[R-meta] Three-level meta-analysis of response ratios when there is more than one "control group"

[Gabriele Midolo]

Dear all,

I have a question that is more methodological but somehow related to
metafor.
I want to conduct an (ecological) meta-analysis on specific leaf area (SLA)
response to increased altitdue (i.e. elevation) in mountain ecosystems.
Primary studies selected report the mean (+ SE and sample size) of SLA
sampled at different altitudinal levels. The picture attached is an example
of how row primary data are normally reported in the articles (modified,
from Seguí et al 2018, fig.1c [https://doi.org/10.1007/s00035-017-0195-9]).
The A, B and C (in red) values represents the mean values of SLA calculated
at 1900, 2200 and 2350 m above the sea level (i.e. altitude) that should,
in my opinion, be suitable for calculating log-transformed response ratios
(RR) indicating how much SLA increases/decreases compared to a population
of plants sampled to a lower altitiude. Thus, given the design of such
studies, I propose that multiple RR (yi) must be calulcated within each
study as follows:

yi1= ln(B/A)
yi2=ln(C/A)
yi3=ln(C/B)
...
if a D value would have been reported by the authors, sampled to a higher
altitdue than 2350 m, then I woul also calculate yi4=ln(D/A), yi5=ln(D/B),
yi6=ln(D/C) for this study.

This approach make sense to me because there is no "proper" control and
treatment and you are not just interested to estimate SLA changes by
comparing mean values reported at higher altitudes with only the one
sampled at the lowest altitudinal level (yi1,yi2), but also between higer
altitudinal levels (yi3). This is also supposed to allow to look in
meta-regession how the altitudinal shift (so, the difference in altitudes
e.g. 300m for yi1) affect the effect size responses. So - and here finally
comes my question - with rma.mv I should be able to safely account for
non-independence by fitting a model with the "random =~1|Experiment/ID"
structure (?). Is this type of data suitable for three-level mixed-effect
meta-analysis? I used already this structure in a previous meta-analysis I
conducted in the past, but back then I was working with multiple treatments
compared to just one single control in each study.
I see some similar meta-analysis in the past have used the r-to-z
transformed effect size and focused on the correlation - in my case -
between altitude and SLA, but not sure this is what I would like to
investigate in the first place...

Hope I was clear, and my apologies if I was messy.

Thanks a lot for reading this
Gabriele


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