Variable Selection and Inference for Ultra-High-Dimensional Survival Data with Missing Covariates Under Proportional Hazards Models

• Activity Number: 455
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Yang Ning*+ and Grace Yi and Baojiang Chen and Nancy Reid
• Companies: University of Waterloo and University of Waterloo and University of Nebraska Medical Center and University of Toronto
• Keywords: Folded concave penalty ; Missing at random ; Proportional hazards model ; Strong oracle property ; Survival data ; Ultra-high dimensional data

Abstract

Proportional hazards models have been perhaps the most popular models used for survival data analysis. Such models, however, break down for settings with high dimensional covariates, which are subject to missingness. In this paper, we address this important problem and develop simultaneous inferential procedures that handle both model selection and parameter estimation for ultra-high dimensional survival data with missing covariates. Our methods are developed for a broad class of folded concave penalties, including the LASSO and SCAD penalties to conduct variable selection. Missing data processes are featured by regression models where selection of important covariates is a serious concern. To improve efficiency, augmented model selection and parameter estimation algorithms are exploited. The strong oracle property and the asymptotic distributions of our proposed estimators are rigorously established. The performance of the proposed methods is numerically assessed through simulation studies, and the usage of our methods is illustrated by a genetic data set.