Non-marginal Variable Screening For Additive Hazards Model With Ultrahigh-dimensional Covariates

As a rapid development in technology for data collection and storage,nowadays the ultrahigh-dimensional data are frequently encountered in many research areas,such as genetic microarray,biomedical imaging and economics.The ultrahigh di-mensionality also makes the traditional statistical methods suffer a great impact,and many traditional methods cannot be applied because they are not suitable for the new requirements.To overcome this issue,many researches have been conduct-ed on variable screening,which can effectively reduce the dimension.The existing variable screening procedures for ultrahigh dimensional data are based on complete data,which taking the censored data out of consideration,so they cannot be di-rectly applied to the survival model.Recently,researches concerning non-marginal variable screening method in ul-trahigh dimensional survival models are mainly conducted in the Cox model,on the contrary,the research concerning non-marginal variable screening method in ultrahigh dimensional additive hazards model is still insufficient.In this article,we keep the research concerning variable screening in the additive hazards model with ultrahigh-dimensional covariates,and propose a non-marginal feature screening procedure.Compared with the existing methods,the method proposed in this arti-cle utilizes the joint effects between covariates,which can effectively identify active covariates that are jointly dependent but marginally independent of the response.Furthermore,We develop an iterative hard-thresholding(IHT)algorithm to effec-tively implement the proposed procedure.We rigorously investigate its convergence properties and further prove that the proposed procedure possesses the sure screen-ing property.We conduct Monte Carlo simulation to evaluate the finite sample performance of the proposed procedure,and demonstrate the proposed procedure through an empirical analysis of a real data example.