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

Hi Ju,

1) As has been discussed on this mailing list on a few occasions: In addition to adding 'Study' as random effects, you should also add random effects for the estimates within studies. So, your 'base' model should be:

MHF$Id <- 1:nrow(MHF)
rma.mv(hedged, var, method="REML", random = ~ 1 | Study/Id, data=MHF)

(otherwise, you are assuming no heterogeneity within studies, which is a very strong assumption)

2) Your 'Egger-like multilevel regression test' model would simply be:

rma.mv(hedged, var, mods = ~ sqrt(var), method="REML", random = ~ 1 | Study/Id, data=MHF)

You then test if sqrt(var) is a significant predictor or not.

3) But 'var' should be a matrix -- after all, that was the point of the earlier discussion. So, if it is, then it would be:

rma.mv(hedged, var, mods = ~ sqrt(diag(var)), method="REML", random = ~ 1 | Study/Id, data=MHF)

Best,
Wolfgang

-----Original Message-----
From: Ju Lee [mailto:juhyung2 at stanford.edu] 
Sent: Thursday, 26 September, 2019 14:58
To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis at r-project.org; James Pustejovsky (jepusto at gmail.com)
Subject: Re: Covariance-variance matrix when studies share multiple treatment x control comparison

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.

Thank you for your time to answer these many questions.
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