FMEM: Functional Mixed Effects Models for Longitudinal Functional Responses

Modeling multivariate age-related imaging variables with dependencies

Neuroimaging techniques have been increasingly used to understand the neural biology of aging brains. The neuroimaging variables from distinct brain locations and modalities can exhibit age-related patterns that reflect localized neural decline. However, it is a challenge to identify the impacts of risk factors (eg, mental disorders) on multivariate imaging variables while simultaneously accounting for the dependence structure and nonlinear age trajectories using existing tools. We propose a mixed-effects model to address this challenge by building random effects based on the latent brain aging status. We develop computationally efficient algorithms to estimate the parameters of new random effects. The simulations show that our approach provides accurate parameter estimates, improves the inference efficiency, and reduces the root mean square error compared to existing methods. We further apply this method to the UK Biobank data to investigate the effects of tobacco smoking on the white matter integrity of the entire brain during aging and identify the adverse effects on white matter integrity with multiple fiber tracts.

Fast Univariate Inference for Longitudinal Functional Models

We propose fast univariate inferential approaches for longitudinal Gaussian and non-Gaussian functional data. The approach consists of three steps: (1) fit massively univariate pointwise mixed effects models; (2) apply any smoother along the functional domain; and (3) obtain joint confidence bands using analytic approaches for Gaussian data or a bootstrap of study participants for non-Gaussian data. Methods are motivated by two applications: (1) Diffusion Tensor Imaging (DTI) measured at multiple visits along the corpus callosum of multiple sclerosis (MS) patients; and (2) physical activity data measured by body-worn accelerometers for multiple days. An extensive simulation study indicates that model fitting and inference are accurate and much faster than existing approaches. Moreover, the proposed approach was the only one that was computationally feasible for the physical activity data application. Methods are accompanied by R software, though the method is "read-and-use", as it can be implemented by any analyst who is familiar with mixed effects model software.