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

Yefeng Yang ye|eng@y@ng1 @end|ng |rom un@w@edu@@u
Sun May 28 13:41:35 CEST 2023

```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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