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

[James Pustejovsky]

Gabriele,

I see what you mean. Your explanation suggests that there would be high
variance in the outcome from study to study, due to examining different
species or other aspects of the study's design. I don't think that this
precludes using the raw means as effect sizes---it just means that there
would be a large between-study variance component. I think this approach
would still make it easier to model how the ES might depend on covariates
that have variation within a given study (such as altitude level).

The difficulty with using the ROM effect size is that when you compare
multiple conditions to a single control condition, there is correlation in
the effect size estimates. In the notation of your original email, you
would have
cov(yi1, yi2) != 0
cov(yi1, yi3) != 0
cov(yi2, yi3) != 0
In fact, there would be very strong dependence because yi3 = yi2 - yi1. So
if you use this approach, it would be critical to account for the sampling
covariance between the effect sizes. Lajeunesse (2011) gives formulas for
the covariances that you'd need.

James

Lajeunesse, M. J. (2011). On the meta-analysis of resposne ratios for
studies with correlated and multi-design groups. Ecology, 92(11), 2049–2055.

On Tue, Apr 10, 2018 at 10:22 AM, Gabriele Midolo <gabriele.midolo at gmail.com
> wrote:

> 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...
>
> Gabriele
>
> 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
>>>
>>>
>>> ​
>>>
>>> _______________________________________________
>>> R-sig-meta-analysis mailing list
>>> R-sig-meta-analysis at r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>
>>>
>>
>

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