Regression Analysis Of Interval-Censored Data

In many branches of learning, such as medicine, biology, insurance, reliability engineering project science, public hygiene, economics, demographics etc, exist problems of estimate and forecast the time of certain events occur. From the obtained data, these data have a common characteristic that the results of surveying are either censored or truncated, especially call it interval-censored when we only know the event happens in certain time area.As to the characteristic of interval-censored data, nowadays the research of interval-censored data mainly focus on the estimation of survival function with this kind data. By contrast, there are less research on residual analysis and regression parametric estimation, therefore few methods are on hand. In this paper, we conclude several methods to estimate the interval-censored data and do residual analysis, such as midpoint residuals, GEL residuals and proposed residuals, mainly use the idea of self-consistency which was suggested by Turnbull in 1976, but all of these methods are complicate in computing.After studying the survival analysis written by Zheng Zukang, suggested by the idea of Class K method, have mainly done three tasks: First, deal with the exactitude observed data and interval-censored data, let y^* = φ₁(y)δ₁ + φ₂(u,vv)δ₂ + φ₃(u)(1-δ₁-δ₂) , where (u,v) is the random interval-censored variable of y, δ₁ = I(y ≤< u),δ₂= I(u < y ≤ v). According the rule of Ey* = Ey, found the conditions which Φ₁ Φ₂ Φ₃ need satisfy, put those satisfied in one species, that is Class X method; Second, Class X was proved not empty and meaningful, and found the best estimation of y in Class K according least variance rule form theory, got pseud data, based on this do residual analysis and regression parameter estimation and discuss the characteristic of estimation; Third, by imitating to prove this method and compare with other methods, found that the method proposed in this paper was more efficient on estimating, and overcame the disadvantages of other methods in computing.