# [R-meta] How to deal with "dependent" Effect sizes?

Angeline Tsui angelinetsui at gmail.com
Mon Feb 26 23:50:59 CET 2018

```Dear James,

Thank you very much for your suggestions. For point 2, it looks like you
suggested me to run a hierarchical regression model where I should capture
dependence across repeated samples by allowing intercepts (in this case,
effect sizes) vary as random effects? And there is no random slopes in this
model? Am I correct?

But I think I do not understand how to incorporate "the dependences" here
because some samples in the study are dependent whereas the other samples
in the study can be independent (for example, there are 5 samples in the
study. Study 1, 2,3 are testing the same group of participants, so they are
dependent with each other. In contrast, Study 4 and 5 are independent of
each other because they test different groups of participants. Study 4 and
5 are also not dependent of Study 1, 2 and 3). In this case, how can I
capture the dependence here?

Sorry for asking more questions and I hope you can give me some directions
here.

Many thanks,
Angeline

On Mon, Feb 26, 2018 at 1:33 PM, James Pustejovsky <jepusto at gmail.com>
wrote:

> Angeline,
>
> My generic suggestion would be to do something like the following:
>
> 1. Either find information or make an assumption about the degree of
> dependence among the effect sizes from the same sample, and then use this
> to construct a "working" variance-covariance matrix for the effect size
> github.io/imputing-covariance-matrices-for-multi-variate-meta-analysis).
> 2. Use rma.mv to estimate the overall average ES and any meta-regressions
> of interest. In rma.mv, you should definitely include a random effect for
> each sample. You might also want to examine whether there is further
> dependence among samples nested within studies, by including a random
> effect for each study.
> 3. Once you've estimated the model with rma.mv, use the functions
> mentioned above to compute robust variance estimates (RVE), clustering at
> the level of studies. Using RVE will ensure that the standard errors,
> hypothesis tests, and CIs for the overall average effect (and/or
> meta-regression coefficient estimates) are robust to the possibility that
> the "working" variance-covariance matrix is inaccurate.
>
> James
>
> On Mon, Feb 26, 2018 at 11:29 AM, Angeline Tsui <angelinetsui at gmail.com>
> wrote:
>
>> Dear James and Wolfgang,
>>
>> Thank you so much for your prompt reply. In this meta-analysis, I am
>> talking about "cohen's d" for my effect sizes. I have a follow up question
>> and I wonder if you can give me some directions:
>>
>> James got my message that the data structure of my meta-analysis. Indeed,
>> I see at least 20 to 30 studies in total (may be more, but I am not sure
>> yet cause I need to contact authors for missing information to estimate the
>> ES). The problem is that some papers reported several samples that are
>> dependent with each other (i.e., they were testing the same group of
>> participants) whereas the other papers are reporting studies that are
>> totally independent (i.e., testing totally different group of
>> participants). Thus, my concern is how to run a meta-regression (for
>> example, a random-effect model to estimate the average ES) when some ES in
>> the dataset are dependent with each other whereas other ES are independent
>> with each other. Should I run two meta-regression models: one for dependent
>> ES only and the other for independent ES only? But I really want to combine
>> all studies together to get a sense of the average ES across all studies?
>> Also, I am planning to run moderator analysis to identify how experimental
>> factors can explain variability across studies. So it will be most useful
>> if I can run meta-regression and moderator analysis using the whole data
>> set.
>>
>>
>> Thanks again,
>> Angeline
>>
>> On Mon, Feb 26, 2018 at 12:19 PM, James Pustejovsky <jepusto at gmail.com>
>> wrote:
>>
>>> I interpreted Angeline's original message as describing the data
>>> structure for one of the papers included in the meta-analysis, but I assume
>>> that the meta-analysis includes more than a single paper with three
>>> samples. Angeline, do you know (yet) the total number of papers from which
>>> you draw effect size estimates? And the number of distinct samples reported
>>> in those papers?
