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

Angeline Tsui angelinetsui at gmail.com
Tue Feb 27 19:27:14 CET 2018

Dear James,

Thank you very much for your detailed reply. It is very useful.


On Tue, Feb 27, 2018 at 10:34 AM, James Pustejovsky <jepusto at gmail.com>

> Angeline,
> There's several different types of dependence at work here. The main issue
> you raised has to do with sampling dependence. For example, the effects
> from studies 1, 2, and 3, are dependent because they are estimated from a
> common sample of individuals. Dealing with this dependence is my step (1)
> from the previous email. Basically, I suggest making an assumption about
> the dependence, such as assuming that the various outcomes used in studies
> 1, 2, and 3 have inter-correlations of 0.5 or 0.6 or something like that.
> This assumption leads to a block-diagonal variance-covariance matrix, where
> studies 1, 2, and 3 form a block. See the linked blog post for an example
> of how to calculate this matrix in R. This matrix becomes the "V" argument
> in rma.mv.
> Next is the question of what sort of random effects to put in the model.
> Here, I suggest starting by including a random effect for every *sample*.
> So studies 1, 2, and 3 would share a common random effect, while study 4
> and study 5 would each have their own random effect. These random effects
> allow for variation in the true effect size parameters. There would not be
> any random slopes in the basic model (because there are no
> covariates/predictor variables). Beyond this, you might consider including
> an additional random effect for every paper or laboratory. This is worth
> considering if the studies that appear together in the same paper tend to
> share common operational procedures, treatment manipulations, or the like,
> which would lead us to expect that their true effect size parameters for
> samples in the same paper would be more similar to each other than to the
> effect sizes from different papers.
> James
> On Mon, Feb 26, 2018 at 4:50 PM, Angeline Tsui <angelinetsui at gmail.com>
> wrote:
>> 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
>>> estimates (see here for more information: http://jepusto.gi
>>> thub.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.
>>>> Please share your thoughts with me.
>>>> 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/package=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,
>>>>>> please
>>>>>> >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

Best Regards,

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