Dear Robert,

Randomise only fits OLS GLM's, i.e. unweighted least squares fits.  That said, randomise can accommodate certain types of repeated measures data, the simplest type of which is paired data.  When you have just two time points, follow the instructions for paired data analysis.  When you have three or more observations per subject, things get slightly trickier.

If you have k>=3 repeated measures, you could simply treat the data like a 2-way ANOVA, modeling one longitudinal factor, and one subject factor, but since you're not doing a proper mixed effects model, the t-statistics won't really be what you want (i.e. they won't be capturing the correct between subject variation in the denominator).  For the paired case, k=2, it happens to works out exactly correct (i.e. OLS & MFX are the same), and the k=3 case probably isn't too far off (if an assumption of compound symmetric correlation--i.e. all equal correlations--within subject is true, and the design is balanced, randomise's OLS results should match a full-blown mixed effects model).  But for imbalanced design (k varying between subject) and k of 4 or more, you probably shouldn't trust OLS to be giving you sensible answers.

The safest approach for k>3 would be to create summary measures for each subject, and then anlayze those with a simple second level model.  For example, if you're interested in slope, or change over time, fit a simple linear regression model for each subject, and then model the images of slope coefficients.

Ideally there would be some scripts cobbled together to aid with such longitudinal analyses, but does this give you an idea of what randomise can and can't do?

-Tom



On Wed, Apr 16, 2008 at 3:50 AM, Robert Terwilliger <[log in to unmask]> wrote:
Dear FSL,

We have been doing DTI analysis using TBSS successfully for some time
now. Our cohort consists of normally developing adolescents.

As a small example of our analysis consider a sample of FA images from
six subjects (we have many more, but this is for simplicity), ages
12-17. I do a "within group" design in which the log of age is the
regressor. The resulting design.mat and design.con files are as
follows:

**************
design.mat
**************
/NumWaves 1
/NumPoints 6
/PPheights 1
/Matrix
-0.145
-0.145
-0.065
0.009
0.143
0.203

*************
design.con
*************
/NumWaves 1
/NumContrasts 1
/PPheights 1
/Matrix
1
-1

The values in design.mat are the demeaned natural log of the subjects' ages.

So far, so good.

Now fast forward a couple of years....This is actually a longitudinal
study, with each subject scanned on an annual basis. As is common in
longitudinal studies, not every subject is scanned every year, for a
variety of reasons.

If we consider only the first year scans as we are doing currently,
each subject can be treated as an independent sample. However, now
some subjects have had three scans, some have two, and a few didn't
make it past the first year.

Is there a way to set up a model in randomise where we can include
multiple DTI scans from the same subject? This would violate the
assumption of independence in the simple model, but we're looking for
a way to account for the within-subject correlation in a mixed-model
design.

Many thanks,

Robert Terwilliger
Laboratory of Neurocognitive Development
University of Pittsburgh




--
____________________________________________
Thomas Nichols, PhD
Director, Modelling & Genetics
GlaxoSmithKline Clinical Imaging Centre

Senior Research Fellow
Oxford University FMRIB Centre