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

[Simon Harmel]

Dear Reza,

Thank you for demonstrating this. If I may ask a follow up question,
are values like vvc necessary for the accurate estimation of the
regression coefficient in matreg's output?

Thanks again,
Simon

On Tue, May 30, 2023 at 11:35 PM Reza Norouzian via
R-sig-meta-analysis <r-sig-meta-analysis using r-project.org> wrote:
>
> 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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> >
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