Empirical Likelihood Inference For Accelerated Failure Time Model Under Right Censored Data

The accelerated failure time model has obvious advantages over the proportional hazard model in the model form and the explanation of the regression coefficient,so it is getting more and more attention in the fields of medicine,biology,statistics,economics and so on.In recent years,the research on the applicable conditions of the accelerated failure time model,the estimation of unknown parameters,and the prediction and fitting of the model have become the focus of attention of scholars at home and abroad.In fact,how to estimate and infer the unknown parameters in the model is the most important problem.However,in practical applications,some unobservable factors are usually presented.At this time,considered to construct partial accelerated failure time model.Empirical likelihood is a nonparametric method.It does not do any parameter assumption on the distribution function of the data,uses data to determine the shape of the confidence region,and does not involve any variance estimation.Since it was proposed in Owen(1988),it has been widely used in statistics.However,in the survival analysis,due to the limitation of the observation time,and the differences of the observed individuals at the beginning or end of the experiment,there is often occur right censored data.If use right censored data to estimate the parameters directly,the cost of calculation will be too high and the prediction effect is poor.The most commonly used method is empirical likelihood estimation based on rank estimation.But the algorithm of this method is more tedious,and the nonmonotonicity of the linear rank(especially logarithmic rank)estimation function will limit the application of the estimation equation in practice.Therefore,the processing of the right censored data is an important part in the study of the accelerated failure time model.A robust model with simple structure,clear meaning and accurate prediction can be established by adopting appropriate data complement methods.In this paper,the data transformation method is applied to the accelerated failure time model with right censored data.Empirical likelihood method is used to improve the efficiency of parameter estimation,and the method of constructing adjustment factors is used to solve the problem that confidence interval is difficult to calculate,and the asymptotic distribution of parameters is obtained.Finally,a simulation is carried out to verify the correctness and effectiveness of the theoretical results.Meanwhile,the theoretical method is applied to the case analysis.The main structure of the paper is as follows:In chapter 1,we first give a brief overview of the research background and significance.Secondly,according to the existing domestic and foreign relevant literature,we systematically introduced the accelerated failure time model,the empirical likelihood inference method and the synthetic data.Finally,we describe the main contents,difficulties and new points of the paper.In chapter 2,we study the parameter estimation and inference problem of accelerated failure time model based on right censored data.Firstly,we briefly introduce the accelerated failure time model.Secondly,based on the data conversion method,apply the empirical likelihood inference to the accelerated failure time model.Then construct adjustment factors and use adjustment empirical likelihood inference to the model.Finally,through numerical simulation and example analysis to prove that use the data conversion method to accelerated failure time model is feasible,and it is reasonable to make statistical inference for unknown parameters by empirical likelihood inference.In chapter 3,we study the parameter estimation and inference problem of partial accelerated failure time model based on right censored data.Firstly,add some items to establish partial accelerated failure time model.Next,constructing empirical likelihood ratio statistics and adjusting factors,the empirical likelihood method is used to estimate the unknown parameters of the model and calculate its confidence interval.Then we prove the asymptotic distribution of the empirical likelihood ratio statistic and its related theorems.Finally,through numerical simulation,it is proved that the empirical likelihood method is also applicable to the statistical inference of partial accelerated failure time model,and compares the estimation effect of empirical likelihood inference under different data conversion methods.In chapter 4,we give a summary of the whole paper,and outline a future research plan.