Efficient estimation via envelope chain in magnetic resonance imaging‐based studies

Magnetic resonance imaging (MRI) is a technique that scans the anatomical structure of the brain, whereas functional magnetic resonance imaging (fMRI) uses the same basic principles of atomic physics as MRI scans but image metabolic function. A major goal of MRI and fMRI study is to precisely delineate various types of tissues, anatomical structure, pathologies, and detect the brain regions that react to outer stimuli (e.g., viewing an image). As a key feature of these MRI‐based neuroimaging data, voxels (cubic pixels of the brain volume) are highly correlated. However, the associations between voxels are often overlooked in the statistical analysis. We adapt a recently proposed dimension reduction method called the envelope method to analyze neuoimaging data taking into account correlation among voxels. We refer to the modified procedure the envelope chain procedure. Because the envelope chain procedure has not been employed before, we demonstrate in simulations the empirical performance of estimator, and examine its sensitivity when our assumptions are violated. We use the estimator to analyze the MRI data from ADHD‐200 study. Data analyses demonstrate that leveraging the correlations among voxels can significantly increase the efficiency of the regression analysis, thus achieving higher detection power with small sample sizes.