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

[Angela Leanne Wilson]

Thank you very much Wolfgang, I appreciate the guidance.

Angela

> On Aug 21, 2023, at 4:19 PM, Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> 
> Attention : courriel externe | external email
> 
> 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