Gradient-induced variable selection in reproducing kernel Hilbert space for survival analysis

• Published in: Journal of statistical computation and simulation Vol. 95; no. 3; pp. 554 - 579
• Main Authors: Tan, Xin, Yan, Mei, Kong, Efang
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 11.02.2025; Taylor & Francis Ltd
• Subjects: Asymptotic methods; Data analysis; Hilbert space; quantile regression; random censoring; Regression models; reproducing kernel Hilbert space (RKHS); Survival; Variable selection
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2024.2433182

The analysis of survival data is often hampered by a potentially very large number of covariates compounded with incomplete data. This paper considers the problem of variable selection where the response is subject to random (right) censoring. We introduce a model-free variable selection procedure via learning the gradients of quantile regression functions with two popular censoring weighting schemes. The key advantage of the proposed approach is that it does not require explicit model assumptions and is computationally efficient. Besides, we also prove its asymptotic consistency and examine its finite sample performance via numerical studies. As an empirical example, the proposed procedure is applied for the analysis of a breast cancer data set.