Between-subject fMRI classification: subjects with different number of runs The main purpose of my work is to discriminate patients vs healthy controls using fMRI and multivariate pattern analysis (MVPA). Since I want to classify at the subject level I performed a separate subject GLM in order to get the parameter estimates for each task condition. Then I transformed beta estimates into t values in order to improve signal to noise ratio. I have 31 controls and 32 patients. All of them completed 3 runs except for 4 patients that only completed 2 runs due to fatigue. 
My question is: since MVPA is very sensitive to uneven classes should I exclude the 4 patients that only completed 2 runs and then balance classes by doing some kind of undersampling of the controls class for instance? My main concern is that those 4 patients have lower signal to noise ratio when compared to the others that completed 3 runs which could undermine classification accuracy.
I searched through several papers and some textbooks but I cant find anything on uneven runs in between-subject classification analysis. I would appreciate it if someone shared some references about this topic.
 A: You really don't have a imbalance problem per se, with 31 controls and 32 patients. What you have is different precision of the within-subject errors, as 4 patients only completed 2 out of 3 runs (presumably for reasons not related to the imaging results per se). The simplest solution would be to down-weight the cases having only 2 instead of 3 runs, corresponding to the lower precision of the per-voxel estimates in those cases. This would presumably be something on the order of $\sqrt{2/3}$ relative to the other cases. 
This is relatively straightforward to handle with penalized logistic regression (ridge or LASSO), which has a very close connection to SVM as explained in Section 9.5 of ISLR. Standard statistical software for logistic regression allows for such case weighting. I do not have experience with libsvm, but if that also allows for case-specific weights then that would provide an answer.
Also, consider what the authors of ISLR have to say about the relative performance of logistic regression and SVM (page 357):

When the classes are well separated, SVMs tend to behave better than logistic regression; in more overlapping regimes, logistic regression is often preferred.

So logistic regression might be preferred unless there are very clear imaging distinctions between your control and patient classes.
You have a fairly difficult problem here, with only 31 cases in the smaller group and a desire to use multiple voxels as features for classification. To avoid overfitting you are limited to about 2 or 3 unpenalized features, or a larger number of penalized features, with that sample size. (The rule of thumb is 10-20 cases in the smaller group per unpenalized feature.) Tuning parameters help prevent overfitting in SVM, similarly to the way that penalized logistic regression works; Chapter 9 of ISLR explains this issue in more detail. My sense is that proper handling of penalization to avoid overfitting will be a more pressing problem here than the relatively small difference in precision due to having only 2 instead of 3 observations for some subjects.
