[R-meta] Response Ratios in nested studies

[Reza Norouzian]

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
> >
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