Parametric Estimation Based On Proportional Hazards Model For Interval-censored Data

In many practical problems, due to the constraints of a variety of subjective and objective conditions, one gets the observational data which is only known that the observational data of interest is greater than (less than) or equal to a num-ber or lies within an interval instead of being observed exactly. Such incomplete data is called censored data in the survival analysis. Censored data includes left-censored, right-censored, interval-censored commonly.Proportional hazards model is one of the most important and the most widely used model in survival anal-ysis, which was originally modeled with the right-censored lifetime data.In the actual statistical study, the data we observed is often the interval-censored data, and left or right-censored can be seen as a special interval-censored Therefore, the studying interval-censored data in proportional hazards model is more theoretical significance and valuable of application. Many scholars also address the problem of parameter estimation of interval-censored data, under the assumption of pro-portional hazards model, however, many methods are required to estimate the baseline hazard function, this makes the asymptotic properties of the parameter estimates and the estimated amount of inference becoming extremely difficult, and loses the advantage of the proportional hazards model inference which does not depend on the part of the non-parametric.And imputation of the left end-point and midpoint does not depend on non-parametric part of the model, does not estimate he baseline hazard function, the estimated value of the regression parameters can be obtained directly. Inspiring of the left endpoint imputation approach and the middle endpoint imputation approach,the author proposed a mixed imputation approach which is a new alternative approach, the author try to reduce interval censored data arising form the proportional hazards model to right-censored data arising form the proportional hazards model and obtain the parameter by constructing partial likelihood function and compare mixed impu-tation approach with left endpoint imputation approach and the middle endpoint imputation approach in a simulation study. The structure of the paper is as follows:The first chapter introduces definition of interval-censored, and current research status of proportional hazards model and the problem that this paper will solve; the second chapter introduces based on right censored data based on Cox model and partial likelihood function; the third chapter describes the left end point imputation approach and the middle end imputation approach and mixed imputation approach; the forth chapter is simulation studies and comparative analyzes; the fifth chapter is summary and outlook.