Hi Harma and Jonathan,
I am writing to address question 3:
>> 3. There has also been some discussion in the SPM mailing list about using
>> total gray matter as a covariate or total intracranial volume (and there are
>> a few more options). When you compare two groups (patient vs control) and
>> you find a lot of regional differences that are all in the same direction
>> (for example always patient > control) this will also create a global
>> difference in gray matter. When you subsequently use total gray matter as a
>> covariate you will mask all interesting regional differences. Therefor I am
>> more inclined to use some measure of total intracranial volume as opposed to
>> total gray matter, despite of the difficulties in determining CSF. Does
>> anyone have any suggestions regarding this topic?
In the statistical literature on observational studies, a covariate is
defined as a variable that is assigned *before* the 'treatment' takes
place. This temporal criterion is designed to exclude that the
treatment variable, i.e. the variable of interest, has an effect on
the covariate. The idea is that one should never include covariates in
the model that are affected by the variable of interest.
If one does so, the model is biased -- sometimes this is called
'treatment bias'. The paper most often cited in this respect is
Rosenbaum Paul R 1984, The consequences of adjustment for a
concomitant variable that has been affected by the treatment, J. Royal
Statist. Soc. Series A, 147:656-666. More informal explanations may be
found in books such as Gelman Hill 2006, Data analysis etc. Chapter 9.7.
The most common effect of including such a covariate is that the
effect of your variable of interest goes away. This is what you refer
with 'masking'. Yet it is unclear that other variables such total
intracranial volume are immune from such effects. This would be the
case if an alternative covariate is indeed uncorrelated with your
variable of interest. Such lack of correlation, however, would be a
property to be inferred from the data, with the ensuing problems. This
differs from having a covariate that logically cannot be affected by
the variable of interest.
Best wishes,
Roberto
Roberto Viviani
Dept. of Psychiatry III
University of Ulm, Germany
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