Empirical Likelihood Inference For Right Censored Data And Recurrent Event Data

In the fields of medicine,biology,public health,etc.,there is a problem of estimating and predicting the occurring time of a given event.That problem is usually solved by statistical theories and methods.The process of parameter estimation based on the normal approximation method often encounters the problem that the asymptotic variance is difficult or impossible to estimate.However,the empirical likelihood method has obvious advantages.It does not need to estimate the variance of unknown parameters.In addition,it also doesn't need to specify the distribution family of the data,and it use the data to determine the shape of the confidence interval.The empirical likelihood method is a non-parametric method,which mainly constructs a general likelihood ratio test statistic for the interested parameters.And it has very favorable asymptotic power properties.In this article,the data structure of the right-censored data and recurrent event data is fully considered,and the empirical likelihood method is applied to right-censored data and recurring event data.The main research contents of this article are:The first research content is the empirical likelihood statistical inference for the right-censored data based on the linear transformation model.Due to the existence of right censored data,Buckley-James estimation equation is adopted.And the expression of response variables was redefined and adjusted empirical likelihood ratio statistics was proposed by constructing adjustment factors.The asymptotic distribution of the adjusted empirical likelihood ratio statistics is obtained through reasoning and demonstration.Then,a large number of numerical simulation results verify the effectiveness and rationality of the proposed method.Under weaker assumptions than the KSV method,the obtained numerical simulation results show that the proposed method is better than the KSV method.Finally,the proposed method is applied to a heart transplant dataset.Here is the second research content.We used a semiparametric rate model with cure rate.The model takes into account the problem that the recurrence rate of the disease is affected by the fact that some patients do not relapse after being cured.The empirical likelihood ratio statistic is proposed based on the semiparametric rate model with cure rate and the empirical likelihood method.And confidence interval of the parameter is obtained.Then,it is verified by numerical simulation that when the sample size is small,the empirical likelihood method solves the insufficient coverage probability of the normal approximation method.Finally,the proposed method is applied to a bladder cancer dataset.