Dear Steve,


> > >Dear Steve,
> > >> I'm very puzzled by results of an SPM99 covariate-only analysis.  I
> > >> exchanged email about this with John Ashburner a week ago, and he said
> > >> that you were really the best person to set me straight.  I know you
> > >> are really busy, but since you were kind enough to comment on Stuarts
> > >> views on p-values, I'm hoping you can provide us some help with his old
> > >> data, which I've inherited.
> > >> We have 18 subjects who were PET scanned (6 scans), then got 3 weeks of
> > >> a drug, then were scanned again.  Since the drug seemed to work, by the
> > >> criterion of reduced symptom severity (in ALL patients-except one who
> > >> stayed the same), we wanted to see correlated regional brain activity.
> > >> A straightforward contrast of two conditions (all pre drug scans vs all
> > >> post drug scans) showed a number of activations and deactivations that
> > >> made sense in terms of the relevant literature.  The problem is that
> > >> when we did a covariate only analysis using the symptom severity
> > >> rating, the activations and deactivations seemed to reverse with each
> > >> other.  Since covariate score is the same for all scans in a given
> > >> session, both analyses are primarily modeling change between sessions.
> > >> I was happy to see pretty much the same areas, only larger, in the
> > >> covariate analysis, because it suggested that the important difference
> > >> between sessions was related to symptom change, but why should the
> > >> activations become deactivations and vice-versa?  Making the stakes
> > >> even higher to properly interpret this, the covariate results
> > >> replicated about 90% in the placebo group, where patients symptoms
> > >> increased or decreased about evenly across sessions.
> > >> This is why the activations/deactivations seem reversed to me.  Since
> > >> all drug subjects went from a higher covariate (more symptoms) in
> > >> session 1 (pre-drug) to a lower numerical rating, and the +covariate
> > >> contrast shows voxels whose activity is positively correlated with the
> > >> covariate, these will be voxels that were higher on day 1 than on day
> > >> 2.  The minus covariate contrast shows voxels where activity is
> > >> negatively correlated with the covariate, and so these will be voxels
> > >> that were higher on day 2 than on day 1 (high activity associated with
> > >> low rating).  Is this wrong?  Why do the areas that were more activated
> > >> in the first session when covariate scores were HIGH come out in the
> > >> -covariate, while voxels more activated in the second session when
> > >> covariate scores were LOW show up in the +covariate??  The covariate
> > >> was subject specific & centered, and I entered scan order as a nuisance
> > >> covariate, so my contrasts were 18 ones, and 18 -ones (with SPM padding
> > >> zeroes).
> >
> > >I think the problem here is that the covariates are collinear with the
> > >confounding block effects. It is not clear to me whether you have
> > >simply been testing for a main effect of treatment (pre vs. post or
> > >symptom severity) or whether you have perfomed 2 activation studies and
> > >have been looking at the symptom time condition interaction (an effect
> > >of symptom severity on activation). I suspect the latter.  In this case
> > >you would have to average all the scans from one seesion for each
> > >patient so that each patient had two images.  You then simply enter
> > >these 36 images into a single covariate model where the covariate would
> > >be symptom severity.  You cannot make inferences about between subject
> > >effects using within-subject error variance and the effect of severity
> > >is a between-subject effect.  To examine the effect of severity on
> > >activations you would repeat the procedure but instead of using the
> > >averge of 6 scans use a contrast image from a first-level analysis
> > >testing for the activation.
> > >With very best wishes - Karl
>
> Dear Karl,
>       The covariates are certainly colinear with the session effects, but
> my covariate analysis did not model the block (session) effect (or the
> conditions given on each day) so how can that hurt? In both the 36-image
> analysis and the contrast-image analysis you suggest above, are we NOT
> modelling the individual subjects?

Good.  But also ensure you are not modeling the scanning session (i.e.
pre and post drug) effects.  If you do the main effect of the covariate
and the session effects will be collinear (assuming the drug improved
symptoms).


> I thought that since the two sessions
> could easily be treated as two conditions with the individual subjects
> modelled, that a covariate only analysis could also model the subjects,
> because the covariate effect would be the same kind of interaction, only
> weighted by degree of change in the covariate.  This probably demonstrates
> my mathematical naivete.  If I understand you correctly, I should use the
> "mean" SPM button to make an average of each subjects preprocessed scans on
> each day.  (By the way, when would you use the "adj mean" vs the plain
> mean?)  Then I should do my covariate only analysis on the 36 resulting
> images as if they all came from the same subject.

Exactly.  The difference between "mean" and "adj mean" is that the
latter is a wieghted mean of the images that accomodates global
differences.  I would use "adj mean" because this is what you would get
if you used a contrast averaging over conditions in a first level
analysis.

>      For your 2nd suggestion, I would be assessing the effect of symptom
> severity on the activation produced by some difference between the
> conditions.  Our 6 scans per day are 2 baseline (no stimulus-no stimulus
> expected), 2 activation (painful stimulus-painful stimulus expected) and 2
> anticipation (no stimulus-pain expected).  So if I wanted to look at the 2
> pain activations vs the 4 scans where we presented no stimulus, I'd do that
> contrast in the usual fixed effect way for each subject on each day (2
> scans vs 4 scans) to get a contrast image, and use the 36 contrast images
> for the covariate only analysis, still acting as if they all came from a
> single subject.  Is this right?

Absolutely.

> Can you get contrast images with this few scans (2 vs4)?

Yes - remember you are not making any inferences at this stage so
degrees of freedome are irrelevant.

> If so I assume the activations and deactivations associated
> with the pain stimulus would produce separate contrast images

No - a contrast is esentially a difference image which preserves all
the information you require for the second-level analysis.
'Deactivations" are tested for by using a reverse contrast at the
second level.

> If I understand you correctly, then I'm good to go.

Then go.

With best wishes - Karl