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

[Gabriele Midolo]

Hi Greta (all),

Thanks for suggesting netmeta, it sound like an interesting alternative.
However, I am wondering if the studies I am dealing with (e.g. as the one
described in my previous email) are comparable to 'multiple-arms studies'
that netmeta uses. Note that different altitudinal levels that can be
reported by multiple studies are not of different "nature" just because
measured to different altitude (m), plus we are interested in the
difference in altitude between each comparison. So, it is not like you have
a control, then two treatments of "Metformin" and "Acarbose" (two different
medicines, I assume?) as in 'Willms1999' of Senn2013 data of netmeta
examples... Don't know if I am explaining here. That's why I proposed (and
ask for confermation) of using three-level meta-analysis via rma.mv in
metafor.

Thanks and with my best,
Gabriele





On 10 April 2018 at 12:36, Gerta Ruecker <ruecker at imbi.uni-freiburg.de>
wrote:

> 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.
>
> Best,
>
> Gerta
>
> 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 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 <https://maps.google.com/?q=Stefan-Meier-Str.+26,+D-79104+Freiburg,+Germany&entry=gmail&source=g>
>
> 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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