TPRM: Tensor partition regression models with applications in imaging biomarker detection

TL;DR

This paper introduces TPRM, a hierarchical tensor partition regression framework that effectively links high-dimensional imaging data with clinical outcomes, improving biomarker detection and disease prediction accuracy.

Contribution

The paper develops a novel hierarchical tensor partition regression model that integrates multiple components for efficient high-dimensional data analysis in medical imaging.

Findings

TPRM outperforms competing methods in simulations.

TPRM accurately predicts Alzheimer's disease status from MRI data.

Efficient MCMC algorithm enables practical application.

Abstract

Medical imaging studies have collected high dimensional imaging data to identify imaging biomarkers for diagnosis, screening, and prognosis, among many others. These imaging data are often represented in the form of a multi-dimensional array, called a tensor. The aim of this paper is to develop a tensor partition regression modeling (TPRM) framework to establish a relationship between low-dimensional clinical outcomes (e.g., diagnosis) and high dimensional tensor covariates. Our TPRM is a hierarchical model and efficiently integrates four components: (i) a partition model, (ii) a canonical polyadic decomposition model, (iii) a principal components model, and (iv) a generalized linear model with a sparse inducing normal mixture prior. This framework not only reduces ultra-high dimensionality to a manageable level, resulting in efficient estimation, but also optimizes prediction accuracy in the search for informative sub-tensors. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulation shows that TPRM outperforms several other competing methods. We apply TPRM to predict disease status (Alzheimer versus control) by using structural magnetic resonance imaging data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.