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

Dear Wolfgang, James

Thank you both for your considerate suggestions.

First of all, I would like to clarify that I will be sending out another
thread related to Wolfgang's comment about adding study ID to random
factors as it has caused some major issues with my current analysis and I
would really like second feedbacks on this matter (on my very next e-mail).

Related to James's suggestion, I will follow up on your newly published
paper and apply this to my code. Since I am using variance-covariance
matrix instead of normal variance (to account for shared control/treatment
groups) and trying to incorporate this to modified egger's test, I am
wondering if means I should be creating a diagonal matrix constituted of sqrt(1
/ n1 + 1 / n2) for all inter-dependent effect sizes?

Best regards,
JU
------------------------------
*From:* James Pustejovsky <jepusto at gmail.com>
*Sent:* Thursday, September 26, 2019 8:26 AM
*To:* Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl>
*Cc:* Ju Lee <juhyung2 at stanford.edu>; r-sig-meta-analysis at r-project.org <
r-sig-meta-analysis at r-project.org>
*Subject:* Re: Covariance-variance matrix when studies share multiple
treatment x control comparison

Ju,

Following up on Wolfgang's comment: yes, adding a measure of precision as
a predictor in the multi-level/multi-variate meta-regression model should
work. Dr. Belen Fernandez-Castilla has a recent paper that reports a
simulation study evaluating this approach. See

Fern?ndez-Castilla, B., Declercq, L., Jamshidi, L., Beretvas, S. N.,
Onghena, P., & Van den Noortgate, W. (2019). Detecting selection bias in
meta-analyses with multiple outcomes: A simulation study. The Journal of
Experimental Education, 1?20.

However, for standardized mean differences based on simple between-group
comparisons, it is better to use sqrt(1 / n1 + 1 / n2) as the measure of
precision, rather than using the usual SE of d. The reason is that the SE
of d is naturally correlated with d even in the absence of selective
reporting, and so the type I error rate of Egger's regression test is
artificially inflated if the SE is used as the predictor. Using the
modified predictor as given above fixes this issue and yields a correctly
calibrated test. For all the gory details, see Pustejovsky & Rodgers (2019;
https://doi.org/10.1002/jrsm.1332).

It's also possible to combine all of the above with robust variance
estimation, or to use a simplified model plus robust variance estimation to
account for dependency between effect sizes from the same study. Melissa
Rodgers and I have a working paper showing that this approach works well
for meta-analyses that include studies with multiple correlated outcomes.
We will be posting a pre-print of the paper soon, and I can share it on the
listserv when it's available.

James

On Thu, Sep 26, 2019 at 3:12 AM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

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 at stanford.edu]
Sent: Thursday, 26 September, 2019 8:13
To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis at 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