Statistical Inference For The Proportional Hazards Model With Covariate-Adjusted

In reliability analysis and life testing,they are often accompanied by censored data.In recent years,the research on censored data has become a hot spot in statistical research.In this thesis,we have studied the statistical inference method of covariate adjustment in the proportional hazards model,the specific research content is divided into the following four parts.The first part introduces the research background and significance of survival analysis,gives the current status of domestic and foreign research on the main method of parameter estimation and the adjustment method of covariate disturbance,and finally summarizes the arrangement of the main research content of this article.The second part mainly introduces the basic concepts of survival function,survival data,survival model,kernel function,and the use of cross-validation method to select the optimal bandwidth,etc.Secondly,the general expression of the proportional hazards model is introduced,and at the same time,the estimated and asymptotic properties of the parameters are given for the covariates without interference.In the third part,the method of covariate adjustment is introduced,the research data is survival data with right censoring.And a non-parametric method for adjusting the disturbed covariate by using a kernel function to construct a smooth function is proposed,which proves that the parameter estimator has excellent properties such as consistency and asymptotic normality.In addition,a practical Minimax(MM)algorithm is used to avoid the problem of irreversible Hessian matrix in the parameter estimation process,the results of simulation experiments show that this method can achieve the adjustment of covariates.In the fourth part,we discussed the parameter adjustment method in the proportional hazards model under biased sampling design.For data with a high censorship rate or a large sample size,if the sample data is processed directly,the budget and cost will be expensive and time-consuming.We will study the estimation of parameters in the proportional hazards model based on the censored data of the biased sampling design.In this paper,we adopt three biased sampling schemes,which are case-cohort design,generalized case-cohort design and outcome-dependent sampling design.Finally,the parameter adjustment method and asymptotic properties are given.