Replicating longitudinal fixel-based analysis approach

28

Welcome Michelle!

First of all, I have a very basic question about how to do the sign-flipping and use the Freedman-Lane method as described in the article of Genc et al. (2018). Is it sufficient to use the option -exchange_whole, as I assume to have independent and symmetric errors? And is it correct that the generation of an empirical null distribution is automatically done with the Freedman-Lane method in the latest version of MRtrix?

  • There is a conflation here between:

    • Restricted exchangeability (see “Whole-block exchangeability” in this manuscript), which is what -exchange_whole does;
    • Independent and symmetric errors (see “Permutations and exchangeability” in the same manuscript), which is indicated via -errors ise or -errors both.

  • Yes, as of version 3.0.0, the null distribution is always generated using the Freedman-Lane method.

Second, similar to Julie, we wanted to analyze the differences between groups over time by first subtracting the time-point 1 from the time-point two image (first level) and then defining the contrast based on group (second level). We use age (and intracranial volume for FD) as covariates, which gives the following contrast: 1 -1 0 (0) for intervention > control at e.g. T2-T1, T1-T2, T3-T1 and T1-T3. If I’m correct, this gives the group-by-time interaction effects, but correct me if I’m wrong!

  • I can’t verify whether or not a particular contrast matrix is or is not correct without also knowing the design matrix in full. But if I assume that your groups are G1 and G2, and your design matrix columns are:

    G1:T2-T1        G2:T2-T1        Age        eICV

    , then that contrast will test the hypothesis that the change from time point T1 to time point T2 is greater in G1 than it is in G2.

  • I find it interesting that you regress intracranial volume only specifically for FD, given that my own suggestion has been the opposite.

  • I suppose that you can refer to this as a “group-by-time interaction effect”. Just be wary that the notion of “interaction” is often queried quite differently in a GLM to how it is done here (due to pre-calculation of the difference over time in this case).

However, for the within group effects, we didn’t use the subtracted images but a paired design matrix and we defined all the contrasts separately (e.g. T2 > T1 for the intervention). This is how we would build the GLM for fMRI data, but I’m not sure if it works the same way for the fixel data?

  • If I’m understanding this correctly, you want to test, only in the intervention group, both T2>T1 (or equivalently T2-T1 > 0) and T3>T1 (or equivalently T3-T1>0). This sounds like “Single group, three measurements”, which, as the FSL GLM Wiki states, can’t be done in randomise in the same way as it is done in feat.

    What you can consider doing with such data is that instead of pre-computing a difference between two time points at the first level and feeding that into a second-level model for a hypothesis test, you instead use all three time points at the first level to estimate a quadratic relationship between your exploratory variable and time, and then at the second level use an F-test to test the hypothesis that both the linear and quadratic terms are zero (i.e. there’s no change of any nature over time). This requires quite a lot more GLM trickery, but it can be done.

  • The particular modality used to generate the data are being fed into the GLM is irrelevant. Where there does seem to be a difference in handling (based on their GLM Wiki page) is specifically between feat and randomise in FSL. While I’m not intimately familiar with how / why these differences arise, statistical inference in MRtrix3 operates on the same principles as randomise, and so I would generally advise that reading the FSl GLM wiki and translating it to FBA should be interpreted through that lens.

Cheers
Rob

1 Like