[R-meta] Response Ratios in nested studies

[James Pustejovsky]

Hi Fred,

Yes, it is definitely possible and sensible to combine the DEF correction
with RVE meta-analysis. However, I think it may be important to use the
initial DEF correction (and accompanying sensitivity analysis), even if it
is only based on ballpark assumptions. Without it, studies with clustered
samples will get an inordinately large amount of weight in the
meta-analysis, leading to imprecise estimates of average effects and
inflated estimates of between-study heterogeneity.

James

On Tue, Oct 19, 2021 at 10:07 AM Farzad Keyhan <f.keyhaniha using gmail.com>
wrote:

> Dear Reza and James,
>
> Thank you so much for your, as always, valuable advice. Can we
> possibly combine your two suggestions?
>
> I mean can we both correct the initial, incorrect sampling variances
> and then apply the clubSandwich package?
>
> The reason is that finding the correct ICC is one issue, but then
> assuming that ICC is going to be the same across the groups is another
> issue which together make such a correction possibly a bit imprecise.
>
> Thanks much,
> Fred
>
>
> 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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>

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