Feature Screening In Ultrahigh-dimensional Additive Cox Model

The research methods of ultrahigh-dimensional variable selection and parameter estimation for the Cox model are considered in the existing literature,and it is known that the existing variable selection research methods cannot effectively identify some important activity predictors.Therefore,this paper proposes to use the additive Cox model for feature screening under ultrahigh-dimensional covariates.This is because that the additive Cox model has strong modeling ability and flexibility in survival analysis.At the same time,additive of the additive Cox can also solve the non-linear problems that the Cox model can not solve.The feature selection method of the additive Cox model with ultrahigh-dimensional covariates studied in this paper can be divided into the following two steps: In the first stage,based on the logarithmic partial likelihood and its first two derivatives in the additive Cox model,the partial logarithmic likelihood is expanded by Taylor expansion and its approximate value is obtained.At the same time,the solution of the maximum approximate logarithmic partial likelihood problem is obtained by the hard threshold rule,thus m variables roughly selected by the first stage joint feature screening method are obtained.In the second stage,we use B-spline to approximate logarithmic partial likelihood to obtain more refined variable selection.Through the above two-stage feature selection method,the whole variable selection and parameter estimation can be effectively completed.In addition,under some regular conditions,this paper also proves that the proposed feature selection method has definite filtering properties.That is to say,the selected set of variables asymptotically contains the actual activity prediction factor with probability tending to 1.Finally,the finite sample performance of the proposed method is illustrated by Monte Carlo simulation results,and the effectiveness of the proposed method is explained by the random simulation results of actual data examples.