Non‐Elliptical Dimension Reduction in Survival Regression

ABSTRACT

Sufficient dimension reduction (SDR) in survival regression aims to identify low‐dimensional structures that preserve the relationship between survival time and predictors. Classical SDR methods, such as sliced inverse regression (SIR), rely on strong assumptions such as linearity, constant variance and coverage conditions, which are often violated in practical data. To address this issue, we propose an SDR framework for survival regression under non‐elliptical predictor distributions. The proposed fused Cox proportional hazards with transformation‐mean methods estimate the survival informative predictor subspace by integrating three components: the Cox proportional hazards direction, single response transformations and kernel fusion over multiple slicing schemes. Numerical studies and real data analysis show that our proposed methods outperform existing SIR‐based approaches, particularly when the linearity condition fails. They also remain robust across various sample sizes, predictor dimensions and censoring levels. Overall, the proposed fused methods offer a reliable tool for dimension reduction in survival regression.