Feature screening for case-cohort studies with failure time outcome

Case-cohort design has been demonstrated to be an economical and efficient approach in large cohort studies when the measurement of some covariates on all individuals is expensive. Various methods have been proposed for case-cohort data when the dimension of covariates is smaller than sample size. However, limited work has been done for high-dimensional case-cohort data which are frequently collected in large epidemiological studies. In this paper, we propose a variable screening method for ultrahigh-dimensional case-cohort data under the framework of proportional model, which allows the covariate dimension increases with sample size at exponential rate. Our procedure enjoys the sure screening property and the ranking consistency under some mild regularity conditions. We further extend this method to an iterative version to handle the scenarios where some covariates are jointly important but are marginally unrelated or weakly correlated to the response. The finite sample performance of the proposed procedure is evaluated via both simulation studies and an application to a real data from the breast cancer study.