Spatial smoothing is an essential step in the analysis of functional magnetic resonance imaging (fMRI) data. One standard smoothing method is to convolve the image data with a three-dimensional Gaussian kernel that applies a fixed amount of smoothing to the entire image. In pre-surgical brain image analysis where spatial accuracy is paramount, this method, however, is not reasonable as it can blur the boundaries between activated and deactivated regions of the brain. Moreover, while in a standard fMRI analysis strict false positive control is desired, for pre-surgical planning false negatives are of greater concern. To this end, we propose a novel spatially adaptive conditionally autoregressive model with variances in the full conditional of the means that are proportional to error variances, allowing the degree of smoothing to vary across the brain. Additionally, we present a new loss function that allows for the asymmetric treatment of false positives and false negatives. We compare our proposed model with two existing spatially adaptive conditionally autoregressive models. Simulation studies show that our model outperforms these other models; as a real model application, we apply the proposed model to the pre-surgical fMRI data of two patients to assess peri- and intra-tumoral brain activity.
Keywords: fMRI analysis; loss function; pre-surgical mapping; spatially adaptive CAR models.