Parametric Estimation Of The Cox Proportional Hazards Model Under Case Ⅰ Interval-censored Data

In this paper, we consider two methods:Coordinate descent and EM algorithm, to deal with the maximum likelihood estimation problem under the Cox proportional hazards model with Case I Interval-censored data.The Cox proportional hazards model and Semi-parametric Cox proportional hazards model of Case I Interval-censored data are introduced, and the calculation procedure of solving the maximum likelihood estimation upon Coordinate descent method as well as EM algorithm is described. In EM algorithm, we describe the process of the EM algorithm theory, then we apply EM algorithm to parametric estimation of the Cox proportional hazards model under Case I Interval-censored data, we propose an approximated likelihood function, obtain likelihood function of complete data by approximated likelihood function, and study the maximum ap-proximated likelihood estimation by maximizing the likelihood function of complete data.Finally, the two estimation methods are explored to simulation data and the s-tudy of complication of cataract treatment, and illustrate the stability and feasibility of the two proposed methods by comparison with the Newton iteration method.