# [R-meta] variance of predicted effect sizes

Crean, Hugh hugh_cre@n @ending from URMC@Roche@ter@edu
Wed Jan 2 22:39:02 CET 2019

```Hello Wolfgang et al.,

Yes to the below and thanks again so much.  To start, I have been trying to implement the simpler approach of just using the weighted average control group effects for those studies not having a control group and as you mention below, using the squared SE as the sampling variance.  I have an additional wrinkle, however, and I cannot find much guidance in the literature.  A few of the studies have their own dependencies (multiple treatment arms in the same study either with or without a control group).  Is there a way of incorporating both sets of dependencies into the V matrix? For now, I am thinking along the lines of using a sensitivity analyses where two estimates are computed -- the first would just add the two estimates together as this would provide a high estimate of the possible covariance and the second would just take the higher of the two covariances.  Neither feels satisfying (aside from difficulties with non-positive matrices) but does at least attempt to recognize these dependent effects.

Best and hope all had wonderful Holidays,

Hugh

-----Original Message-----
Dear Hugh,

It sounds to me that you want to do something like Becker (1988) describes in section 5.2. Then you would use the squared standard error of the predicted value (from the meta-regression model) as the sampling variance of the control group estimate of the standardized mean change.

There is an additional complication that there is then a dependency between the effect sizes (i.e., the difference in the standardized mean change between the treatment and control group) for studies with both treatment and control groups and effect sizes for studies with just a treatment group (and also between the effect sizes from studies with treatment groups only). These covariances can be computed as described in 5.2 and would need to be put into the 'V' matrix of rma.mv() (if you intend to use metafor). Actually implemting this would require a bit of work though. Showing how to do this with metafor would be a nice little exercise/project for a motivated student.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Crean, Hugh
Sent: Sunday, 11 November, 2018 23:22
To: 'r-sig-meta-analysis using r-project.org'
Subject: [R-meta] variance of predicted effect sizes

Hello,

Colleagues and myself are working on a meta-analysis of sleep interventions.  Many of the studies are only single arm pre-post studies and we are following the advice of Becker (1988) and Morris and DeShon (2002) to impute missing control group effect sizes.  We are planning on using meta regression to compute predicted effect sizes for those studies missing control information.  However, I cannot quite figure how to compute and/or get the standard error for this estimate.  Would one run a simple meta- analysis on the predicted scores for those with the data and use the provided se (and variance)?

Hugh

Hugh F. Crean, Ph.D.
School of Nursing
University of Rochester
601 Elmwood Avenue
Rochester, New York  14620

(585) 276-5575

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