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

[Timothy MacKenzie]

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 using 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 using gmail.com>, <r-sig-meta-analysis using 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 using 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 using 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 using 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 using 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
>> >>
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