[R-meta] Correcting gain effects in nested studies

[James Pustejovsky]

See Taylor, Pigott, and Williams (2022;
https://doi.org/10.3102/0013189X211051319) for how to handle
cluster-randomized trials that involve gain scores or covariate adjustment.
They provide a shiny app too. The technical details are also described in
Appendix E of the What Works Clearinghouse handbook (Version 5;
https://ies.ed.gov/ncee/WWC/Docs/referenceresources/Final_WWC-HandbookVer5_0-0-508.pdf).
See pp. 173-174

The methods described in these sources are consistent with the "general
recipe" for standardized mean difference estimates as described here:
https://www.jepusto.com/alternative-formulas-for-the-smd/

James

On Tue, May 7, 2024 at 7:14 PM Zhouhan Jin <zjin65 using uwo.ca> wrote:

> Hello All,
>
> Hedges (2007) provides formulas for adjusting SMD effects (g) and their
> SEs for when primary studies have a nested design (below).
>
> But I want to compute gain effects (ex. SMCC in metafor::escalc) from my
> nested studies, not SMDs.
>
> So, how can I adjust my SMCCs and their SEs for nestedness in the primary
> studies?
>
>
> adjusted_g =  g * sqrt(1 - ((2 * (n_bar - 1) * icc) /
>                   (n_cluster * n_bar - 2)))
>
> adjusted_SE =  ((Nt+Nc)/(Nt*Nc))*(1 + ((n_bar- 1)*icc)) +
>     ( g^2 * (
>       (((N_tot -2)*(1-icc)^2 ) + (n_bar*(N_tot - 2*n_bar)*icc^2) +
>          (2* (N_tot - 2*n_bar) * icc * (1 - icc)) ) /
>         ((2* (N_tot-2)) * ( (N_tot-2) - (2* (n_bar-1)*icc) ))
>     )  )
>
> Thanks a lot!
>
> Best wishes,
>
> Zhouhan
>
>

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