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Dear Sean,

It sounds as if you'd like to compare the slopes of the decay or increase
along time between two groups, is this right?

For a minimal example, say you have 4 subjects, 2 in each group, each
subject being scanned twice. I'd assemble the design matrix in this way:

Data  EV1 EV2 EV3 EV4 EV5 EV6
(subj1,scan1)  age  0  1  0  0  0
(subj2,scan1)  age  0  0  1  0  0
(subj3,scan1)  0  age  0  0  1  0
(subj4,scan1)  0  age  0  0  0  1
(subj1,scan2)  age  0  1  0  0  0
(subj2,scan2)  age  0  0  1  0  0
(subj3,scan2)  0  age  0  0  1  0
(subj4,scan2)  0  age  0  0  0  1

where EV1 and EV2 contain the ages for the subjects at the time of their
respective scans. EV1 is the regressor for the slope of group A (formed by
subjects 1 and 2) with respect to the age difference between the two scans.
EV2 is similar, but for group B. EV3 to EV6 are for the subject-specific
intercepts.

The contrasts to compare the slopes would be [1 -1 0 0 0 0] and [-1 1 0 0 0
0].

There are exchangeability restrictions given the repeated-measures design,
so to run this in randomise, define a design.grp file with one
exchangeability group per subject. (note that the "group" here isn't the
same as the groups A and B, but represent exchangeability groups, in a way
that permutations happen only within subject). The groups A and B can be of
different sizes, but all subjects need to have both scans.

In this set up, the age difference is what is going to explain the observed
difference in the signal for each group separately, which are then compared
by the two contrasts. It is ok then the fact that the time intervals are
not all the same. There is no need to further take some global age effect
into account, as this is captured by the subject-specific regressors.

Hope this helps!

All the best,

Anderson




2013/1/23 Sean F Walsh <[log in to unmask]>

> Dear FSLers
>
> I would appreciate advice as to the best way to set up the following
> problem. I have 2 structural scans per subject in 2 groups. The second scan
> is a few years after the first but the time difference between scans will
> not be exactly the same between subjects. I would like to discover the
> difference in change over time between the two groups, or the group*time
> interaction. I would like to do this while controlling for difference in
> age between the two groups, but not difference in age between scan1 and
> scan2 (as I am interested in those effects).
>
> Would it be possible to set up the model as something similar to:
>
> Design matrix
>
> Control2 Control1 Patient2 Patient1 Age1stScan Age2ndScan
>
> (where all 6 columns are filled in with 0s in the rows that don't pertain
> to that column)
>
>
> Contrasts
>
> 1            -1         -1         1                 0                  0
> -1            1          1        -1                 0                  0
>
> ?
>
> Would this also take away the effect of age difference between scans
> (which I don't want to remove)? Is it possible to do something like this
> without creating a type of scan2-scan1 subtraction image for each person?
> Is the problem here going to be the group column? If so is this easier to
> accomplish if not using permutation stats?
>
> Many thanks in advance,
>
> Sean
>