[R-meta] account for uncertainty of predictors in meta-analysis

[Viechtbauer, Wolfgang (NP)]

Indeed. This goes back to van Houwelingen et al. (2002):

https://www.metafor-project.org/doku.php/analyses:vanhouwelingen2002

and even further to Becker (1992; DOI: 10.3102/10769986017004341).

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Reza Norouzian via R-sig-meta-analysis
>Sent: Wednesday, 31 May, 2023 6:35
>To: R Special Interest Group for Meta-Analysis
>Cc: Reza Norouzian
>Subject: Re: [R-meta] account for uncertainty of predictors in meta-analysis
>
>Yefeng,
>
>Along the same lines, I believe metafor gained the matreg() function a
>while back for conducting *post-hoc* latent regression from rma.mv()
>models. Using this approach, you can regress any of your outcome
>categories on another one and obtain a regression coefficient for it
>(code below).
>
>Kind regards,
>Reza
>
>V <- vcalc(vi=1, cluster=author, rvars=c(v1i, v2i), data=dat.berkey1998)
>
>mvml = rma.mv(yi, V, mods = ~ outcome + 0,
>              random = ~ outcome | trial, struct="UN",
>              data=dat.berkey1998,
>              method="ML", cvvc="varcov", control=list(nearpd=TRUE))
>
># Predicting AL from PD:
>matreg(y="AL", x="PD", R=mvml$G, cov=TRUE, means=coef(mvml), V=mvml$vvc)
>
># Predicting PD from AL:
>matreg(y="PD", x="AL", R=mvml$G, cov=TRUE, means=coef(mvml), V=mvml$vvc)
>
>On Mon, May 29, 2023 at 3:43 AM Mike Cheung via R-sig-meta-analysis
><r-sig-meta-analysis using r-project.org> wrote:
>>
>> Hi Yefeng,
>>
>> Covariates in meta-regression are treated as a design matrix. I do not see
>> how it can handle covariates with sampling variances.
>>
>> A structural equation modeling (SEM) approach can easily handle it. You may
>> refer to
>> https://stats.stackexchange.com/questions/58310/can-i-include-an-effect-size-
>as-an-independent-variable-in-a-meta-regression/58534
>> for a discussion.
>>
>> Best,
>> Mike
>>
>> On Sun, May 28, 2023 at 7:42 PM Yefeng Yang via R-sig-meta-analysis <
>> r-sig-meta-analysis using r-project.org> wrote:
>>
>> > Dear community,
>> >
>> > Do any experts have any ideas on how to use univariate methods to quantify
>> > the (bivariate) relationship between the two true outcomes? I know
>> > multivariate meta-analysis can do this. But I am asking whether it is
>> > possible to use any univariate methods to do this. See the details below
>> > based on an example dataset from metafor.
>> >
>> > Suppose my dataset has two outcomes PD and AL, which are contained in the
>> > column "outcome" in the dataset. Now I want to estimate the correlation or
>> > covariance between PD and AL.
>> >
>> > The multivariate approach is as follows:
>> > dat <- dat.berkey1998 # dataset from metafor
>> > rma.mv(yi, V, mods = ~ outcome - 1, random = ~ outcome | trial,
>> > struct="UN", data=dat)
>> > The correlation between the random effects in the output is the parameter
>> > of my interest.
>> >
>> > If we reshape the dataset to create two columns to contain PD and AL,
>> > separately, we can use an univariate method to estimate the correlation
>> > between them:
>> > rma.mv(PD ~ AL, V, random = ~ 1 | study/trial, data=dat)
>> >
>> > But in this way, we do not account for the uncertainty in AL. Or more
>> > precisely, the sampling variance in AL is not accounted for. So the
>> > estimated model coefficient is a sort of overall correlation between PD and
>> > AL, which is a sort of weighted average of correlation between true PD and
>> > AL and estimated PD and AL. Except for the Bayesian method (which uses the
>> > trick of measurement error), any solutions for this? This question can be
>> > generalized as when using estimated effect size or outcomes as predictors
>> > in the context of meta-analysis, what are the potential or best practices?
>> > Very much appreciate any comments.
>> >
>> > Best,
>> > Yefeng