Study On AFT Model Of Covariates With Measurement Error Under Case-cohort Sampling

In the field of survival analysis,the accelerated failure time model(AFT model for short)as a semi-parametric model is loved by many scholars.For large sample problems,researchers always hope to use the least cost to get the most effective data,so as to get the results closest to all samples.Therefore,it is particularly important to find an appropriate sampling method to improve information utilization.In addition,in some practical applications,due to human or objective factors,the collected data often inevitably have measurement errors.When the measurement errors are relatively large,ignoring the errors will have a great impact on the analysis and inference of the model.Based on this,this paper mainly studies the parameter estimation of AFT model under case-cohort sampling and the parameter estimation of covariates affected by measurement errors in AFT model under case-cohort sampling.The first chapter mainly introduces the background and significance of the research,the research status at home and abroad and the main content of the research.The second chapter mainly introduces the semi-parametric model,survival data,measurement error model,biased sampling method and the detailed steps of Newton-Raphson iterative algorithm.The third chapter mainly studies the parameter estimation of AFT model under Case-cohort sampling.Firstly,the data structure of AFT model is given under Case-cohort sampling,and then the data obtained after Case-cohort sampling is applied to the smooth Gehan weighted estimation equation of AFT model to obtain the inverse probability weighted estimation (?)IPW of AFT model.Then,the asymptotic properties of (?)IPW and the corresponding proof process are given,Finally,numerical simulation and example analysis further verify that the inverse probability weighting estimation method is effective for correcting the bias caused by Case-cohort sampling.The results of numerical simulation and example analysis show that the parameter estimator(?)Naive without inverse probability weighting estimation method is biased after Case-cohort sampling,but the parameter estimator (?)IPW with inverse probability weighting estimation method is unbiased.The fourth chapter mainly studies the parameter estimation of covariates affected by measurement errors in AFT model under Case-cohort sampling.Firstly,the AFT model with measurement error in covariates under Case-cohort sampling and the data structure of the model are introduced.Then the measurement error in covariates of AFT model is corrected by analog extrapolation method,the parameter estimators (?)SIMEX of the model are obtained through simulation step,estimation step and extrapolation step.Then the asymptotic properties of parameter estimators (?)SIMEX and the corresponding proof process are given.Finally,through numerical simulation and example analysis,it is verified that it is feasible to correct the measurement error by using analog extrapolation method when the covariate of AFT model has measurement error.The numerical simulation results show that the parameter estimators(?)SIMEX are unbiased when the measurement errors obey different distributions and there are different levels of measurement errors.