FEAT 2 Practical - Multi-Level

Practical Overview

Paired t test

We have a group of 6 subjects scanned under two different conditions, A (left hand motor function) and B (right hand). Is there a significant A-B paired difference generalisable to the population from which the subjects are drawn? (Note that this is a stroke study, and hence comparing left and right motor function is particularly interesting in this case.)

We want the A-B paired mean difference within a mixed effects model, taking into account the within-subject fixed effects variances and the between-subject random effect variance. This is done as a two-level analysis:

• Level 1: Single-session analyses; there are [6 subjects] * [2 sessions] = 12 first-level FEAT analyses. These have already been done for you.
• Level 2: Between-subject analysis; we input the COPEs from Level 1 (there are 5 contrasts at Level 1 and hence 5 separate second-level analyses), and estimate the mean (paired) difference for each.

Note that as well as the COPEs, FEAT passes the variance of these COPEs ("varcopes"), and even the uncertainty in the variance of these COPEs ("tdofs" - degrees-of-freedom), between the different levels.

The first level analyses are held in 6 different directories in ~/fsl_course_data/fmri/ptt, one for each subject. The subject directories are ac at cm df dn eg. Within these are the first-level FEAT directories, which have already been run for you.

Each first-level analysis contained 5 contrasts (each related to finger tapping - i.e. "index" finger only, "sequential" order, etc.). Thus there are 5 copes in the stats subdirectory of each first-level .feat directory. The higher-level analysis will be carried out independently on these contrasts, i.e. a second-level analysis of all subjects' first-level "index" contrasts, a separate second-level analysis of all first-level "sequential" contrasts, etc. Each of these second-level analyses will form a separate cope??.feat directory inside a newly-created .gfeat directory.

• cd ~/fsl_course_data/fmri/ptt

• Type Feat &
  (Feat_gui &     on Mac)
  

• Change First-level analysis to Higher-level analysis

• Change the Number of inputs to 12 (6 subjects * 2 conditions)

• Press Select FEAT directories. Now, you need to fill the first level FEAT directories in a sensible order. You could either put them in order:
  .../ac/ac_left.feat .../ac/ac_right.feat .../at/at_left.feat (etc.)
  or you could enter all the "lefts" first and then all the "rights":
  .../ac/ac_left.feat .../at/at_left.feat .... .../ac/ac_right.feat (etc.)
  

  We recommend the latter, because this matches the example paired t-test in the FEAT manual, and also matches the way the paired t-test is setup for you if you use the "model setup wizard" (explained below).

  Note that you can often avoid having to tediously hand-select each of these first-level FEAT directories separately, using the Paste button. If you press this, a new free-text window comes up, within which you can paste text (in this case the list of first-level FEAT directories) which you can copy, e.g. from a list in a terminal. Press Clear to clear the text window. Then in your terminal, inside the ptt directory, type
  ls -d1 `pwd`/??/??_left.feat ; ls -d1 `pwd`/??/??_right.feat
  This gives you a complete listing of the full pathnames of the FEAT directories in the right order. (The `pwd` part tells the shell to replace what's within the quotes with the result of running the command - in this case, filling out the full pathname of the current directory. The ? characters are expanded by the shell to fit any single character, in alphabetical order, hence all the "left" FEAT directories are listed first, and then all the "right".) You can now highlight this list with the mouse, and paste it into the FEAT paste window with the middle mouse button (or possibly by clicking in the paste window and typing control-y).

• When this is done, set the Output directory to ~/fsl_course_data/fmri/ptt/ptt_ols.gfeat

• Go to the Stats tab and select the Mixed Effects: Simple OLS option. Also, make sure that the Use automatic outlier de-weighting button is not turned on. It is important that these two settings are chosen, otherwise the analysis will not be quick enough to be of use to you in the time that we have available for the practical. Normally, we recommend that the more accurate FLAME 1 option is used in combination with outlier de-weighting, for the reasons outlined in the lectures. However, in the interest of speed, in this practical we choose the faster OLS option without outlier de-weighting.

• With this design you can use the Model setup wizard, which provides an easy way of setting up a few simple designs. Select two groups, paired and press Process. You will now see the design matrix that has been created for you. To understand how this is controlled in detail, open the Full model setup.

