Two Estimation Problems For Interval-censored Data

In many practical problems, due to the constraints of a variety of subjective and objective conditions, we often can not obtain the exact failure time,but only know that the failure time of interest is greater than (less than) or equal to a number or lies within an interval.Such incomplete data is called censored data in the survival analy-sis.Censored data includes left-censored,right-censored,interval-censored data,and so on.In the actual statistical study,the data we observed is often the interval-censored data, and left or right-censored data can be seen as a special interval-censored da-ta.Therefore, the study of statistical inference based on the interval-censored data is more significant.This paper discusses two estimation issues based on interval-censored data.Firstly,the Cox proportional hazards model is most commonly used regression model in survival analysis.One main reason is there exists a simple and efficient in-ference procedure,the partial likelihood approach,which dose not have to deal with the baseline hazard function and solve the regression parameter’s estimation based on the right-censored data perfectly.But for the interval-censored data,we can’t use partial likelihood approach directly.The literature[13] proposed the mixed imputation approach,which changes interval-censored data to right-censored data and gives a algo-rithm to solve the Cox model’s parameter inference issues,but failed to provide precise evidence of asymptotic properties of estimators.In this thesis,we give a rigorous proof for the consistency and asymptotic normality of estimators resulting from the mixed imputation approach.Sccondly,stress-strength model is widely used in engineering reliability studies,which has adequate researches for accurate data.But there is still a lot of research space for stress-strength model under censored data,especially interval-censored data.Therefore,it is necessary to study the statistical inference of stress-strength model based on interval-censored data.This thesis adopts the self-consistency algorithm of Turnbull(1976) to resolve the inference problems of stress-strength model based on interval-censored data.The structure of this paper is as follows:Chapter1introduces the definition of interval-censored data and the current research status of Cox model and stress-strength model under interval-censored data. Chapter2introduces Cox model,the derivation of partial likelihood function,and the mixed imputation approach, and then we prove the asymptotic properties of estimators resulting from mixed imputation approach.Chapter3derives the expression of W in stress-strength model under interval-censored data and applies the self-consistency algorithm, which can be used to estimate the distri-bution function of the interval-censored lifetime data,into the estimation of W;next we introduce non-parametric maximum likelihood estimation’s asymptotic properties based on self-consistency algorithm,and obtain W’s estimator’s asymptotic proper-ties;finally,we conduct the extensive simulation studies and comparative analysis be-tween the self-consistency algorithm, the left endpoint imputation approach,the middle endpoint imputation approach and the mixed imputation approach into stress-strength model.Chapter4gives some summary and discussion about the future research.