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You have one summary statistic image per subject, so you are essentially using the two level summary statistic approach https://pdfs.semanticscholar.org/6ed1/05062770d089d86e9bcc7827f54487a22017.pdf .  Providing the time intervals between the scans were fairly consistent (giving you a balanced design), then this approach should be fine for making inferences that generalise to the population ( https://www.amstat.org/asa/files/pdfs/P-ValueStatement.pdf should be a much bigger concern).

A tissue map generated from the mid-point image contains values close to zeros and ones.  If you sum up these values within a region and multiply by the volume of a voxel, then you get the tissue volume.  If you multiply the values in the tissue class image by the Jacobian determinants for the early scan and the late scan, then you have estimates of the tissue volumes in those scans.  I guess the reviewer wants you to use these data, where j1 is the Jacobian determinant of the mapping from mid-point to first scan, j2 is the Jacobian determinant of the mapping from mid-point to second scan, c is a tissue map, and t is a time interval:

    y1 = j1 * c

    y2 = j2 * c

If you do a 1st level analysis, then the design matrix would be

    X = [1 -t/2

         1  t/2];

the GLM fit would be:

    b = inv(X)*[y1; y2]

and the contrast image to take to the 2nd level would simply be b(2).  i.e.

    b(2) = c*(j2 - j1)/t

The jd_*.nii files generated by the pairwise registration is (j2 - j1)/t, so if you multiply the contents of these by the tissue map, you get exactly the same as the contrast image from the summary statistic approach.

For those who have the symbolic toolbox, you can try pasting the following into MATLAB:

    syms t j1 j2 c 

    y1 = j1 * c;

    y2 = j2 * c;

    y  = [y1; y2]; % Data vactor

    X = [1 -t/2

         1  t/2];  % Single subject design matrix

    b = X\y;       % Fit the GLM

    simplify(b(2)) % The 1st level contrast image

Best regards,

-John

On 13 June 2017 at 12:17, gabriel robert <[log in to unmask]> wrote:

Dear Spm experts

We ran the pairwise longitudinal tool from SPM12 and then followed the procedure as suggested by Pr Ashburner in previous threads (ie segment the midpoint image, multiply the grey matter map in native space by the JD maps in native space and normalize it using a study specific Template from the midpoint image and run stats).

We then used a linear regression to test for an effect of a variable (lifetime number of given event asssed at time point 2) against the normalized grey matter changes and got some reasonable results.

We submit our results to a journal and one of the comments suggest  that the linear regression does not model the within-subject covariance and therefore recommended us to compute a within-subject dummy-matrix as following:

BL: subject-specific, segmented, DARTEL-registered, smoothed image,

FU: subject-specific, segmented, DARTEL-registered, smoothed image multiplied with the between-time point Jacobian

I have therefore 2 questions:

1/ Do we need to automatically use the within-subject ANOVA when adopting a longitudinal approach such as with the pairwise tool ? Whereas I clearly get that the linear regression does not account for the within subject covariance for the clinical/behavioral scores, it seemed to me that the pairwise longitudinal tool is appropriate to model the within-subject covariance for the brain metrics. So, if we use a "lifetime" number of events, linear regression should be statistically correct to me but I am unsure.

2/ I cannot clearly figure out what would mean the FU scans multiplied by the JD maps ?

I acknowledge this is not a pure SPM question but rather a more general longitudinal stats one but any help would be much appreciated,

Many thanks

Gabriel