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

Tue May 15 20:37:15 CEST 2018

Hi,

The data is just a simplified version of the actual dataset. I included it to show the structure of the data. We also thought of only using the last sampling year, but then you´ll lose a lot of information. So I was looking for a way to include all data. So if I only have to include it in the random structure of the model, as you suggest, then I don´t see any further problems.

Thanks a lot!

Koenraad

From: Gabriele Midolo <gabriele.midolo at gmail.com>
Sent: dinsdag 15 mei 2018 18:42
To: Koenraad van Meerbeek <koenraad.vanmeerbeek at bios.au.dk>; r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] How to conduct a meta-analysis on multiple-treatment studies with a repeated measure designs?

Hi Koenraad,
I've put r-sig-meta-analysis back in the discussion too.
Data are fine to me but I don't see the number of replicates and sd values, so I can't calculate the variance-covariance matrix myself. However, assuming you have these values, you should be able to easly calculate it with the code I've sent you?
Note that I still think it could be worthy to account for replication due to different years as I wrote in the previous email (with random effect accounting for different year levels nested within each study). Something I saw quite often in ecological meta-analysis is to drop all "previous" observation from experiments and compare treatment and control of the last year only for each experiment reported by the study to avoid replication, but this can lead to important loss of information, I think. Of course, this also depend on the context of your study?
Maybe some of the other people will have better inputs on this.
With my best,
Gabriele

On 15 May 2018 at 13:34, Koenraad van Meerbeek <koenraad.vanmeerbeek at bios.au.dk<mailto:koenraad.vanmeerbeek at bios.au.dk>> wrote:
Hi Gabriele,

Thanks for the reply. I will look at the paper you mentioned.

So in response to Michael´s mail, should I post my example data table like this:
structure(list(Study = c(1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L), Treatment = structure(c(1L, 2L, 3L, 1L, 2L, 3L, 1L, 4L, 5L, 1L, 4L, 5L), .Label = c("Control", "TR1", "TR2", "TRa", "TRb"), class = "factor"), Year = c(1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L), Species_div = c(1.35, 0.78, 0.23, 1.3, 0.65, 0.2, 1.74, 1.34, 1.12, 1.69, 1.21, 0.98), Magnitude = c(0, 0.75, 1.5, 0, 0.75, 1.5, 0, 0.5, 1, 0, 0.5, 1), Duration = c(1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L)), class = "data.frame", row.names = c(NA,
-12L))

This is the output of the dput I get.

Best,

Koenraad

From: Gabriele Midolo <gabriele.midolo at gmail.com<mailto:gabriele.midolo at gmail.com>>
Sent: dinsdag 15 mei 2018 13:25
To: Koenraad van Meerbeek <koenraad.vanmeerbeek at bios.au.dk<mailto:koenraad.vanmeerbeek at bios.au.dk>>
Cc: r-sig-meta-analysis at r-project.org<mailto:r-sig-meta-analysis at r-project.org>
Subject: Re: [R-meta] How to conduct a meta-analysis on multiple-treatment studies with a repeated measure designs?

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<http://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<http://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<mailto: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<http://res.mv> <- rma.mv<http://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<http://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<https://maps.google.com/?q=Ny+Munkegade+114,+8000+Aarhus+C,+Denmark&entry=gmail&source=g>
E-mail: koenraad.vanmeerbeek[at]bios.au.dk<http://bios.au.dk>
Mobile: +32 479 206957

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