[R-meta] Response Ratios in nested studies

[Farzad Keyhan]

Thank you Reza and James. BTW, for nested studies that have more than
two groups (say two treatments + 1 control groups), if I manage to
capture the raw data by some form of image-processing tool, can I
compute the ICC for all groups (not just for each pair of groups)
using:


         ICC::ICCbare(groups, observations, data)

Thank you,
Fred

On Tue, Oct 19, 2021 at 8:38 PM James Pustejovsky <jepusto using gmail.com> wrote:
>
> 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
>
>
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