A Reader Writes: Basic FMRI Questions

Mine's bigger

I recently received an email with some relatively basic questions about FMRI, and both the question and answers might apply to some of you. Admittedly, I am not 100% sure about the weighting of the regressors for the ANOVA, but I think it's pretty close. Whatever, man; I'm union.

Some of the words have been changed to protect the identity of the author.

Dear Andrew,
Thanks for your message. My background is in medicine and I am trying  to do fmri research!
I will be grateful for your help: 
1. How do you interpret the results of the higher and first level fsl analysis - I am used to p values and Confidence intervals - are fMRI results read in a similar way?
2. Importantly- I have a series of subjects and we are interested to look at effect of [a manipulation] on their response to [cat images] over one year, we have four time points one before the operation and three after. These time points are roughly 4 months apart.
Our Idea was to see how the response to [cat images] changes over time- with each subject serving as their own control- How do I analyse that? We have some missing time points as well- subjects did not come for all the time points!
Simon Legree
Hi Simon,
Congratulations on your foray into FMRI research; I wish you the best of luck, and I hope you find it enjoyable and rewarding!
In response to your questions:
1. FMRI results also use p-values and confidence intervals, but these are calculated at every single voxel in the brain. For example, if you are looking at the average BOLD response to [cat images] at each voxel, a parameter will be estimated at that voxel, along with a particular p-value and confidence interval. What you'll notice in the FSL GUI is a cluster thresholding which will only display a specified number of spatially contiguous voxels all passing the same p-threshold.
One crucial difference between first and higher-level analyses in FSL (and any FMRI analysis, really) is the degrees of freedom. At the first-level, the degrees of freedom is specified as the number of time points minus the number of regressors; at the second-level (or higher level) the degrees of freedom is specified as the number of time points that went into that higher-level analysis - which is usually the number of subjects included in the analysis. Unless you are doing a case study, you usually will not be dealing with the degrees of freedom at the individual level. (However, see documentation on mixed-effect analyses like AFNI's 3dMEMA, which will take individual variance and degrees of freedom into account.)
2. For an analysis with each patient serving as their own control, you would probably want to do a paired t-test or repeated-measures ANOVA for each subject. For the paired t-test, you would need to weight each cluster of regressors so that they sum to +1 and -1, respectively; in your case, +1*Before, -0.33*After1, -0.33*After2, -0.33*After3. However, if you hypothesize that there is a linear response over time, you might want to do an ANOVA and weight the timepoints linearly; e.g., for a decreasing response over time, +0.66*Before, +0.33*After1, -0.33*After2, -0.66*After3. There are a number of different ways you could do this. As for the subjects with missing time points, you would need to take that into account when weighting your regressors; I also recommend doing a sanity check by doing the analysis both with the timepoint-less subjects and with them. If there is a huge discrepancy between the two analyses, it might suggest that there is something else correlated with missing time points.

Hope this helps!