  With the rapid growth of modern technology, many large-scale biomedical
studies have been/are being/will be conducted to collect massive datasets with
large volumes of multi-modality imaging, genetic, neurocognitive, and clinical
information from increasingly large cohorts. Simultaneously extracting and
integrating rich and diverse heterogeneous information in neuroimaging and/or
genomics from these big datasets could transform our understanding of how
genetic variants impact brain structure and function, cognitive function, and
brain-related disease risk across the lifespan. Such understanding is critical
for diagnosis, prevention, and treatment of numerous complex brain-related
disorders (e.g., schizophrenia and Alzheimer). However, the development of
analytical methods for the joint analysis of both high-dimensional imaging
phenotypes and high-dimensional genetic data, called big data squared (BD$^2$),
presents major computational and theoretical challenges for existing analytical
methods. Besides the high-dimensional nature of BD$^2$, various neuroimaging
measures often exhibit strong spatial smoothness and dependence and genetic
markers may have a natural dependence structure arising from linkage
disequilibrium. We review some recent developments of various statistical
techniques for the joint analysis of BD$^2$, including massive univariate and
voxel-wise approaches, reduced rank regression, mixture models, and group
sparse multi-task regression. By doing so, we hope that this review may
encourage others in the statistical community to enter into this new and
exciting field of research.
