[R-meta] Response Ratios in nested studies

[James Pustejovsky]

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
>

	[[alternative HTML version deleted]]