Research On Variable Selection Of Partially Linear Additive Cox Model

Cox proportional risk model plays an important role in survival analysis.It can use risk functions to study the relationship between variables and survival functions,and initially process survival data with censoring.However,data in real life often do not meet the Cox proportional risk assumption.For this type of data,a partially linear additive Cox model is introduced to achieve variable selection research for time-dependent covariates.The main research content of this article is divided into the following three parts:(1)By fitting the nonparametric part of a partially linear additive Cox model with a B-spline curve,the problem of selecting unknown component functions in the model is transformed into the problem of dealing with the selection of system arrays in linear combinations,and spline fitting of partially linear additive Cox models is realized.(2)Bi-level variable selection method is introduced for censored survival data in partially linear additive Cox models,where covariates are naturally grouped.Compared with group variable selection,group selection and individual variable selection can be performed simultaneously within the selected group,improving model estimation accuracy.(3)By comparing the performance of the group variable selection method and the two-level variable selection method under five indicators through simulation analysis,the effectiveness of the two-level variable selection method in a partially linear additive Cox model was verified.Two different types of cancer data sets were introduced,and the results showed that the variables screened by the two-level variable selection method had the highest correlation with survival time,which was of practical significance in tackling cancer diseases.Study has shown that the prediction error of the two-level variable selection method in the partially additive Cox model is better than that of the group variable selection method.The two data sets introduced reflect the effectiveness of the two-level variable selection method.