[R-meta] Covariance-variance matrix when studies share multiple treatment x control comparison
Ju, Following up on Wolfgang's comment: yes, adding a measure of precision as a predictor in the multi-level/multi-variate meta-regression model should work. Dr. Belen Fernandez-Castilla has a recent paper that reports a simulation study evaluating this approach. See Fern?ndez-Castilla, B., Declercq, L., Jamshidi, L., Beretvas, S. N., Onghena, P., & Van den Noortgate, W. (2019). Detecting selection bias in meta-analyses with multiple outcomes: A simulation study. The Journal of Experimental Education, 1?20. However, for standardized mean differences based on simple between-group comparisons, it is better to use sqrt(1 / n1 + 1 / n2) as the measure of precision, rather than using the usual SE of d. The reason is that the SE of d is naturally correlated with d even in the absence of selective reporting, and so the type I error rate of Egger's regression test is artificially inflated if the SE is used as the predictor. Using the modified predictor as given above fixes this issue and yields a correctly calibrated test. For all the gory details, see Pustejovsky & Rodgers (2019; https://doi.org/10.1002/jrsm.1332). It's also possible to combine all of the above with robust variance estimation, or to use a simplified model plus robust variance estimation to account for dependency between effect sizes from the same study. Melissa Rodgers and I have a working paper showing that this approach works well for meta-analyses that include studies with multiple correlated outcomes. We will be posting a pre-print of the paper soon, and I can share it on the listserv when it's available. James On Thu, Sep 26, 2019 at 3:12 AM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
Hi Ju, Glad to hear that you are making progress. Construction of the V matrix can be a rather tedious process and often requires quite a bit of manual work. I have little interested in generalizing fsn() for cases where V is not diagonal, because fsn() is more of interest for historical reasons, not something I would generally use in applied work. However, the 'Egger regression' test can be easily generalized to rma.mv() models. Simply include a measure of the precision (e.g., the standard error) of the estimates in your model as a predictor/moderator and then you have essentially a multilevel/multivariate version thereof (you would then look at the test of the coefficient for the measure of precision, not the intercept). I also recently heard a talk by Melissa Rodgers and James Pustejovsky (who is a frequent contributor to this mailing list) on some work in this area. Maybe he can chime in here. Best, Wolfgang -----Original Message----- From: Ju Lee [mailto:juhyung2 at stanford.edu] Sent: Thursday, 26 September, 2019 8:13 To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis at r-project.org Subject: Re: Covariance-variance matrix when studies share multiple treatment x control comparison Dear Wolfgang, I deeply appreciate your time looking into this issue, and this has been immensely helpful. I was able to incorporate all possible inter-dependence among effect sizes by adding different layers of non-independence to our dataframe. I manually calculated hedges'd based on based on Hedges and Olkin (1985), and it generates exactly same value as hedges' g in escalc() "SMD" function. So hopefully I am doing everything right using the equation we've discussed earlier. I have been also wondering if it is possible to account of this variance-covariance structure that I've constructed when running publication bias analysis, for example, when using fsn() function or modified egger's regression test (looking at intercept term of residual ~ precision meta-regression using rma.mv). I had no luck so far finding information on this, and I would appreciate if you have any suggestions related to this Thank you for all of your valuable helps! Best regards, JU