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 thecorresponding 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-time1, 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
Charlestown, MA 02129
Phone: +1-617-724-5652
Email:
mreu...@nmr.mgh.harvard.edu
reu...@mit.edu
Web : http://reuter.mit.edu
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