Study On The Adjustment Method Of Disturbed Covariate Under Case-cohort Sampeling In The Cox Model

Epidemiological research is a hot topic in the medical field today and has attracted much attention from scholars.When studying these epidemics,it is particularly important for scholars to use sampling methods that reduce costs and improve efficiency.However,when collecting large-scale epidemiological data,data of censoring and truncation may result.In addition,due to the influence of uncertain factors such as the sampling environment or sampling technique,the data will be contaminated,which will bring certain influence to the research.This article will use survival analysis and other related theories to study the method of adjusting the disturbed covariates under Case-cohort sampling in the Cox model.The first chapter mainly introduces the research background and significance,domestic and foreign research reviews,and also gives the main research content of this article.Chapter 2 introduces biased sampling,related theories of Cox models,basic theories of kernel functions,Newton-Raphson iterative algorithms and MM algorithms.Chapter 3 first gives the data structure of the undisturbed covariates and the disturbed covariates in the Cox model under the Case-cohort sampling method,then use the kernel function smoothing method to adjust the disturbed covariates,then use the Newton-Raphson iterative algorithm to perform numerical simulations and find that when the sample size is small,the use of the Newton-Raphson iterative algorithm may appear to be irreversible.In order to avoid this situation,a new MM algorithm is used to construct a substitution function to estimate the parameter estimates of the disturbed covariates in the Cox model.Numerical simulation results show that:the parameter estimates of the undisturbed covariate and the adjusted covariate are unbiased;the result of the NewtonRaphson iterative algorithm is very close to the simulation result of the MM algorithm;as the sample size increases,the interference with covariates becomes more and more obvious.Chapter 4 proves that the disturbed-adjusted covariates in the Cox model are consistent,and the parameter estimates after the interference-adjusted covariates have consistency and asymptotic normality,and give the proof process;at the same time,through empirical analysis,it is shown that the use of higher-order kernel function smoothing method to adjust the disturbed covariate is also effective for actual data,indicating that the covariate adjustment method used in this article is feasible.