Variable Selection in Ultra-high Dimensional Feature Space for the Cox Model with Interval-Censored Data

TL;DR

This paper introduces new variable selection methods for the Cox model with interval-censored data in ultra-high dimensional settings, using penalized likelihood approaches that achieve oracle properties and perform well in practice.

Contribution

It develops and proves the effectiveness of penalized variable selection methods with folded concave and adaptive lasso penalties for the Cox model under interval censoring in ultra-high dimensions.

Findings

Methods achieve oracle property under certain penalties.

Numerical experiments demonstrate satisfactory empirical performance.

Application to genome-wide association study illustrates practical utility.

Abstract

We develop a set of variable selection methods for the Cox model under interval censoring, in the ultra-high dimensional setting where the dimensionality can grow exponentially with the sample size. The methods select covariates via a penalized nonparametric maximum likelihood estimation with some popular penalty functions, including lasso, adaptive lasso, SCAD, and MCP. We prove that our penalized variable selection methods with folded concave penalties or adaptive lasso penalty enjoy the oracle property. Extensive numerical experiments show that the proposed methods have satisfactory empirical performance under various scenarios. The utility of the methods is illustrated through an application to a genome-wide association study of age to early childhood caries.