Best subset selection with shrinkage: sparse additive hazards regression with the grouping effect

Abstract

Sparse modeling plays a ubiquitous role in modern statistical regression. In particular, high-dimensional survival analysis has drawn a lot of attention as a result of the popularity of microarray studies involving survival data. In this paper, we focus on a scenario where predictors are strongly correlated, also known as grouping effect, which is highly desirable when analysing high-dimensional microarray data. To perform simultaneous variable selection and estimation under this circumstance, we propose the $l_2$-regularized best-subsets estimator under the framework of additive hazards models based on a polynomial algorithm for the best subset selection. Moreover, we establish comprehensive statistical properties, including oracle inequalities under estimation loss for the proposed estimator. The proposed method is demonstrated by simulation studies and illustrated by a real data example.

Keywords:

• Survival data analysis
• high-dimensional features
• best subset selection
• grouping effects

Mathematics Subject Classifications:

• 62N02
• 62J07

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Key R&D Program of China [grant number 2022YFA1008000], National Natural Science Foundation of China [grant number 12101584], China Postdoctoral Science Foundation [grant numbers 2021TQ0326 and 2021M703100], Fundamental Research Funds for the Central Universities [grant number WK2040000047], Hefei Postdoctoral Research Project Funds in 2021, and Anhui Postdoctoral Research Project Funds in 2021.