Modeling state-related fMRI activity using change-point theory.

The general linear model (GLM) approach has arguably become the dominant way to analyze functional magnetic resonance imaging (fMRI) data. It tests whether activity in a brain region is systematically related to some known input function. However, the GLM becomes impractical when the precise timing and duration of psychological events cannot be specified a priori. In this work, we introduce a new analysis approach that allows the predicted signal to depend non-linearly on the input. The approach uses ideas from statistical control theory and change-point theory to model slowly varying processes for which the onset times and durations of underlying psychological activity are uncertain. Our approach is exploratory in nature, while retaining the inferential capabilities of the more rigid modeling approach. It is a multi-subject extension of the exponentially weighted moving average (EWMA) method used in change-point analysis. We extend existing EWMA models for individual subjects (a single time series) so that they are applicable to fMRI data, and develop a group analysis using a hierarchical model, which we term HEWMA (Hierarchical EWMA). The HEWMA method can be used to analyze fMRI data voxel-wise throughout the brain, data from regions of interest, or temporal components extracted using ICA or similar methods. We validate the false-positive rate control of the method and provide power estimates using simulations based on real fMRI data. We further apply this method to an fMRI study (n=24) of state anxiety. A toolbox implementing all functions in Matlab is freely available from the authors.