[R-meta] 3 candidate random structures

[Timothy MacKenzie]

Dear James,

This is great, thank you very much!

Tim

On Wed, Aug 4, 2021 at 2:47 PM James Pustejovsky <jepusto using gmail.com> wrote:

> Hi Tim,
>
> In your data, do the outcome numbers correspond to categories that are
> comparable across studies? In other words, does outcome = 1 in study 1 mean
> the same thing as outcome = 1 in study 2? Or, alternately, are they just ID
> variables, with arbitrary labels that could be re-ordered within each study
> without losing any information?
>
> The reason I ask is that your first set of random effects (~ outcome |
> study) would only make sense if the outcome variable corresponds to
> categories that are comparable across studies.
>
> To question about which specification is most appropriate for the data
> structure, I'll comment below.
>
> Specification A: list(~ outcome | study, ~ time |
> interaction(study,outcome)), struct=c("HCS","HAR")
>
> This specification includes correlated random effects for each
> study-outcome, which have a common influence across groups and time-points.
> It also includes auto-regressive random effects across time-points for each
> study-outcome combination. Since gr does not appear in the random effects
> ID terms, the assumption is that the auto-regressive random effects have a
> common influence across groups within each study. That seems a bit
> restrictive.
>
> Specification B:   list(~ outcome | study, ~ time |
> interaction(study,gr,outcome)), struct=c("HCS","HAR")
>
> This specification includes correlated random effects for each
> study-outcome, which have a common influence across groups and time-points.
> It includes auto-regressive random effects across time-points for each
> study-outcome -group combination. The structure of the auto-regressive
> random effects is assumed to be common across study-outcome-group
> combinations. That might be reasonable, but given that you're allowing the
> study-level random effects to have a unique variance for each outcome, it
> does lead one to wonder why the time-point random effects are treated as
> homogeneous across outcomes.
>
> Specification C:   list(~ outcome | interaction(study,gr), ~ time |
> interaction(study,gr,outcome)), struct =c("HCS","HAR")
>
> This specification includes correlated random effects for each
> study-outcome-group, which have a common influence across time-points. It
> includes auto-regressive random effects across time-points for each
> study-outcome -group combination. The structure of the auto-regressive
> random effects is assumed to be common across study-outcome-group
> combinations. Relative to B, specification C seems less reasonable as a
> starting point because it does not allow for study-level variation that is
> common across groups.
>
> Specification D:   list(~ outcome | study, ~ outcome |
> interaction(study,gr), ~ outcome | interaction(study,gr,time)), struct
> =c("HCS","HCS","HCS")
>
> I've added this specification as a further hypothetical
> alternative---hypothetical because it's not actually possible to fit it
> with rma.mv(), due to the constraint that you can only have two sets of
> random effects with a term on the left hand side of the bar. But
> hypothetically, this might be another parameterization to consider. It
> includes correlated random effects for each study-outcome, each
> study-group-outcome, and each study-group-outcome-timepoint, capturing the
> idea of a (multivariate) outcome, nested within time-points, nested within
> groups, nested within studies. It might be simplified in various ways, such
> as by using ~ 1 | instead of ~ outcome | at one or more levels.
>
> In any case, as you noted in your query, ultimately these different
> specifications should be investigated empirically.
>
> Cheers,
> James
>
> On Wed, Jul 28, 2021 at 11:12 AM Timothy MacKenzie <fswfswt using gmail.com>
> wrote:
>
>> Dear Colleagues,
>>
>> I just wanted to clarify that I fully understand that the 3 models that I
>> suggested need to be empirically tested with my data. However, my question
>> is that:
>>
>> Given that I'm new to the `rma.mv()` function in metafor, I was wondering
>> if the candidate syntax that I have used (below) matches the general
>> definition of my data structure (i.e., studies>groups>outcomes>time)?
>>
>> Thank you for your assistance, Tim
>>
>> list(~ outcome | study, ~ time | interaction(study,outcome)), struct
>> =c("HCS","HAR")
>>
>> list(~ outcome | study, ~ time | interaction(study,gr,outcome)), struct
>> =c("HCS","HAR")
>>
>> list(~ outcome | interaction(study,gr), ~ time |
>> interaction(study,gr,outcome)), struct =c("HCS","HAR")
>>
>> # Data structure:
>> study gr time outcome
>> 1       1   0     1
>> 1       1   0     2
>> 1       1   1     1
>> 1       1   1     2
>> 1       1   2     1
>> 1       1   2     2
>> 1       2   0     1
>> 1       2   0     2
>> 1       2   1     1
>> 1       2   1     2
>> 1       2   2     1
>> 1       2   2     2
>> 2       1   0     1
>> 2       1   0     2
>> 2       2   0     1
>> 2       2   0     2
>>
>> On Mon, Jul 26, 2021 at 1:06 PM Timothy MacKenzie <fswfswt using gmail.com>
>> wrote:
>>
>> > Dear Meta-Analysis Experts,
>> >
>> > Several of my studies (15 out of 50) have a data structure similar to
>> what
>> > I'm showing below. That is, each such study has multiple experimental
>> > groups ("gr"), tested several times, on 2 or more outcomes.
>> >
>> > I'm considering 3 different random structures (below). But I was
>> wondering
>> > which one better aligns to such studies' data structure?
>> >
>> > Thank you for your expertise,
>> > Tim
>> >
>> > list(~ outcome | study, ~ time | interaction(study,outcome)), struct
>> > =c("HCS","HAR")
>> >
>> > list(~ outcome | study, ~ time | interaction(study,gr,outcome)), struct
>> > =c("HCS","HAR")
>> >
>> > list(~ outcome | interaction(study,gr), ~ time |
>> > interaction(study,gr,outcome)), struct =c("HCS","HAR")
>> >
>> > # Data structure:
>> > study gr time outcome
>> > 1       1   0     1
>> > 1       1   0     2
>> > 1       1   1     1
>> > 1       1   1     2
>> > 1       1   2     1
>> > 1       1   2     2
>> > 1       2   0     1
>> > 1       2   0     2
>> > 1       2   1     1
>> > 1       2   1     2
>> > 1       2   2     1
>> > 1       2   2     2
>> > 2       1   0     1
>> > 2       1   0     2
>> > 2       2   0     1
>> > 2       2   0     2
>> >
>>
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