Functional magnetic resonance imaging (fMRI) data contain high levels of
noise and artifacts. To avoid contamination of downstream analyses, fMRI-based
studies must identify and remove these noise sources prior to statistical
analysis. One common approach is the "scrubbing" of fMRI volumes that are
thought to contain high levels of noise. However, existing scrubbing techniques
are based on ad hoc measures of signal change. We consider scrubbing via
outlier detection, where volumes containing artifacts are considered
multidimensional outliers. Robust multivariate outlier detection methods are
proposed using robust distances (RDs), which are related to the Mahalanobis
distance. These RDs have a known distribution when the data are i.i.d. normal,
and that distribution can be used to determine a threshold for outliers where
fMRI data violate these assumptions. Here, we develop a robust multivariate
outlier detection method that is applicable to non-normal data. The objective
is to obtain threshold values to flag outlying volumes based on their RDs. We
propose two threshold candidates that embark on the same two steps, but the
choice of which depends on a researcher's purpose. Our main steps are dimension
reduction and selection, robust univariate outlier imputation to get rid of the
effect of outliers on the distribution, and estimating an outlier threshold
based on the upper quantile of the RD distribution without outliers. The first
threshold candidate is an upper quantile of the empirical distribution of RDs
obtained from the imputed data. The second threshold candidate calculates the
upper quantile of the RD distribution that a nonparametric bootstrap uses to
account for uncertainty in the empirical quantile. We compare our proposed fMRI
scrubbing method to motion scrubbing, data-driven scrubbing, and restrictive
parametric multivariate outlier detection methods