Hi Alex,
the parameter is a single number that happens to be
measured at time 1 right, eg baseline age? Lets call
that parameter 'A' for the discussion below. Also
you have exactly 2 time points in all subjects?
There is two alternatives:
1. Simple approach (2-stage-model): You compute the
atrophy rate (e.g. percent thickness change) on the
cortex (long_mris_slopes) for each subject. At this
point you have 1 measure per subject and work
cross-sectionally. You can use qdec or mri_glmfit to
correlate 'A' (independent parameter) with the
thickness change (dependent variable). This is OK if
you have the same number of time points and the same
time distance in all subjects. Details here:
https://surfer.nmr.mgh.harvard.edu/fswiki/LongitudinalTwoStageModel
2. Better approach: use Linear Mixed Effects models
(we have matlab tools for that). This model is more
flexible (different manycolumn of ones, time points,
different time intervals, even subjects with a
single time point can be added). You'd setup a
system like
Y_ij = beta_0 + b_i + beta_1 * A_i + beta_2 t_ij +
beta_3 A_i * tij + error_ij
where Y_ij is the thickness of subject i at time
point j (known)
t_ij is the time from baseline of the j measurement
in subject i (known),
A_i is the variable you measure at baseline in
subject i (known),
the model will estimate the following:
b_i (a random effect) is the subject specific
intercept (offset from the global intercept beta_0)
beta_1 another intercept offset caused by A
beta_2 the slope with respect to time (fixed effect,
so it will be the same for all subjects, can also be
modelled as a mixed effect)
beta_3 the interaction of A and time (<- you are
interested in this)
Testing if the interaction beta_3 is different from
zero will show you where A has an effect on the
slope.
For the model above the X matrix would have 4
columns:
1 A T (A.*T)
where 1 is a column of 1's, A the A_ij (Ai repeated
j times for each subject), T=t_ij and the coordinate
wise product of A and T. Contast [ 0 0 0 1] tests
the interaction. You'd tell the function that you
want the intercept to be a random effect by passing
[ 1] (selecting the first column). If you also want
to have t_ij as a random, you can pass [1 3 ] .
Details here:
https://surfer.nmr.mgh.harvard.edu/fswiki/LinearMixedEffectsModels
Best, Martin
On
10/20/2014 03:20 PM, Alexandru Hanganu wrote:
Dear FreeSurfer Experts,
How could the longitudinal
analysis be performed in order to show whether a
parameter at time 1 is predictive of
changes in cortical thickness over time ? and can the corresponding
regions be shown in FreeSurfer ?
In a statistical analysis, as we
see it, we must perform the
correlation between the
parameter at time 1 and the
cortical thickness
difference (or ROI) time 2-time 1, yet in
this case we cannot see
it on the cortex.
Thank you,
Alex
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--
Dr. Martin Reuter
Instructor in Neurology
Harvard Medical School
Assistant in Neuroscience
Dept. of Radiology, Massachusetts General Hospital
Dept. of Neurology, Massachusetts General Hospital
Research Affiliate
Computer Science and Artificial Intelligence Lab,
Dept. of Electrical Engineering and Computer Science,
Massachusetts Institute of Technology
A.A.Martinos Center for Biomedical Imaging
149 Thirteenth Street, Suite 2301
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Phone: +1-617-724-5652
Email:
mreuter@nmr.mgh.harvard.edu
reuter@mit.edu
Web : http://reuter.mit.edu