# [R-meta] Covariance-variance matrix when studies share multiple treatment x control comparison

Ju Lee juhyung2 @end|ng |rom @t@n|ord@edu
Thu Sep 26 14:57:35 CEST 2019

```Dear Wolfgang,

Thank you for your response and sorry I forgot to CC the mailing list!
I am currently running my egger's regression test as shown below. My previous understanding was that I should look at the p-value of intercept term (following a previously published R code) if I run a "mixed" model using precision as moderator variable against residuals, but according to your comments I should be looking at the precision coefficients instead? So based on my outputs below, significance testing of plot asymmetry is at p=0.09 and not p=0.3823?

Also, if I find significant violation of plot asymmetry in such case what additional options do I have to test these issues? I am currently calculating FSN which are extremely higher than proposed thresholds and removing influential outliers and re-fitting the model. But because rma.mv does not allow me to use other methods like trim and fill I wonder if these two other methods would be enough in case we detect plot asymmetry.

Best regards,
JU

>Full.egger.es<-rma.mv(hedged,var, method="REML", random = ~ 1 | Study, data=MHF)
>MHF\$residuals<-residuals.rma(Full.egger.es)
>MHF\$precision<-1/sqrt(MHF\$var)
>egger.full<-rma.mv(residuals~precision,var,data=MHF,random = ~ 1 | Study)
>egger.full

Multivariate Meta-Analysis Model (k = 857; method: REML)

Variance Components:

estim    sqrt  nlvls  fixed  factor
sigma^2    0.9929  0.9964    182     no   Study

Test for Residual Heterogeneity:
QE(df = 855) = 4106.3487, p-val < .0001

Test of Moderators (coefficient(s) 2):
QM(df = 1) = 2.7267, p-val = 0.0987

Model Results:

estimate      se     zval    pval    ci.lb   ci.ub
intrcpt      0.0817  0.0936   0.8727  0.3828  -0.1017  0.2651
precision   -0.0392  0.0238  -1.6513  0.0987  -0.0858  0.0073  .

---
Signif. codes:  0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1

________________________________
From: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Sent: Thursday, September 26, 2019 1:12 AM
To: Ju Lee <juhyung2 using stanford.edu>; r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>; James Pustejovsky (jepusto using gmail.com) <jepusto using gmail.com>
Subject: RE: Covariance-variance matrix when studies share multiple treatment x control comparison

Hi Ju,

Glad to hear that you are making progress. Construction of the V matrix can be a rather tedious process and often requires quite a bit of manual work.

I have little interested in generalizing fsn() for cases where V is not diagonal, because fsn() is more of interest for historical reasons, not something I would generally use in applied work.

However, the 'Egger regression' test can be easily generalized to rma.mv() models. Simply include a measure of the precision (e.g., the standard error) of the estimates in your model as a predictor/moderator and then you have essentially a multilevel/multivariate version thereof (you would then look at the test of the coefficient for the measure of precision, not the intercept).

I also recently heard a talk by Melissa Rodgers and James Pustejovsky (who is a frequent contributor to this mailing list) on some work in this area. Maybe he can chime in here.

Best,
Wolfgang

-----Original Message-----
From: Ju Lee [mailto:juhyung2 using stanford.edu]
Sent: Thursday, 26 September, 2019 8:13
To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
Subject: Re: Covariance-variance matrix when studies share multiple treatment x control comparison

Dear Wolfgang,

I deeply appreciate your time looking into this issue, and this has been immensely helpful.
I was able to incorporate all possible inter-dependence among effect sizes by adding different layers of non-independence to our dataframe.

I manually calculated hedges'd based on based on Hedges and Olkin (1985), and it generates exactly same value as hedges' g in escalc() "SMD" function. So hopefully I am doing everything right using the equation we've discussed earlier.

I have been also wondering if it is possible to account of this variance-covariance structure that I've constructed when running publication bias analysis, for example, when using fsn() function or modified egger's regression test (looking at intercept term of residual ~ precision meta-regression using rma.mv). I had no luck so far finding information on this, and I would appreciate if you have any suggestions related to this

Thank you for all of your valuable helps!
Best regards,
JU

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