Sparse Regularization for Tensor Covariates in the Cox Regression Model

Music City Center 

This study investigates disease survival through medical imaging by directly incorporating the imaging data as tensor-structured covariates within the Cox regression model for right-censored survival outcomes. The objective is to estimate the coefficients of these tensor covariates to identify imaging subregions significantly associated with survival time. However, a challenge arises due to the limited sample size relative to the ultrahigh dimensionality of the imaging data. To address this, an algorithm is proposed that integrates sparse regularization into tensor decomposition, shrinking the coefficients of subregions irrelevant to survival time to zero. A comprehensive simulation study is conducted to evaluate the performance of the proposed algorithms in estimating tensor parameters.

Cox regression

Tensor-structured covariates

Sparse regularization

Right censoring

Piecewise smoothness 

Lifetime Data Science Section