Variable selection in the joint frailty model of recurrent and terminal events using Broken Adaptive Ridge regression

TL;DR

This paper presents a new variable selection method for joint frailty models of recurrent and terminal events using Broken Adaptive Ridge regression, which is consistent and applicable with diverging covariates.

Contribution

Introduces a novel BAR penalty-based method for variable selection in joint frailty models, with proven asymptotic properties and practical application to ICU data.

Findings

BAR method outperforms MIC in simulations

Method identifies key risk factors in ICU data

Estimator is consistent and asymptotically normal

Abstract

We introduce a novel method to simultaneously perform variable selection and estimation in the joint frailty model of recurrent and terminal events using the Broken Adaptive Ridge Regression penalty. The BAR penalty can be summarized as an iteratively reweighted squared $L_2$-penalized regression, which approximates the $L_0$-regularization method. Our method allows for the number of covariates to diverge with the sample size. Under certain regularity conditions, we prove that the BAR estimator implemented under the model framework is consistent and asymptotically normally distributed, which are known as the oracle properties in the variable selection literature. In our simulation studies, we compare our proposed method to the Minimum Information Criterion (MIC) method. We apply our method on the Medical Information Mart for Intensive Care (MIMIC-III) database, with the aim of investigating which variables affect the risks of repeated ICU admissions and death during ICU stay.