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

[Reza Norouzian]

Simon,

If you mean the point estimates alone, not necessarily. In fact, to
estimate the (un)standardized coefficients knowing the G or H matrices
alone (simply covert G and H to correlation matrices, if standardized
coefficients are desired) suffices:

G = mvml$G
# Predicting AL from PD:
solve(G[2, 2], G[1, 2]) # compare to matreg() output in previous post

# Predicting PD from AL:
solve(G[1, 1], G[2, 1]) # compare to matreg() output in previous post

The vvc is added to improve the SEs of the coefficients leading to more
reliable inferentials (p-values, CIs etc.) given that G and H matrices are
derived from latent variables (true or equivalently random effects)
not from the observed data.

Reza

On Thu, Jun 1, 2023 at 10:33 PM Simon Harmel <sim.harmel using gmail.com> wrote:

> 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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