Statistical Inference On Informative Interval-censored Data

Interval-censored data often occur in the research of epidemiology, economics, medicine and sociology. Traditional statistical methods and models for interval-data are almost based on the hypothesis that the failure time and the observation time are independent. But in practice the hypothesis is always invalid. Dependent interval-censored has recently attracted a great deal of attention. The correct dependentent of assumption between failure time and observation time is important. The proper assumption will enhance the efficiency of estimation and get the better statistical conclusions. Copula function is widely used in dependent censoring. We described the joint distribution function of failure time and observation time with copula function and used the joint distribution function to research the distribution of denpendenting interval-censored data in different models.In this article, We research Weibull of parametric model, proportional hazard model and nonparametric model. We construct the maximum likelihood function of different models with copula function. For the solution of maximum likelihood function of different models,We used respectively Nelder-Mead algorithm,Newton-Raphson algorithm and PAVA algorithm.Otherwise,Different assumption about copula function will have different influence on the estimation result. Thus, we make sensitivity analysis of the influence by simulation.