Sure Joint Screening for High Dimensional Cox's Proportional Hazards Model Under the Case-Cohort Design

This study develops a sure joint feature screening method for the case-cohort design with ultrahigh-dimensional covariates. Our method is based on a sparsity-restricted Cox proportional hazards model. An iterative reweighted hard thresholding algorithm is proposed to approximate the sparsity-restricted, pseudo-partial likelihood estimator for joint screening. We rigorously show that our method possesses the sure screening property, with the probability of retaining all relevant covariates tending to 1 as the sample size goes to infinity. Our simulation results demonstrate that the proposed procedure has substantially improved screening performance over some existing feature screening methods for the case-cohort design, especially when some covariates are jointly correlated, but marginally uncorrelated, with the event time outcome. A real data illustration is provided using breast cancer data with high-dimensional genomic covariates. We have implemented the proposed method using MATLAB and made it available to readers through GitHub.