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

[James Pustejovsky]

Gabriele,

If all of the studies use SLA as the outcome measure, would it make sense
to model the mean levels directly (instead of calculating proportionate
changes)? In other words, use the mean SLA level as the effect size. If it
makes sense conceptually, I think this would be a good way to go because
then the effect size estimates at each altitude level would be independent
of each other, conditional on the true mean levels for that study, and a
three-level meta-analysis model would be a natural fit.

James

On Sun, Apr 8, 2018 at 11:12 AM, Gabriele Midolo <gabriele.midolo at gmail.com>
wrote:

> 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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