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