Single-index models with functional connectivity network predictors.

Functional connectivity is defined as the undirected association between two or more functional magnetic resonance imaging (fMRI) time series. Increasingly, subject-level functional connectivity data have been used to predict and classify clinical outcomes and subject attributes. We propose a single-index model wherein response variables and sparse functional connectivity network valued predictors are linked by an unspecified smooth function in order to accommodate potentially nonlinear relationships. We exploit the network structure of functional connectivity by imposing meaningful sparsity constraints, which lead not only to the identification of association of interactions between regions with the response but also the assessment of whether or not the functional connectivity associated with a brain region is related to the response variable. We demonstrate the effectiveness of the proposed model in simulation studies and in an application to a resting-state fMRI data set from the Human Connectome Project to model fluid intelligence and sex and to identify predictive links between brain regions.

Functional data analysis for longitudinal data with informative observation times.

In functional data analysis for longitudinal data, the observation process is typically assumed to be noninformative, which is often violated in real applications. Thus, methods that fail to account for the dependence between observation times and longitudinal outcomes may result in biased estimation. For longitudinal data with informative observation times, we find that under a general class of shared random effect models, a commonly used functional data method may lead to inconsistent model estimation while another functional data method results in consistent and even rate-optimal estimation. Indeed, we show that the mean function can be estimated appropriately via penalized splines and that the covariance function can be estimated appropriately via penalized tensor-product splines, both with specific choices of parameters. For the proposed method, theoretical results are provided, and simulation studies and a real data analysis are conducted to demonstrate its performance.

Biclustering Multivariate Longitudinal Data with Application to Recovery Trajectories of White Matter After Sport-Related Concussion.

Biclustering is the task of simultaneously clustering the samples and features of a data set. In doing so, subsets of samples that exhibit similar behaviors across subsets of features can be identified. Motivated by a longitudinal diffusion tensor imaging study of sport-related concussion (SRC), we present the problem of biclustering multivariate longitudinal data in which subjects and features are grouped simultaneously based on longitudinal patterns rather than magnitude. We propose a penalized regression based method for solving this problem by exploiting the heterogeneity in the longitudinal patterns within subjects and features. We evaluate the performance of the proposed methods via a simulation study and apply them to the motivating dataset, revealing distinctive patterns of white-matter abnormalities within subgroups of SRC cases.