[R-meta] Response Ratios in nested studies

[James Pustejovsky]

Looks like it hasn’t minted yet. Here’s a link to the journal site:
https://onlinelibrary.wiley.com/doi/full/10.1002/sim.9226

> On Oct 19, 2021, at 6:20 PM, Reza Norouzian <rnorouzian using gmail.com> wrote:
> 
> Dear James,
> 
> I think the link (https://doi.org/10.1002/sim.9226) in your post
> wasn't functional.
> 
> Kind regards,
> Reza
> 
>> On Tue, Oct 19, 2021 at 9:30 AM James Pustejovsky <jepusto using gmail.com> wrote:
>> 
>> Hi Fred,
>> 
>> This is a good question. I am in the same boat as Reza, as I don't know of
>> any methods work that examines the issue (though it seems like the sort of
>> thing that must be out there?). I'm going to respond under the assumption
>> that you don't have access to raw data and are just working with reported
>> summary statistics from a set of studies, some or all of which ignored the
>> clustering issue.
>> 
>> My first thought would be to use the same sort of cluster-correction that
>> is used for raw or standardized mean differences. The variance of the LRR
>> is based on a delta method approximation, and it can be expressed as
>> 
>> vi = se1^2 / m1^2 + se2^2 / m2^2,
>> 
>> where se1 = sd1 / sqrt(n1) and se2 = sd2 / sqrt(n2) are the standard errors
>> of the means in each group (calculated ignoring clustering, assuming a
>> sample of independent observations). The issue with clustered data is that
>> the usual standard errors are too small because of dependent observations.
>> The usual way to correct the issue is to inflate the standard errors by the
>> square root of the design effect, defined as
>> 
>> DEF = (n-lower - 1) * ICC + 1,
>> 
>> where n-lower is the number of lower-level observations per cluster (or the
>> average number of observations per cluster, if there is variation in
>> cluster size) and ICC is an intra-class correlation describing the
>> proportion of the total variation in the outcome that is between clusters.
>> 
>> If we assume that the ICC is the same in each group, then the design effect
>> hits both standard errors the same way, and so we can just use
>> 
>> vi = DEF * (se1^2 / m1^2 + se2^2 / m2^2),
>> 
>> In some areas of application, it can be hard to find empirical information
>> about ICCs, in which case you may just have to make some rough assumptions
>> in calculating the DEF then conduct sensitivity analysis for varying values
>> of ICC.
>> 
>> If my initial assumption is wrong and you do have access to raw data, then
>> the following recent article might be of help:
>> https://doi.org/10.1002/sim.9226
>> 
>> Best,
>> James
>> 
>>> On Fri, Oct 15, 2021 at 9:00 PM Farzad Keyhan <f.keyhaniha using gmail.com> wrote:
>>> 
>>> Hello All,
>>> 
>>> I recently came across a post
>>> (
>>> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-October/003330.html
>>> )
>>> that discussed an issue that is relevant to my meta-analysis.
>>> 
>>> In short, if some studies have nested structures, and the effect size
>>> of interest is log response ratio (LRR), is there a way to adjust the
>>> sampling variances (below) before modeling the effect sizes?
>>> 
>>> vi = sd1i^2/(n1i*m1i^2) + sd2i^2/(n2i*m2i^2)
>>> 
>>> Thank you,
>>> Fred
>>> 
>>> _______________________________________________
>>> R-sig-meta-analysis mailing list
>>> R-sig-meta-analysis using r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>> 
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