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

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.