Abstract

Multi-dimensional arrays are referred to as tensors. Tensor-valued predictors are commonly encountered in modern biomedical applications, such as electroencephalogram (EEG), magnetic resonance imaging (MRI), functional MRI (fMRI), diffusion-weighted MRI, and longitudinal health data. In survival analysis, it is both important and challenging to integrate clinically relevant information, such as gender, age, and disease state along with medical imaging tensor data or longitudinal health data to predict disease outcomes. Most existing higher-order sufficient dimension reduction regressions for matrix- or array-valued data focus solely on tensor data, often neglecting established clinical covariates that are readily available and known to have predictive value. Based on the idea of Folded-Minimum Average Variance Estimation (Folded-MAVE: Xue and Yin, 2014), the authors propose a new method, Partial Dimension Folded-MAVE (PF-MAVE), to address regression mean functions with tensor-valued covariates while simultaneously incorporating clinical covariates, which are typically categorical variables. Theorems and simulation studies demonstrate the importance of incorporating these categorical clinical predictors. A survival analysis of a longitudinal study of primary biliary cirrhosis (PBC) data is included for illustration of the proposed method.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Mean dimension folding subspace; minimum average variance estimation; sufficient dimension folding subspace; survival analysis; tensor data

International Standard Serial Number (ISSN)

1559-7067; 1009-6124

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Springer, All rights reserved.

Publication Date

01 Feb 2026

Download

Full Text Link

Share

 
COinS