  In task fMRI analysis, OLS is typically used to estimate task-induced
activation in the brain. Since task fMRI residuals often exhibit temporal
autocorrelation, it is common practice to perform prewhitening prior to OLS to
satisfy the assumption of residual independence, equivalent to GLS. While
theoretically straightforward, a major challenge in prewhitening in fMRI is
accurately estimating the residual autocorrelation at each location of the
brain. Assuming a global autocorrelation model, as in several fMRI software
programs, may under- or over-whiten particular regions and fail to achieve
nominal false positive control across the brain. Faster multiband acquisitions
require more sophisticated models to capture autocorrelation, making
prewhitening more difficult. These issues are becoming more critical now
because of a trend towards subject-level analysis, where prewhitening has a
greater impact than in group-average analyses. In this article, we first
thoroughly examine the sources of residual autocorrelation in multiband task
fMRI. We find that residual autocorrelation varies spatially throughout the
cortex and is affected by the task, the acquisition method, modeling choices,
and individual differences. Second, we evaluate the ability of different
AR-based prewhitening strategies to effectively mitigate autocorrelation and
control false positives. We find that allowing the prewhitening filter to vary
spatially is the most important factor for successful prewhitening, even more
so than increasing AR model order. To overcome the computational challenge
associated with spatially variable prewhitening, we developed a computationally
efficient R implementation based on parallelization and fast C++ backend code.
This implementation is included in the open source R package BayesfMRI.
