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

Gabriele Midolo gabriele.midolo at gmail.com
Tue Apr 10 17:22:28 CEST 2018

 Dear James (all),

Thanks for your ideas, very appreciated.
I understand what you mean, but SLA can be calculated on different species
which are likely to report very different magnitude depending on the
species. Plus I think the ratios calculated with "ROM" should provide a
standardized measure of how much a single species' SLA changes in response
to altitudinal shift, that is what I think might be interesting to measure
in the context of my study.
I am not unkeen to use your option of course, I am just wondering if a
three-level meta-analysis could deal with a type of independency described
above, or it can work with data that share multiple treatment "doses"
compated to a single control...


On 10 April 2018 at 16:21, James Pustejovsky <jepusto at gmail.com> wrote:

> 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/s0003
>> 5-017-0195-9]).
>> 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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>> R-sig-meta-analysis at r-project.org
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