  Note that the Inputs (1-12) must correspond to the order you entered the first-level FEAT directories. Also note that the first column (labelled Group) corresponds to groupings of inputs that will share the same random effects (RE) variance in this level of the model. Here, we let all subjects have the same RE variance (i.e. the Group column should be left as all 1s)

  There are 7 EVs:

  • EV 1 models the A-B (left-right) paired difference
  • EVs 2-7 are confounds which model out each subject's mean (this is what makes the design a paired t test)

  Click on the Contrasts & F-tests tab. There are two contrasts setup for you by the wizard. EVs 2-7 are confounds of no interest and so do not appear in the contrasts. Hence, the contrasts only involve EV1. Change the Titles to read:

  • left > right
  • right > left

• Press Done.

• The default Post-stats are fine. So you are now ready to run the analysis. Press Go, and wait for the results - this second-level analysis should take about 5 minutes. The web browser that appears monitors the overall progress.

• Higher-level FEAT runs produce .gfeat directories. The top-level web report provides links to the previous level reports, a registration summary page (have a look at this, you may later need to reload the page if you view it before it's completed) and to the separate higher-level reports. LOOK AT YOUR DATA - in particular it is always important to look at the registration summary report page very carefully, to check that all lower-level registrations succeeded. (If any of the lower-level FEATs look like the registration has failed badly, you need to fix this before re-running the higher-level FEAT. The simplest way to do this is to start the FEAT GUI, change Full analysis to Registration only, select the first-level FEAT directory with the problematic registration and change the registration settings. The first thing to try is to reduce the search to No search (assuming that the data is roughly oriented correctly) and/or to change the DOF.)

• In the results page you get a link to the group results from running the group-level analysis on each first-level contrast. Within each contrast you get a group-level results page showing the standard post-stats output. However, note that the "time course" outputs in these higher-level results no longer refer to "time" (despite the heading). They refer to subject (or session) number. In this case that is the 12 subjects in the study, and it is effect size shown on the vertical axis, rather than normalised MRI signal. Have a look at this and the other parts of the results webpage and make sure you understand what is being shown.

• If you get spare time at the end of this session, there are two other analyses of interest:

  • In the FEAT GUI, load in the design.fsf from the .gfeat directory. Change the modelling/estimation method to Mixed Effects: FLAME 1, which is nearly as accurate as full FLAME and nearly as fast as OLS. Change the output directory name to reflect this option. Under the Data tab, deselect all of the lower-level copes except 2 - this tells the group FEAT to only run the second-level analysis on the second of the first-level contrasts, not all 5. After completion (5-10 minutes), compare with the OLS results. The FLAME results do look "nicer", as well as there being some new plausible activations that were not previously found.

  • Whilst the above is running, get another analysis ready to run - revert to the OLS option, and change the model to the simpler unpaired t test (use the wizard, and make sure that you understand the EVs and contrasts that the wizard sets up for you), re-run and compare with the paired t-test results.

Group difference with multiple sessions for each subject

We want the mean group difference, within a mixed effects model, taking into account the within-subject fixed effects variances and the between-subject random effect variance. This is done in THREE levels:

• Level 1: Within-session analysis (there are [2 groups] * [5 subjects] * [3 sessions] = 30 of these first level FEAT analyses, which have already been done for you)
• Level 2: Between-session analysis (in which we input the data from Level 1, and estimate each subject's mean response)
• Level 3: Between-subject analysis (in which we input the data corresponding to the subject means from Level 2, model the between-subject variances and estimate the group mean difference)

Because each subject only has 3 sessions, we do not run a mixed effects second-level analysis to get an estimation of each subject's mean response. The reason for this is that we would not be able to get a good estimation of the within-subject session-to-session variance with just 3 sessions. Hence we choose to ignore the session-to-session variance by using a fixed effects analysis at this second level. See here for a more involved discussion of the choice of a fixed effects analysis.

In addition to this, the analysis cannot be combined into a single second-level analysis. This is tempting as a design matrix can easily be formed containing each subject's mean (across sessions) as a separate EV, and then contrasts can be formed to test the mean across all subjects. The problem with this model is that there are two separate sources of variability (session-to-session and subject-to-subject) but they cannot be modelled properly (with the correct weighting) in a single level.

The first-level analyses are held in the directories ~/fsl_course_data/fmri/3lev/patients and controls. Within these directories are a directory for each subject, each containing the three first-level FEAT directories which have already been run for you. So, let's start with the level 2, within-subject analysis

• cd ~/fsl_course_data/fmri/3lev

• Type Feat &

• Change First-level analysis to Higher-level analysis.

• Change the Number of inputs to 30 (2 groups * 5 subjects * 3 sessions).

