[R-meta] guidance for modeling SMCC type effect size

[Stefanou Revesz]

Hi Reza,

Thank you so much! A quick follow-up, when you say "If in each study,
true SMCCs at all intervals across the conditions are assumed to have
their own auto-regressively correlated structure as well", I wonder
how conditions could have their own autoregressive structure and why
that could be necessary?

Thanks again!

On Sun, Sep 12, 2021 at 2:57 PM Reza Norouzian <rnorouzian using gmail.com> wrote:
>
> Dear Stefanou,
>
> The modeling functions like rma.mv(), rma.uni() etc. don't generally
> depend on the type of effect size. That aside, just to make sure, did
> you compute the change from each pre-test to each follow-up post-test,
> or the change from each testing occasion to the following one (e.g.,
> pre-test to post-test1, post-test1 to post-test2 ...)?
>
> Regardless of how you define the intervals, if your studies include a
> control (C) and multiple treatment conditions (T1, T2,...) that occur
> across the studies, you can create a 'condition' variable to
> distinguish between the control and the treatments' SMCCs (yi) in each
> study over the intervals you have defined:
>
> study condition  yi  interval_id id
> 1     T1        .1   0           1
> 1     T1        .3   1           2
> 1     T2        .7   0           3
> 1     T2        .2   1           4
> 1     C         .4   0           5
> 1     C         .5   1           6
> 2     T2        .6   0           7
> 2     C         .9   1           8
>
> In which case, a starting point might be:
>
> rma.mv(yi ~ condition*interval_id, V = Some_V_matrix, random = list(~
> interval_id | study, ~ 1 | id), struct = "HAR")
>
> This model assumes that in each study, true SMCCs at all intervals are
> auto-regressively correlated with each other regardless of the
> conditions they belong to. If in each study, true SMCCs at all
> intervals across the conditions are assumed to have their own
> auto-regressively correlated structure as well, then, you can
> consider:
>
> rma.mv(yi ~ condition*interval_id, V = Some_V_matrix, random = list(~
> interval_id | study, ~ interval_id | interaction(study,condition), ~ 1
> | id), struct = c("HAR","HAR") )
>
> In both models, when the interaction term is decomposed to its simple
> effects for each condition, you get the average SMCC for each
> condition (e.g., T1, T2, or C) across the intervals for your studies.
>
> For your second type of effect size (y_i = SMCC_T - SMCC_C, v_i =
> v_{i_{SMCC_T}} + v_{i_{SMCC_C}}), pretty much everything I said above
> applies. However, in this case, you're basically modeling some sort of
> simple effect for each treatment's change vs the control's change
> across the intervals for your studies. So, by fitting the above model
> but using this type of effect size, you'll be asking how such simple
> effects change over the interval you have considered.
>
> I believe these metrics for effect size are nowadays less commonly
> used, partly because you can use an SMD metric, which among other
> things doesn't require direct knowledge of pre-post correlations for
> their computation, model them using multivariate-multilevel models,
> and present the results in perhaps more intuitive ways to your
> audience.
>
> Does that help?
>
> Reza
>
>
>
> Reza
>
>
> On Sun, Sep 12, 2021 at 6:15 AM Stefanou Revesz
> <stefanourevesz using gmail.com> wrote:
> >
> >
> > Dear Experts,
> >
> > I need some guidance for modeling two types of effect sizes (for two
> > different meta-analyses) using the rma.mv() program in metafor.
> >
> > First, I have computed the standardized mean change (SMCC) between
> > each pre-test and the follow-up post-tests in each of
> > multiple-treatment studies.
> >
> > Second, I have computed the difference in standardized mean changes
> > (SMCC) between a treatment and a control group at each pre-test to
> > post-test intervals in each of multiple-treatment studies.
> >
> > The reason I want to use rma.mv() is that each of my studies could
> > produce multiple of these types of effect sizes. But I wonder what
> > would be a starting point for modeling these two types of effect size?
> >
> > Any help is appreciated,
> > Stefanou
> >
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