[R-meta] Meta-analyzing studies that failed to account for their nested data

Dear James and Mikkel,

Thank you both. In my case, the primary studies have used AN(C)OVAs
with (non-)random assignment of classes to conditions. I have the
Means and SDs of student-level data for conditions.

Based on:
https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf
, I should use the unbiased version of equation E.5.1 to compute the
SMD effect size (g):

g = wb / s * sqrt(  1 - (2*(n-1)*icc / N - 2)  ) ; s = pooled standard
deviation; n = ave. cluster size; N = n_t + n_c;  w = hedges'
correction factor

Based on the same document, the standard error of g (SE[g]) for
cluster-assignment studies is (equation E.7.1 under "Cluster
assignment"):

SE[g] = w * sqrt(  (SE_uc / s )^2 * eta + (g^2 / (2*h))  ); eta =  1 +
(n - 1)*icc; h = ( [(N-2)-2*(n-1)*icc ]^2 ) / ((N-2)*(1-icc)^2 +
2*(N-2*n)*icc*(1-icc)  )

where SE_uc = regression coefficient standard errors uncorrected for
clustering in the primary studies.

Am I pointing to the correct formulas? If yes, I don't have SE_uc in
my primary studies, what should I do?

Thanks,
Tim M


------ Forwarded Message ------
From: Mikkel Vembye <mikkel.vembye at gmail.com>
Date: Fri, Oct 1, 2021 at 6:54 AM
Subject: Re-re: [R-meta] Meta-analyzing studies that failed to account
for their nested data
To: <fswfswt at gmail.com>, <r-sig-meta-analysis at r-project.org>


Hi Tim,

Just to follow up on James, WWC do also have a nice description of how
they handle cluster trials and quasi-experiments:

https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-508_09212020.pdf

Mikkel


On Thu, Sep 30, 2021 at 11:09 PM James Pustejovsky <jepusto at gmail.com>
wrote:

For studies that claim to find negligible ICCs, I would guess that they

base this judgement either on a) failing to reject a test of ICC = 0 or b)
a rule of thumb. a) is not a good justification because with few classes,
the test will have little power. b) is arbitrary and even small ICCs (of
say 0.02 or 0.04) can be consequential for estimating the variance of the
effect size estimate. I would use the ICC adjustment regardless.

To your second question, yes these adjustments are also important for

quasi-experiments.

James

On Thu, Sep 30, 2021 at 10:53 PM Timothy MacKenzie <fswfswt at gmail.com>

wrote:

Dear James,

Many thanks for this information. Certainly this is serious.

I should add that a few of the (newer) studies in my pool say that
they found their ICCs to be negligible and opted for the single-level
analyses (maybe I should not adjust the sampling variances in these
cases, correct?).

Also, I'm assuming that I can use these sampling variance adjustments
for quasi-experiments where schools/centers themselves haven't been
randomly recruited as well?

Thanks,
Tim M

On Thu, Sep 30, 2021 at 9:40 PM James Pustejovsky <jepusto at gmail.com>

wrote:

Hi Tim,

One important issue here is that the sampling variance of the effect

size estimate calculated from such a study will be inaccurate---possibly
even an order of magnitude smaller than it should be. If you ignore this,
the consequence will be to make the effect size estimates appear far more
precise than they actually are.

To properly correct the sampling variance estimate, you would need to

know the intra-class correlation describing the proportion of the total
variation in the outcome that is at the cluster level (in this case, what
fraction of the total variance is between classes?). If this isn't
reported, then it may be possible to develop a reasonable estimate based on
external information. The Cochrane Handbook describes how to correct the
sampling variance based on an imputed intra-class correlation:

https://training.cochrane.org/handbook/current/chapter-23#section-23-1

Hedges (2007; https://doi.org/10.3102/1076998606298043) and (2011;

https://doi.org/10.3102/1076998610376617) provides slightly more
elaborate methods that can be used if you have more details about the study
designs. Hedges and Hedberg's Variance Almanac (
http://stateva.ci.northwestern.edu/) is a helpful source for developing
estimates of ICCs for educational outcomes.

James

On Thu, Sep 30, 2021 at 4:58 PM Timothy MacKenzie <fswfswt at gmail.com>

wrote:

Hello All,

I've noticed almost all the studies I have selected for meta-analysis
have ignored the nested structure of their data (subjects nested in
classrooms) and have conducted only single-level analyses.

I've extracted the condition-level summaries from those studies

(i.e.,

Means and SDs for C vs. T groups).

But I'm wondering if I can/should make any adjustment to my
meta-regression model to account for the nested structure of the data
in those studies AND if not, whether such a situation poses a
limitation to my meta-analysis?

Thank you very much for your assistance,
Tim M