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

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