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

[Timothy MacKenzie]

Much appreciated, Mikkel. I saw that. BTW, there is no Table 5, it's a typo
in the WWC document (I found other typos as well).

But I have both ANOVAs and a few ANCOVAs from primary studies that did
cluster assignment but ignored nesting structure, with barely any R^2
reported in them.

My understanding is that I should find a more general SE[g] that only
requires icc, am I correct in thinking this way?

Thanks,
Tim M

On Fri, Oct 1, 2021 at 12:32 PM Mikkel Vembye <mikkel.vembye using gmail.com>
wrote:

> Hi Tim,
>
> Glad that I/we can help. You find the ANCOVA examples (both uncorrected
> and corrected) in Table 3.
>
> [image: image.png]
>
> I forgot to mention that you also can find some corrections to Hedges
> (2007) in Table 5.
>
> All the best,
> Mikkel
>
> Den fre. 1. okt. 2021 kl. 19.21 skrev Timothy MacKenzie <fswfswt using gmail.com
> >:
>
>> 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
>> >> >>
>> >> >> _______________________________________________
>> >> >> R-sig-meta-analysis mailing list
>> >> >> R-sig-meta-analysis using r-project.org
>> >> >> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>
>

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