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

Gerta Ruecker ruecker at imbi.uni-freiburg.de
Tue Apr 10 12:36:02 CEST 2018

Dear Gabriele,

This looks like a network meta-analysis (multiple treatment comparison) 
as it is popular in medicine when comparing multiple treatments for the 
same condition in a meta-analysis. You may try the R package netmeta 
https://cran.r-project.org/web/packages/netmeta/ that is designed to 
this aim.

Note that what you call "response ratios" are not response ratios in the 
sense of an effect measure for a binary outcome, since your outcome is 
not binary. I would rather call this ratios of means. In netmeta, you 
can choose this effect measure by taking as summary measure (argument 
sm) sm = "ROM". The logarithm is then applied automatically.



Am 08.04.2018 um 18:12 schrieb 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 
> <http://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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Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Stefan-Meier-Str. 26, D-79104 Freiburg, Germany

Phone:    +49/761/203-6673
Fax:      +49/761/203-6680
Mail:     ruecker at imbi.uni-freiburg.de
Homepage: https://portal.uni-freiburg.de/imbi/persons/ruecker?set_language=en

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