Broken Adaptive Ridge Regression for Right-Censored Survival Data

TL;DR

This paper introduces a censored Broken Adaptive Ridge (CBAR) method for variable selection in right-censored survival data within the AFT model, demonstrating consistency, oracle properties, and grouping effects.

Contribution

The paper extends BAR to the AFT model for survival data, providing a scalable, consistent, and oracle-efficient variable selection method with grouping for correlated covariates.

Findings

CBAR is consistent for variable selection.

CBAR has oracle properties for parameter estimation.

CBAR effectively handles high-dimensional data.

Abstract

Broken adaptive ridge (BAR) is a computationally scalable surrogate to $L_0$-penalized regression, which involves iteratively performing reweighted $L_2$ penalized regressions and enjoys some appealing properties of both $L_0$ and $L_2$ penalized regressions while avoiding some of their limitations. In this paper, we extend the BAR method to the semi-parametric accelerated failure time (AFT) model for right-censored survival data. Specifically, we propose a censored BAR (CBAR) estimator by applying the BAR algorithm to the Leurgan's synthetic data and show that the resulting CBAR estimator is consistent for variable selection, possesses an oracle property for parameter estimation {and enjoys a grouping property for highly correlation covariates}. Both low and high dimensional covariates are considered. The effectiveness of our method is demonstrated and compared with some popular penalization methods using simulations. Real data illustrations are provided on a diffuse large-B-cell lymphoma data and a glioblastoma multiforme data.