Variable Screening Study Of Case-Ⅰ Interval-censored Data With Nonignorable Missing Covariates

With the advancement of science and technology,people’s ability to collect and store data has been greatly improved,and the scale and complexity of data have grown explosively.Ultrahigh-dimensional data frequently appear in various industries and scientific research fields.At this time,statisticians often encounter three challenges:computational complexity,statistical accuracy,and algorithm stability.Since the Sure Independence Screening(SIS)method was proposed,the variable screening problem of ultrahigh-dimensional data has been widely concerned by scholars at home and abroad.For variable screening research under ultrahigh-dimensional survival data,many scholars have considered the screening of right-censored data,but few people have discussed the screening of case-Ⅰ interval-censored data.However,covariates in instance data often contain missing,this thesis mainly studies the following two problems:(1)Variable screening research of case-Ⅰ interval-censored data with random missing covariates;For this problem,based on the Cox proportional hazards model,this thesis employs the inverse probability weighting method to construct a weighted likelihood function under incomplete covariates,and extends the three screening methods applicable to right-censored data to case-Ⅰ interval-censored data.The three methods are :Iterative Sure Independence Screening(ISIS),Principled Sure Independence Screening(PSIS)and Sure joint feature screening(SJS).In the simulation study,the data processed by K Nearest Neighbors(KNN)imputation and the data processed by inverse probability weighting are compared under three screening methods;(2)Variable screening research of case-Ⅰ interval-censored data with nonignorable missing covariates;for this problem,under the nonignorable missing mechanism,a weighted rank objective function is proposed for the case-Ⅰ interval censored data based on the Cox model,and according to the proposed weighted rank objective function,the SJS method based on Lasso initial value is used.In addition to the two questions raised on the Monte Carlo simulation,this thesis also applies the proposed screening method to the instance data of Alzheimer’s disease,to explore important variables that have a significant impact on the transformation of Alzheimer’s disease.The explanatory variables used included not only clinical observations from the Alzheimer’s Disease Neuroimaging Initiative(ADNI),but also a large number of single nucleotide polymorphisms(SNPs)from the subjects.The obtained numerical simulation and case study results fully verify the feasibility and effectiveness of the proposed method.