[R-meta] Beta Coefficients (Predicted Means?) For Inclusion in Meta-Analysis

[Röver, Christian]

Dear Scott,

from the article it sounds like the quoted "intercept" parameters would
in fact correspond to the estimated mean outcome (disability score):

  "The beta coefficients for the intercept are the expected scores
  for the outcome measure at the data collection point."

The corresponding "data collection point" then is shown in each table,
so that the numbers you quote should then correspond to the mean score
at post-treatment time point.

Along with each coefficient estimate, they quote a standard error (SE),
which might be the number you'd actually need for a meta analysis (?).

In case you in fact require standard deviations instead (e.g. for
subsequent calculations), deriving these from the quoted standard
errors would probably be tricky, since they have fitted a somewhat
complex hierarchical model here. Not sure whether one could possibly
reverse-engineer at least an estimate of these from Table 6 (Are the
numbers in brackets supposed to be standard deviations? Maybe one could
derive a pooled standard deviation from these.).

Cheers,

Christian



On Sat, 2021-01-30 at 08:00 +1100, Scott Tagliaferri wrote:
> Hi All,
> 
> I would like to get some advice on including the following article in
> meta-analysis. I have requested data from authors but have not been
> successful. The article is open access so hopefully it is accessible.
> 
> https://www-ncbi-nlm-nih-gov/pmc/articles/PMC4921225/
> 
> The report the intercepts from Hierarchical Linear Modeling Analyse
> in
> table 3 for one of the outcomes of importance. Would these values be
> able to be used as the mean in analysis, with the SE converted to SD?
> An example of their reported data is below.
> 
> Post-Treatment
> Fixed Effect Beta Coefficient SE t-ratio df p-value
> Level 1 Intercept
>  CS Rot 15.092 1.586 9.518 90 <0.001
>  CS ExtRot 14.301 2.030 7.045 90 <0.001
>  NCs Rot 17.219 1.421 12.122 90 <0.001
>  NCs ExtRot 13.695 1.813 7.553 90 <0.001
> Level 1 Linear
> d
>  CS Rot −0.609 0.116 −5.268 90 <0.001
>  CS ExtRot −0.625 0.143 −4.365 90 <0.001
>  NCs Rot −0.702 0.141 −4.968 90 <0.001
>  NCs ExtRot −0.878 0.120 −7.318 90 <0.001
> Level 1 Quadratic
> d
>  CS Rot 0.014 0.003 4.256 688 <0.001
>  CS ExtRot 0.017 0.004 4.875 688 <0.001
>  NCs Rot 0.014 0.004 3.441 688 <0.001
>  NCs ExtRot 0.025 0.004 5.936 688 <0.001
> 
> Thanks,
> 
> Scott.
> 
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