Bayesian Scalar-on-Tensor Quantile Regression for Longitudinal Data on Alzheimer's Disease

TL;DR

This paper introduces a Bayesian tensor quantile regression model tailored for high-dimensional longitudinal imaging data, effectively capturing complex brain-behavior relationships in Alzheimer's disease with improved estimation and feature selection.

Contribution

It presents a novel Bayesian approach that models visit-invariant and visit-specific effects in longitudinal tensor data, utilizing low-rank decomposition and efficient MCMC inference.

Findings

Enhanced parameter estimation and feature selection in simulations

Improved prediction performance over existing methods

Provided new insights into brain-cognition relationships in Alzheimer's data

Abstract

As a general and robust alternative to traditional mean regression models, quantile regression avoids the assumption of normally distributed errors, making it a versatile choice when modeling outcomes such as cognitive scores that typically have skewed distributions. Motivated by an application to Alzheimer's disease data where the aim is to explore how brain-behavior associations change over time, we propose a novel Bayesian tensor quantile regression for high-dimensional longitudinal imaging data. The proposed approach distinguishes between effects that are consistent across visits and patterns unique to each visit, contributing to the overall longitudinal trajectory. A low-rank decomposition is employed on the tensor coefficients which reduces dimensionality and preserves spatial configurations of the imaging voxels. We incorporate multiway shrinkage priors to model the visit-invariant tensor coefficients and variable selection priors on the tensor margins of the visit-specific effects. For posterior inference, we develop a computationally efficient Markov chain Monte Carlo sampling algorithm. Simulation studies reveal significant improvements in parameter estimation, feature selection, and prediction performance when compared with existing approaches. In the analysis of the Alzheimer's disease data, the flexibility of our modeling approach brings new insights as it provides a fuller picture of the relationship between the imaging voxels and the quantile distributions of the cognitive scores.