Hi Gallen,
please find my response inline.
Hope this helps,
Kersten
-----Original Message----- From: "Gong, Liang" LGONG2@mgh.harvard.edu Reply-to: Freesurfer support list freesurfer@nmr.mgh.harvard.edu To: Freesurfer@nmr.mgh.harvard.edu Freesurfer@nmr.mgh.harvard.edu Cc: mreuter@nmr.mgh.harvard.edu mreuter@nmr.mgh.harvard.edu Subject: [Freesurfer] About the contrast matrix in LME toolbox Date: Thu, 28 Dec 2017 00:03:35 +0100
Dear LME developer and expert,
I am using LME recently, based on longitudinal brain structural data, but I have two confusions in using it.
1) I followed the tutorial at: https://surfer.nmr.mgh.harvard.edu/ fswiki/LinearMixedEffectsModels However, I don’t actually understand the Contrast matrix design in this tool. In the example the contrast C matrix is a 3*14, is there any explain about this matrix design?
The contrast matrix creates linear combinations of the estimated parameters (betas) by assigning a weight (typically +1, 0, or -1) to the entry corresponding to that parameter. These linear combinations are used to formulate and test hypotheses about the effects of interest.
For the given univariate example, the columns of the contrast matrix correspond to the intercept (1), the main effect of time (2), the main effects of group and their interactions with time (3-8) and several covariates of no interest and possibly their interactions with time (9- 14). The global test ("Is there at least one difference between any pair of groups?") is broken down into three single comparisons, and this is reflected by each row.
For my study, I want to explore 3 treatment (2 therapy methods and 1 waitlist) effects on the brain structural, If I want to explore the main effect of treatment, how could I write the Contrast matrix, and whether I can explore each treatment effect on the brain structural? And how can explore the time*treatment effect contrast matrix?
Your contrast matrix could have the following columns:
1. Intercept 2. Time 3. Therapy 1 group 4. Interaction of therapy 1 group with time 5. Therapy 2 group 6. Interaction of therapy 2 group with time
This matrix implies that we use "waiting list" as the reference category. You could add further columns for covariates such as age-at- baseline, gender, ICV, etc. I also assume that therapy 1, therapy 2, and waiting list do not have any overlapping patients, i.e. are distinct groups.
To explore the main effect of treatment group it is statistically sufficient to ask: Is there a difference between waiting list and therapy 1, and is there a difference between therapy 1 and 2. This means that your contrast matrix for the global test of the main effect of treatment group will have two rows: in the first row, set column 3 to +1, and in the second row, set column 5 to +1 and column 3 to -1.
Since you only have three groups, while the univariate example has four groups, this means that you can remove columns 7 and 8 of the example's contrast matrix. For the same reason, you can also drop the third row of the contrast matrix.
Next, to explore differences between treatment groups separately, there are three possible tests: you can test therapy 1 group vs therapy 2 group, and either therapy group against the waiting list group. For this purpose, use three contrast matrices each with a single row. Assuming the above order of columns 1 to 6, set column 3 to +1 for therapy 1 vs waiting list. Alternatively, set column 5 to +1 for therapy 2 vs waiting list. Or, set column 3 to +1 and column 5 to -1 for therapy 1 vs therapy 2. All columns that are not explictly mentioned here should be set to zero.
To test single interactions between treatment and time, i.e. the differences in slopes, you can proceed in the same way, but use columns 4 and 6 instead of columns 3 and 5.
Needless to say, to assess the effect of therapy, you are primarily interested in the differential change across time (if the first measurement was done prior to therapy; i.e. pre-post therapy), not in overall differences of groups (which are undesirable). This of course means that the interaction of group and time, using columns 4 and/or 6 of the above contrast matrix, is much more relevant the simple group comparison using columns 3 and/or 5.
Finally, note that in the LME toolbox, all above tests are F-tests.
2) For the mass-univariate analysis, the example C matrix is 3*17, and it will explore the group differences in the rate of change over time among the four groups, and if I get the four group difference maps, How can I know the difference between each two groups? If I need to do the another qdec file and do the following steps as mris_preproc and mri_surf2surf?
The difference between the 3*17 matrix in the mass-univariate example and the 3*14 matrix in the univariate example is that there are four additional predictors - one quadratic effect of time, and three quadratic time * group interaction effects - and one removed predictor (ICV, which does not make much sense for thickness analyses). It is possible, but not necessary to use quadratic terms. In that sense, one might equally use a simpler 3*13 matrix for the given example.
The difference between each two groups across time, i.e. the difference in their slopes, can be tested in the same way as in the univariate example and as explained above. No additional processing is necessary.
Thank you very much! Best,
Gallen