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

Mike Cheung m|kew|cheung @end|ng |rom gm@||@com
Mon May 29 10:43:33 CEST 2023

```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
>
>
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>
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