[R-meta] Choice of measure in escalc().
James Pustejovsky
jepu@to @end|ng |rom gm@||@com
Mon May 6 16:37:26 CEST 2019
Cedric,
Here are some initial comments. It would be great for others to share their
perspectives as well, as well to share any references that cover this set
of ES measures. (I don't know of good ones. My usual go-to ref is
Borenstein in the Handbook of Research Synthesis and Meta-Analysis, but he
covers only MC and SMCR.)
I think the over-arching point to keep in mind is that ES measures are
really modeling assumptions about the equivalence or approximate
equivalence of effects across studies. Thus, choosing an appropriate ES is
analogous to determining an appropriate assumption for any other
statistical model---the choice should be based on consideration of the
substantive context of the analysis, the data available to you, and on
evidence in the data you have.
* |"MC"| for the /raw mean change/.
>
Raw mean change is only appropriate if all of the studies use a common
scale. If that is the case, it is an attractive measure because the
meta-analysis results can then be interpreted on the same scale as the
results of each primary study. If studies use different measurement scales,
then MC is not appropriate.
* |"ROMC"| for the /log transformed ratio of means/ (Lajeunesse, 2011).
ROMC is appropriate if a) all of the studies use measures that can be
treated as ratio scales (i.e., where the zero of the scale really
corresponds to absence of the outcome, so that it is sensible to talk about
percentage changes in the outcome). The central assumption of ROMC is that
effects (whether treatment effects or natural changes over time) are
approximately proportionate to the baseline level of the outcome.
If studies all use a common scale, then MC or ROMC might be appropriate.
The choice between them really depends on whether you think effects are
(approximately) proportionate to baseline or are (more or less) unrelated
to baseline levels.
The remaining effect sizes are all forms of standardized mean difference.
They are useful when studies all make use of different scales. Each measure
uses a different component of variance to standardize the effects, so you
can think of the measures as making different assumptions about how best to
(linearly) equate the outcome scales across studies.
> * |"SMCR"| for the /standardized mean change/ using raw score
>
standardization.
>
* |"SMCRH"| for the /standardized mean change/ using raw score
> standardization with heteroscedastic population variances at the two
> measurement occasions (Bonett, 2008).
>
SMCR and SMCRH use the standard deviation of the raw scores at pre-test to
equate effects across studies. This is sensible if a) the magnitude of
effects are (more or less) unrelated to baseline levels and b) the scales
do not have range restriction or unreliability issues at baseline. If (b)
is a concern, then it might be more sensible to use the post-test SD
instead (see comments in ?escalc to that effect). As far as I can tell, the
only difference between SMCR and SMCRH is in how their sampling variances
are computed. SMCRH alls that the population variance at post-test might be
different than the population variance at pre-test, whereas SMCR assumes
that the population variances are equal.
> * |"SMCC"| for the /standardized mean change/ using change score
> standardization.
>
SMCC uses the standard deviation of the outcome change scores to equate
effects across studies. In practice, it is sometimes possible to compute
SMCC even when SMCR or SMCRH cannot be computed, which I think is one of
the main reasons SMCC is used. Personlly, I think of SMCC as an ES of last
resort because I don't think most scales are designed to have stable change
score variation. For example, a small change in the reliability of a scale
could create fairly large changes in the SD of change scores on that scale.
In contrast, if the scale is fairly reliable, a small change in reliability
will have only a small effect on the SD of the raw score, making the
SMCR/SMCRH less sensitive to differential measurement reliability.
James
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