treatment and duration of the study as
> moderator variables.
>
> Study
>
> Treatment
>
> Year
>
> Species diversity
>
> Magnitude
>
> Duration
>
> 1
>
> Control
>
> 1
>
> 1.35
>
> 0
>
> 1
>
> 1
>
> TR1
>
> 1
>
> 0.78
>
> 0.75
>
> 1
>
> 1
>
> TR2
>
> 1
>
> 0.23
>
> 1.50
>
> 1
>
> 1
>
> Control
>
> 2
>
> ...
>
> ...
>
> 2
>
> 1
>
> TR1
>
> 2
>
>
>
>
>
> 2
>
> 1
>
> TR2
>
> 2
>
>
>
>
>
> 2
>
> 2
>
> Control
>
> 1
>
>
>
>
>
> 1
>
> 2
>
> TRa
>
> 1
>
>
>
>
>
> 1
>
> 2
>
> TR2b
>
> 1
>
>
>
>
>
> 1
>
> 2
>
> Control
>
> 2
>
>
>
>
>
> 2
>
> 2
>
> TRa
>
> 2
>
>
>
>
>
> 2
>
> 2
>
> TR2b
>
> 2
>
>
>
>
>
> 2
>
>
> We started to calculate the log response ratio:
> dat <- escalc(measure = "ROM", n1i = dat$n1i, n2i = dat$n2i, m1i =
> dat$m1i,  m2 = dat$m2i, sd1i = dat$sd1i, sd2i = dat$sd2i)
>
> And then fitted following mixed effects model:
> res.mv <- rma.mv(yi, vi, mods = ~ Magnitude + Duration, random = ~ Study|
> ID, data=dat)
>
> We did not yet try to calculate a variance-covariance matrix as the Gleser
> & Olkin (2009) example, because we did not know how to take the repeated
> measures design into account.
>
> How do you suggest to proceed? Expand the res.mv with a
> variance-covariance matrix? How would you do that? Or aggregate the data
> (across years) in some way and then follow the Gleser & Olkin (2009)
> example?
>
> Best,
>
> -----
> Koenraad Van Meerbeek
> Postdoctoral researcher
> Center for Biodiversity Dynamics in a changing world (BIOCHANGE)
> Section for Ecoinformatics & Biodiversity
> Department of Bioscience | Aarhus University
> Ny Munkegade 114, 8000 Aarhus C, Denmark
> E-mail: koenraad.vanmeerbeek[at]bios.au.dk
> Mobile: +32 479 206957
>
>
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