Tensor response quantile regression with neuroimaging data

Collecting neuroimaging data in the form of tensors (i.e. multidimensional arrays) has become more common in mental health studies, driven by an increasing interest in studying the associations between neuroimaging phenotypes and clinical disease manifestation. Motivated by a neuroimaging study of post‐traumatic stress disorder (PTSD) from the Grady Trauma Project, we study a tensor response quantile regression framework, which enables novel analyses that confer a detailed view of the potentially heterogeneous association between a neuroimaging phenotype and relevant clinical predictors. We adopt a sensible low‐rank structure to represent the association of interest, and propose a simple two‐step estimation procedure which is easy to implement with existing software. We provide rigorous theoretical justifications for the intuitive two‐step procedure. Simulation studies demonstrate good performance of the proposed method with realistic sample sizes in neuroimaging studies. We conduct the proposed tensor response quantile regression analysis of the motivating PTSD study to investigate the association between fMRI resting‐state functional connectivity and PTSD symptom severity. Our results uncover non‐homogeneous effects of PTSD symptoms on brain functional connectivity, which cannot be captured by existing tensor response methods.