Penalized Variable Selection with Broken Adaptive Ridge Regression for Semi-competing Risks Data

TL;DR

This paper introduces a novel penalized variable selection method called broken adaptive ridge (BAR) for semi-competing risks data, effectively identifying significant covariates in illness-death models with shared frailty, demonstrated through simulations and a colon cancer study.

Contribution

It proposes the BAR penalty for variable selection in semi-competing risks models, addressing correlation between events and enabling event-specific covariate effect estimation.

Findings

BAR outperforms existing methods in simulation studies

The method achieves the oracle property and grouping effect

Applied successfully to colon cancer data

Abstract

Semi-competing risks data arise when both non-terminal and terminal events are considered in a model. Such data with multiple events of interest are frequently encountered in medical research and clinical trials. In this framework, terminal event can censor the non-terminal event but not vice versa. It is known that variable selection is practical in identifying significant risk factors in high-dimensional data. While some recent works on penalized variable selection deal with these competing risks separately without incorporating possible correlation between them, we perform variable selection in an illness-death model using shared frailty where semiparametric hazard regression models are used to model the effect of covariates. We propose a broken adaptive ridge (BAR) penalty to encourage sparsity and conduct extensive simulation studies to compare its performance with other popular methods. We perform variable selection in an event specific manner so that the potential risk factors and covariates effects can be estimated and selected, simultaneously corresponding to each event in the study. The grouping effect, as well as the oracle property of the proposed BAR procedure are investigated using simulation studies. The proposed method is then applied to real-life data arising from a Colon Cancer study.