[R-meta] variance of predicted effect sizes

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Mon Jan 7 16:51:36 CET 2019

Hi Hugh,

"Is there a way of incorporating both sets of dependencies into the V matrix?" Probably, but one would have to work out the correct equations for the covariances (I am not aware of anybody who has done this already).


>-----Original Message-----
>From: Crean, Hugh [mailto:hugh_crean using URMC.Rochester.edu]
>Sent: Wednesday, 02 January, 2019 22:39
>To: Viechtbauer, Wolfgang (SP); 'r-sig-meta-analysis using r-project.org'
>Subject: RE: variance of predicted effect sizes
>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
>Best and hope all had wonderful Holidays,
>-----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.
>-----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
>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)?
>Thanks in advance,
>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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