[R-meta] Sample-size weighting of estimates of response ratios?

[Will Hopkins]

Thanks for this reply, Wolfgang. I've searched the metafor documentation for
"rma.uni" and for "weight matrix", but I can't see how one specifies the
covariance matrix when weighting is done only by sample size. With the mixed
model in SAS, weighting by the inverse of the variances is done the long way
by holding the residual for each study estimate to its variance. (Doing it
the elegant way is achieved with a weight statement specifying the inverse
of the variance, and there is a single residual set to unity.) Presumably
the standard error of each estimate is somehow still included in the meta
(how else could you get meaningful uncertainty in the mean effect and an
estimate of heterogeneity?), even though the weighting is only by sample
size, but I can't see how. Do you still set the covariance matrix to a
diagonal of the variances, but you now include a weighting by sample size?

Will

-----Original Message-----
From: Viechtbauer, Wolfgang (NP)
<wolfgang.viechtbauer using maastrichtuniversity.nl> 
Sent: Sunday, April 16, 2023 11:11 PM
To: R Special Interest Group for Meta-Analysis
<r-sig-meta-analysis using r-project.org>
Cc: Will Hopkins <willthekiwi using gmail.com>
Subject: RE: [R-meta] Sample-size weighting of estimates of response ratios?

Dear Will,

metafor allows the user to adjust the weights to any weights deemed
reasonable. See the 'weights' argument in rma.uni() and the 'W' argument in
rma.mv() (in the latter case, one can specify an entire weight matrix).

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis 
>[mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Will 
>Hopkins via R-sig-meta-analysis
>Sent: Sunday, 16 April, 2023 3:36
>To: 'R Special Interest Group for Meta-Analysis'
>Cc: Will Hopkins
>Subject: [R-meta] Sample-size weighting of estimates of response ratios?
>
>I know that metafor allows meta-analysis of response ratios (aka factor 
>effects or ratios of means), but I can't find in the metafor 
>documentation whether it's possible to weight the individual study 
>estimates with their effective sample size rather than the usual 
>inverse of the square of the standard error.  Bakbergenuly et al. 
>(2020) recommended this approach to reduce the downward bias in the
meta-analyzed mean ratio and heterogeneity.
>I am not a user of metafor, but I need to be able to state whether it's 
>available for a manuscript I am revising with a colleague (Dave 
>Rowlands) about better approaches than standardization when meta-analyzing
means.
>Wolfgang, is it already available, or if not, do you intend to implement
it?
>
>We use SAS's proc mixed for metas, with the elegant method of setting 
>the residual variance to unity, but I don't know how to adapt this 
>method to weighting by sample size. If anyone on this list can 
>enlighten me, that would also be cool, thank you.
>
>Will
>
>Bakbergenuly I, Hoaglin DC, Kulinskaya E. Estimation in meta-analyses 
>of response ratios. BMC Med Res Methodol. 2020;20(1):263.
>doi:10.1186/s12874-020-01137-1