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

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at 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 at 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 at 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