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

[Reza Norouzian]

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
> >
> >
> >         [[alternative HTML version deleted]]
> >
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