A group analysis using the Multiregression Dynamic Models for fMRI networked time series

Connectivity studies of the brain are usually based on functional Magnetic Resonance Imaging (fMRI) experiments involving many subjects. These studies need to take into account not only the interaction between areas of a single brain but also the differences amongst those subjects. In this paper we develop a methodology called the group-structure (GS) approach that models possible heterogeneity between subjects and searches for distinct homogeneous sub-groups according to some measure that reflects the connectivity maps. We suggest a GS method that uses a novel distance based on a model selection measure, the Bayes factor. We then develop a new class of Multiregression Dynamic Models to estimate individual networks whilst acknowledging a GS type dependence structure across subjects. We compare the efficacy of this methodology to three other methods, virtual-typical-subject (VTS), individual-structure (IS) and common-structure (CS), used to infer a group network using both synthetic and real fMRI data. We find that the GS approach provides results that are both more consistent with the data and more flexible in their interpretative power than its competitors. In addition, we present two methods, the Individual Estimation of Multiple Networks (IEMN) and the Marginal Estimation of Multiple Networks (MEMN), generated from the GS approach and used to estimate all types of networks informed by an experiment -individual, homogeneous subgroups and group networks. These methods are then compared both from a theoretical perspective and in practice using real fMRI data.