> I have been examining the issue of including a global covariate in VBM
> analyses and the meaning of results that include it, and I am a bit
> confused. I give some background below but the basic question pertains to
> understanding the differences between proportional scaling and ANCOVA and
> whether a global should be included at all.. For example, in an example
> given below a propsca global was included in a VBM of males vs. females.
> However, wouldn't including a global based on proportional scaling be
> saying that males have more gray matter per voxel? Might it not be the case
> that because of their bigger heads males have more voxels with gray matter
> in them and not a greater gray matter density?

Most people who study shape use a multi-variate framework.  Shape is based
on the relationship between the positions of corresponding features, after
accounting for size, position and orientation.  Unfortunately, we do not
have enough subjects to do a full multi-variate analysis, so we restrict our
analyses to being mass-univariate, and possibly use a "global" as a confound,
or use some kind of proportional scaling.  We attempt to answer a more
clinically interesting question by limiting our investigation to identifying
regions of increased or decreased GM.

Using no "globals" and a "modulated" analysis is intended to show regions
of absolute volumetric difference in grey matter.

Using total grey matter as a confound will show regions of absolute difference
that can not be explained by the total grey matter differences.

Using proportional scaling to total grey matter will show differences where
a region contains a disproportionately large or small region of total grey
matter.  For example, a structure may normally represent 2% of the total
brain grey matter, but in patients it may represent 1.5%.

The males versus females test is a tricky one.  Human males are generally
bigger than females, with bigger heads.  If you were doing an analysis of nose
sizes, then it is likely that males would have bigger noses. Maybe you would
want to know if this extra size was still significant if total head size was
taken into account, either by modelling head size as a covariate, or by
proportionally scaling the noses such that they were rendered proportional to
the total head size (giving us a measure of nose as a percentage of head volume).

Normally, a brain with e.g twice the volume of another brain will not have
twice as much grey matter.  The relationship between grey and white-matter
volume approximately obeys a power law, with a 4/3 exponent (Zhang &
Sejnowski, PNAS 97(10):5621-5626, 2000).  If we use a proportional scaling
model based on whole brain volume, our null hypothesis is that grey matter
volume varies linearly with brain volume.  This is simply not true, although
it may serve as a useful first approximation.

The choice of model is up to the investigator, and it really does depend what
you want to test.  I would really rather not be give any firm recommendations.
When a VBM experiment is written up, the model should be accurately described.
Different models will give different results, which may appear to conflict
with each other.

>
> What happens in the case of disease states such as a degenerative dementia?
> Why would proportional scaling be better than ancova in this case or should
> a global not be included as there could be a correlation between regional
> and global changes in gray matter, i.e., large regional changes affecting
> the global covariate. I've reviewed the explanation of propsca vs. ancova
> differences in HBF-1 but I don't think it makes these issues clearer.

In the case of dementia, the total intra-cranial volume is often used to
proportionally scale the data.  Thus, each structure/region is treated as
a proportion of intra-cranial volume.  Head sizes vary, so this normalisation
should reduce the residual variance from the model.

Best regards,
-John

>
> Any thoughts on these issues would be appreciated. Info from background
> list emails are below.
>
> Darren
> --------------
>
> In an email from 1/24/03 KJF and JA recommend proportional scaling as
> perhaps the most meaningful, with the suggestion that normalization to the
> total gray matter volume may be best. JA gave an example of comparision
> between males and females. In this case one would want to remove the
> confound of males having a bigger head size.
>
> In an email from 5/1/2003, JA suggests that either ANCOVA or proportional
> scaling may be used. " There doesn't necessarily need to be a single global
> correction if the ANCOVA approach is used.  There could be several, and the
> choice of "globals"  depends on the hypothesis you have.  If you simply
> want to look at any absolute volumetric difference, then you wouldn't use
> any globals.  If you  want to see regional GM differences that cannot be
> explained by differences  in whole brain volume, then you would use whole
> brain volume. The alternative to covarying out the effects of some
> "global(s)", would be to proportionally scale the data.  This involves
> dividing the values by e.g.whole brain volume, such that the intensities
> are normalised to whole-brain volume."
>
> A July 22 posting makes reference to some of the above emails and a
> statement that either proportional scaling or ANCOVA could be used
> depending on goals of the analysis, but no further explanation is given.

--
Dr John Ashburner.
Functional Imaging Lab., 12 Queen Square, London WC1N 3BG, UK.
tel: +44 (0)20 78337491  or  +44 (0)20 78373611 x4381
fax: +44 (0)20 78131420  http://www.fil.ion.ucl.ac.uk/~john