[R-meta] Meta-analysis - missing study-specific variance

[Viechtbauer, Wolfgang (NP)]

In that case, you essentially want this (assuming that the dataset is called 'dat', the variable with the sample sizes 'ni', and the variable with the standardized regression coefficients 'beta'):

dat$id1 <- dat$id2 <- 1:nrow(dat)
V <- diag(1/dat$ni)
rownames(V) <- dat$id1

res <- rma.mv(beta, V=0, random = list(~ 1 | id1, ~ 1 | id2), R=list(id1=V), Rscale=FALSE, data=dat)
robust(res, cluster=id1)

The only paper I know of that, on a general/conceptual level, touches on this approach is:

Nakagawa, S., Noble, D. W. A., Lagisz, M., Spake, R., Viechtbauer, W., & Senior, A. M. (2023). A robust and readily implementable method for the meta-analysis of response ratios with and without missing standard deviations. Ecology Letters, 26(2), 232-244. https://doi.org/10.1111/ele.14144

but the context is quite a bit different. We also used a similar approach in:

Haslam, N., McGrath, M. J., Viechtbauer, W., & Kuppens, P. (2020). Dimensions over categories: A meta-analysis of taxometric research. Psychological Medicine, 50(9), 1418-1432. https://doi.org/10.1017/S003329172000183X

but again with a rather different context and the paper gives little details on this method. I also touched on this approach in this post:

https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-March/000731.html

I will have to leave it at that due to lack of time.

Best,
Wolfgang

>-----Original Message-----
>From: Angela Leanne Wilson [mailto:awils046 using uottawa.ca]
>Sent: Monday, 21 August, 2023 21:41
>To: Viechtbauer, Wolfgang (NP)
>Cc: R Special Interest Group for Meta-Analysis; Angeline Tsui
>Subject: Re: Meta-analysis - missing study-specific variance
>
>Hello Wolfgang,
>
>Thank you very much for this guidance. Unfortunately I do not have the entire
>correlation matrices, and I only have the p-values for a small portion of
>included studies. So it looks like Option 2 is the most viable choice.
>
>Could you please direct me to which R package I would use (and/or any resources
>to consult) in order to understand and perform this? I am new to using R and
>meta-analysis, so any guidance you could provide would be incredibly helpful.
>
>Many thanks,
>Angela
>
>> On Aug 21, 2023, at 3:53 AM, Viechtbauer, Wolfgang (NP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>
>> Attention : courriel externe | external email
>>
>> Dear Angela,
>>
>> You would need the entire correlation matrix of all variables involved in a
>regression model to compute the sampling variance of a standardized regression
>coefficient of such a model. I assume that this is not available to you.
>>
>> I see a few alternative options:
>>
>> 1) Do you have the p-values corresponding to these regression coefficients? If
>so, you could use this to compute the partial correlation coefficients and
>conduct the meta-analysis using those. See:
>>
>> https://wviechtb.github.io/metafor/reference/escalc.html#partial-and-semi-
>partial-correlations
>>
>> 2) You could fit a model that assumes that the sampling variances of the
>standardized regression coefficients are inversely proportional to the sample
>sizes and then use robust inference methods. Making this work isn't entirely
>straightforward, so I wouldn't suggest to consider this approach unless 1) is not
>an option.
>>
>> Best,
>> Wolfgang
>>
>>> -----Original Message-----
>>> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On
>>> Behalf Of Angela Leanne Wilson via R-sig-meta-analysis
>>> Sent: Monday, 21 August, 2023 4:11
>>> To: r-sig-meta-analysis using r-project.org
>>> Cc: Angela Leanne Wilson
>>> Subject: [R-meta] Meta-analysis - missing study-specific variance
>>>
>>> Hello all,
>>>
>>> I am conducting a meta-analysis to summarize effect sizes from different
>studies
>>> that ran mediation analysis.
>>>
>>> I have extracted the standardized regression coefficients (i.e., the indirect
>>> effects from each mediation study) as the effect size. I also have the sample
>>> size for each study, however I found that only a few studies reported any
>>> error/variance estimate (probably because the authors have reported a
>>> standardized regression coefficient and thus they did not report any
>>> error/variance of the corresponding regression coefficient). In this case, it
>>> means that many studies in my meta-analysis lack study-specific variance
>>> information.
>>>
>>> My understanding is that the study-specific variance is needed to calculate
>the
>>> weight for each study when calculating the average effect size across studies.
>>> May I ask if you can suggest what I need to do to estimate the study-specific
>>> variance?
>>>
>>> (Apologies I do not have any code as I cannot begin the analysis without first
>>> resolving this issue)
>>>
>>> Many thanks,
>>> Angela
>>>
>>> Angela Wilson (she, her/elle)
>>> Doctoral Candidate, Clinical Psychology
>>> University of Ottawa
>>> Healthy Active Living and Obesity (HALO) Research Group
>>> Children’s Hospital of Eastern Ontario (CHEO), Research Institute
>>> Email: awils046 using uottawa.ca