Response function for group analysis

[ThijsDhollander]

Hey Phoebe,

Hope you’re doing well.

@phoebe.thomson

@ThijsDhollander you mentioned in your most recent reply here that

@ThijsDhollander

On a completely separate note, in studies related to development, I’d also get the response function(s) only from the most developed subject(s) in the spectrum/range that’s being studied; for other reasons. And also within those subjects, you’re after the response functions representing the most developed tissue, I’d argue. There’s different ways of looking at this latter scenario though; several of which are “ok”, but they all mean something different…

Just wondering if it would be possible to elaborate on this point?

Sure, up to some extent! So this is actually what I did in practice for example in this work. Some of the relevant insight into why you might want to calibrate the response functions, in particular the single-fibre white matter one, from the older / more developed subjects is also hidden in plain sight in this talk on the most recent version of the response function estimation algorithm, in particular the bit starting from 1:26. The diagram / sketch that I often used to talk about 3-tissue CSD (the one with the triangle) is useful to explain this. When you analyse your whole cohort and want to make the 3-tissue output (or derived metrics, e.g. FD) comparable, you want 2 things wrt response functions:

1. Use the same unique triplet of WM-GM-CSF response functions for all subjects, as the response functions essentially represent the “units” of your resulting metrics later on. So to compare apples with apples, it’s all got to be expressed in the same units, aka the same triplet of WM-GM-CSF response functions.

2. To make sure those metrics aren’t biased, you want the model to fit the data. Even more so, fit it equally well across your whole population, young and old. Here’s where the diagram in the talk is useful: 3-tissue CSD with non-negative compartments will be able to fit what i inside the triangle. The response function calibration on the other hand, determines the corners of the triangle. So essentially, the triangle needs to be large enough to capture all signals later on.

Now, for very young subjects, i.e. when things still change a lot due to development, the most developed bits of WM will be to the far top left corner of that triangle. If you were to e.g. calibrate the response functions (for example sake) based of the youngest subjects specifically, the top left corner of the triangle might not extend far enough to capture the most developed bits of white matter in the older subjects. That would introduce a bias in the fit for the most developed bits of WM in the older subjects. In specific cases, this can lead to an inversion in the kind of pattern you’d expect in those bits. Older subjects might even appear “less” developed than younger ones due to these particular kinds of biases. That’s obviously not desired.

So calibrating the response functions for all subjects and using the average over all ages, lands you somewhere halfway. The problem is less severe then compared to calibrating based of the youngest subjects only, but it’s still present for the same reasons. The solution then is to use the older / more developed end of the spectrum. In this way, most WM of most subjects will fit well, without substantial biases in the 3-tissue signal representation.

So how much does this matter in practice? Well, I know very well from experience it does matter for neonatal age ranges. Be in touch privately if you need more details on that. However, for your specific scenario:

@phoebe.thomson

More specifically, in our study we have a longitudinal sample of 8-14 year-olds with and without ADHD. Some researchers in our team are using the entire dataset, while others a subset (e.g., controls only, or one timepoint only).

So that’s already quite a bit older than neonates or even babies for that matter. I also know from experience that at that point, it’s far far (far far) less of a worry, in terms of the points I described above. So that should hopefully already put you a bit at ease there.

@phoebe.thomson

Based on this thread and our goals, would it be valid to create a single unique response function (or set of response functions for multi-tissue), and have everyone use this same response function regardless of the subset of data being studied?

Yes, so that’s point 1 above. I can reassure you it’s perfectly possible and should work very well. As mentioned in point 1 above, it’s also a requirement if you want to be able to compare the FODs or compartments in a, well, comparable way. Not using the same unique (set of) response functions will make this very… different. I would strongly advise against it. So the gist: no worries, it will work well.

@phoebe.thomson

If so, would you suggest using controls at the most developed/final timepoint to create this response function (even if some studies may only investigate timepoint 1 or ADHD individuals, for example)? Or do you think averaging over all subjects and timepoints would be most appropriate here?

So likely the choice here makes little difference, because of the “older” age range. However, exactly because of that, it should be entirely safe to use a subset of subjects. You only need 1 technically, so a small batch of them is far more than robust enough. So if you want to play it on the safest side possible, simply pick the controls at the most developed/final time point. So the gist: I anticipate it won’t make much of a difference, but if you want to be safe “regardless”, pick the most developed controls.

I hope that helps, but feel free to be in touch if you need more insights or proper wording to explain stuff, etc…

Cheers & take care,
Thijs