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

[Viechtbauer, Wolfgang (NP)]

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