>>>
>>> Incidentally, some colleagues and I have been looking at the techniques
>>> that have been used in practice to conduct meta-analyses with dependent
>>> effect sizes (across several different journals in psychology, education,
>>> and medicine). Along the way, we're noting a number of ways in which the
>>> reporting of such studies could be improved. One basic thing that we'd love
>>> to see consistently reported is the total number of studies, the total
>>> number of (independent) samples, and the total number of effect size
>>> estimates (preferably also the range) after all inclusion/exclusion
>>> criteria have been applied. For instance, fill in the blank:
>>>
>>> The final sample consisted of XX effect size estimates, drawn from XX
>>>> distinct samples, reported in XX papers/manuscripts. Each paper reported
>>>> results from between 1 and XX samples (median = XX) and contributed between
>>>> 1 and XX effect size estimates (median = XX).
>>>
>>>
>>> On Mon, Feb 26, 2018 at 10:55 AM, Viechtbauer Wolfgang (SP) <
>>> wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
>>>
>>>> For cluster-robust inference methods, there is the robust() function in
>>>> metafor. James' clubSandwich package (https://cran.r-project.org/pa
>>>> ckage=clubSandwich) also works nicely together with metafor. However,
>>>> generally speaking, these methods work *asymptotically*. clubSandwich
>>>> includes some small-sample corrections, but I doubt that James would
>>>> advocate their use in such a small k setting. So I don't think
>>>> cluster-robust inference methods are an appropriate way to handle the
>>>> dependency here.
>>>>
>>>> What kind of 'effect sizes' are we talking about here anyway?
>>>>
>>>> Best,
>>>> Wolfgang
>>>>
>>>> >-----Original Message-----
>>>> >From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-
>>>> >project.org] On Behalf Of Angeline Tsui
>>>> >Sent: Monday, 26 February, 2018 17:27
>>>> >To: Mark White
>>>> >Cc: r-sig-meta-analysis at r-project.org
>>>> >Subject: Re: [R-meta] How to deal with "dependent" Effect sizes?
>>>> >
>>>> >Hello Mark,
>>>> >
>>>> >Thanks for sharing your manuscript with me. I will take a look.
>>>> >
>>>> >But, if anyone knows how to deal with dependent ES using metafor,
>>>> >let me know.
>>>> >
>>>> >Best,
>>>> >Angeline
>>>> >
>>>> >On Mon, Feb 26, 2018 at 10:26 AM, Mark White <markhwhiteii at gmail.com>
>>>> >wrote:
>>>> >
>>>> >> I did a meta-analysis that dealt with a lot of studies with dependent
>>>> >> variables at the participant level. I got a great deal of help from
>>>> >this
>>>> >> group (and others), and I settled eventually on robust variance
>>>> >estimation.
>>>> >> See pages 21 to 23 here (https://github.com/markhwhite
>>>> ii/prej-beh-meta/
>>>> >> blob/master/docs/manuscript.pdf) on how I came to that decision and
>>>> >some
>>>> >> great references for using their robumeta package. I'm sure there is
>>>> a
>>>> >way
>>>> >> to do this in metafor, as well.
>>>> >>
>>>> >> On Mon, Feb 26, 2018 at 10:08 AM, Angeline Tsui
>>>> ><angelinetsui at gmail.com>
>>>> >> wrote:
>>>> >>
>>>> >>> Hello all,
>>>> >>>
>>>> >>> I am working on a meta-analysis that may contain dependent effect
>>>> >sizes.
>>>> >>> For example, there are five studies in a paper. However, study 1, 2
>>>> >and 3
>>>> >>> tested the same group of participants whereas study 4 and 5 tested
>>>> >>> different groups of participants. This means that the effect sizes
>>>> in
>>>> >>> study
>>>> >>> 1, 2 and 3 are dependent of each other, whereas study 4 and 5 are
>>>> >>> independent of each other. In this case, how should I incorporate
>>>> >these
>>>> >>> studies in a meta-analysis? Specifically, my concern is that if I
>>>> put
>>>> >all
>>>> >>> five studies in a meta-regression, then I am not ensuring that each
>>>> >effect
>>>> >>> size is independent of each other.
>>>> >>>
>>>> >>> Thanks,
>>>> >>> Angeline
>>>> >>>
>>>> >>> --
>>>> >>> Best Regards,
>>>> >>> Angeline
>>>>
>>>> _______________________________________________
>>>> R-sig-meta-analysis mailing list
>>>> R-sig-meta-analysis at r-project.org
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>>>>
>>>
>>>
>>
>>
>> --
>> Best Regards,
>> Angeline
>>
>
>

--
Best Regards,
Angeline

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