• Press Select FEAT directories. Now, you need to specify the first level FEAT directories in a sensible order: control subject 1 sessions 1, 2, 3 then control subject 2 sessions 1, 2, 3, etc., followed by all the patient sessions. You can use the following command in the terminal to create the list to paste into the Paste window:
  ls -d1 `pwd`/*/*/*.feat

• Set the Output directory to ~/fsl_course_data/fmri/3lev/lev2.gfeat

• Go to the Stats tab and select the Fixed-effects option.

• Press Full model setup. Note that the Inputs (1-30) correspond to the order you entered the first-level FEAT directories. As this is a FE analysis the Group column is ignored so leave all these entries as 1 (if we had lots of sessions and did a ME analysis instead then we would use a unique number in this column for each subject - within each subject we would estimate a separate variance).

• We need 10 EVs - one for each subject mean. Change the 0s to 1s appropriately, in such a way that each EV models a different subject mean. If you are not sure that you are doing the correct thing then ensure that your design matrix looks the same as the one shown below.

• We now need to setup the contrasts. We need to pass the 10 parameter estimates (PEs) corresponding to the 10 subject means through to the third level as COPEs. To enable this , we need to have a contrast for each subject mean that just selects that parameter. Use the design matrix shown below for guidance.

• Press Done and ensure that the design matrix is the same as:
  
  

• The default Post-stats are fine (in fact the post-stats don't affect what gets passed up to third-level). So you are now ready to run the second-level analysis. Press Go, wait for the result web pages and then view them carefully.

• Type Feat &

• Change First-level analysis to Higher-level analysis

• Change Inputs are lower-level FEAT directories to Inputs are 3D cope images from FEAT directories (the inputs will be the 10 cope images, one for each subject mean, from the second-level analysis).

• Change the Number of inputs to 10 (2 groups * 5 subjects = 10 copes from level 2, each corresponding to a subject mean)

• Press Select cope images and enter the COPEs from the second level in order from 1-10. This ensures that 1-5 correspond to controls and 6-10 correspond to patients. These will be inside the cope1.feat/stats directory which is inside the second-level .gfeat directory that you just created.

  

  The relevant command for pasting the list is
  

  ls -d1 `pwd`/lev2.gfeat/cope1.feat/stats/cope?.nii.gz ; ls -d1 `pwd`/lev2.gfeat/cope1.feat/stats/cope??.nii.gz
  

  
  Can you see why this needs two separate parts, one with a single '?' and one with two? Can you see why you can't just use '*' instead of having two commands?

• Set the output directory to lev3.gfeat

• Go to the Stats tab and, again to save time, select the OLS option and make sure Use automatic outlier de-weighting is turned off.

• You can use the wizard to setup a two groups, unpaired analysis (make sure the "Number of subjects in first group" is set appropriately). Note that the Inputs (1-10) correspond to the order you entered the second level COPEs. Here, the control subjects are modelled with one RE variance and the patient subjects with a different RE variance (i.e. Rows 1-5 of the Group column should be 1 and Rows 6-10 should be 2). The two EVs model the different means for the different groups.

• However, instead of this model, let's first try and set it up another way. We still have two EVs, but now one EV represents the overall mean of both groups, and a second EV represents the difference between the two group means. This can be done using EV1 = [1 1 1 1 1 1 1 1 1 1]' and EV2 = [1 1 1 1 1 -1 -1 -1 -1 -1]'. Set up these two EVs.

  Do you think there is anything wrong with setting the design up in this way?

  Press View Design and you will see that there is indeed a problem with setting the design up this way. We have a design matrix that is not "separable" with respect to the variance groupings.

  We are trying to set up a design with different RE variance groupings for the control subjects and patient subjects. However, within each EV, inputs from only one of the variance groups can have non-zero values. We have violated this here. If we only had one variance group instead, then these two ways of setting up the model would be equivalent.

• So, to be able to have these variance groupings we must setup the design using EVs which are separable with respect to the variance groups. For this we need a different EV for each group mean. Re-run the wizard to go back to the recommended unpaired t-test.

• We now have the following contrasts:
  • C1: "controls-patients" [1 -1]
  • C2: "patients-controls" [-1 1]
  • C3: "controls" [1 0]
  • C4: "patients" [0 1]

• Go to Post-stats. Reduce the Z threshold to 1.7 (with this artificially small number of subjects the effect is weak!). The other defaults are fine. So you are now ready to run the third-level analysis; press Go.

• While you wait for the analysis to finish, check the second-level analysis results - did you notice that one or more of the first-level registrations (that we had already run for you) had failed? Make sure that you can find these, and if you have enough time try and fix them and re-run the analysis.

• Don't forget to check the results of the third-level analysis when it is finished.

This is the end of the Multi-level FEAT practical.