The Canadian Journal of Statistics has published a special issue on Neuroimaging Data Analysis. A selection of the introduction from guest editors Farouk Nathoo, Linglong Kong, and Grace Y. Yi appears below:
This special issue of the Canadian Journal of Statistics is devoted to neuroimaging data analysis. This is a burgeoning field involving mathematical, statistical, and computational methods with an emphasis on neuroscience and the analysis of data arising from a wide array of neurochemical, structural, and functional imaging modalities. These include computed axial tomography, diffusion tensor imaging (DTI), magnetic resonance imaging (MRI), functional magnetic resonance imaging (fMRI), magnetic resonance spectroscopy, positron emission tomography (PET), single photon emission tomography, electroencephalography (EEG), and magnetoencephalography.
There is tremendous potential for the development of new methods for statistical inference in these settings. There is also a pressing need for efficient computational approaches and the development of machine learning techniques for the prediction of disease outcomes. The goal of this issue is to highlight cutting‐edge research in this area, with eight regular articles and one discussion article showcasing solutions to a broad range of statistical and machine learning problems involving neuroimaging data.
The issue begins with a discussion article by Liu and Zhu, who develop statistical neurological disease mapping for heterogeneous neuroimaging studies. A focus of this work is characterizing heterogeneity in hippocampal surface data derived from MRI at both the individual and group levels. Considered as functional responses, the authors employ an image‐on‐scalar multivariate varying coefficient model incorporating a hidden Markov random field to relate the imaging response to covariates and detect diseased regions at the subject level.
The second article focusses on survival analysis and neuroimaging data: Dai et al. consider the important problem of modelling the time to progression from mild cognitive impairment to Alzheimer’s disease. In this context, longitudinal structural MRI is used to obtain images of cortical thickness. These images are then used as space‐ and time‐varying covariates in a parametric survival model relating disease progression to cortical thickness, with spatial random effects included.
In the third article, Lan, Reich, and Bandyopadhyay consider the analysis of white matter fibre tracts obtained using DTI with an application that focuses on the corpus callosum, the information highway connecting the brain hemispheres. They examine the changes associated with cocaine use. DTI data arise as spatially varying 3 × 3 positive definite matrices representing the location‐specific diffusion of water molecules. Standard approaches reduce this matrix‐valued response to a simple scalar summary, thereby ignoring useful information.
In the fourth article, Wang et al. study the important issue of reproducibility in fMRI analysis and consider statistical tests for fingerprinting. The task is to identify a subject from repeated imaging via connectivity measures such as correlation matrices based on matching. The authors explore permutation testing in this context. They consider the corresponding hypotheses, sensitivity, and power and develop a Poisson approximation to the null distribution that facilitates faster computation.
In the fifth article, Hart, Malone, and Fiecas consider the non‐stationary modelling of EEG multivariate time series data arising from twin studies; the goal is to infer the heritability of EEG characteristics. The authors focus on so‐called EEG microstates, which are latent states of a relatively short duration where the recorded activity is stationary. The objective is to characterize the number of microstates, the dynamics within each microstate, and the heritability of microstates.
In the sixth article, Mohammed and Dey also consider the analysis of EEG data but with rather different objectives. They first consider source localization wherein the objective is to map the scalp‐level EEG multivariate time series back to a possible configuration of neural source activity within the brain. The estimated parameters representing the source activity are then used to predict a binary response through a probit model.
In the seventh article, Ding et al. consider regression analysis for functional responses derived from neuroimaging and with scalar‐valued covariates and time‐dependent coefficient functions. The coefficient functions are approximated by being projected onto a sieve basis, leading to a multivariate linear regression where the data dimensions diverge with the sample size.
In the eighth article, Li, Nan, and Zhu work with neuroimaging and genetic data and consider settings where the interest lies in relating neuroimaging data, specifically PET data that provide images of the brain glucose metabolism, to single‐nucleotide polymorphism (SNP) data. Typical approaches employ mass univariate testing where individual associations between voxels and SNPs are explored. The authors consider a stepwise approach where the first stage employs a multivariate group lasso to screen ROI–gene pairs, where the ROIs comprise groups of voxels and both the ROIs and genes are summarized using principal components. In the second stage, each selected ROI–gene pair is decomposed into its constituent voxels and SNPs, and another multivariate group lasso is solved to select voxel–SNP pairs.
In the final article, Harezlak et al. consider the important problem of statistical analysis of multimodal neuroimaging data. The application is an HIV study where the binary response indicates the presence or absence of HIV, and it is interesting to relate this response to cortical thickness structural imaging data obtained from MRI. In addition, the authors consider connectivity information associated with the regions of cortical thickness where the connectivity measures are themselves obtained from DTI.