Semiparametric Regression Analysis of Bivariate Interval-Censored Data

Survival analysis is a long-lasting and popular research area and has numerous applications in all fields such as social science, engineering, economics, industry, and public health. Interval-censored data are a special type of survival data, in which the survival time of interest is never exactly observed but is known to fall within some observed interval. Interval-censored data arise commonly in real-life studies, in which subjects are examined at periodical or irregular follow-up visits. In this dissertation, we develop efficient statistical approaches for regression analysis of bivariate intervalcensored data, in which the two survival times of interest are correlated and both have an interval-censored data structure. Chapter 1 first describes the structure of interval-censored data in detail, and four real-life data sets are presented for illustrations. A literature review is provided regarding the existing semiparametric regression models and methods on intervalcensored data. The last section of this chapter provides some important background knowledge to be used in later chapter of this dissertation, such as Kendall’s τ and Dirichlet process mixture model. Chapter 2 proposes a novel and fast EM algorithm for regression analysis of bivariate current status data based on the Gamma-frailty proportional hazards (PH) model. Monotone splines are adopted to approximate the unknown conditional baseline cumulative functions. A three-stage data augmentation is proposed and leads to a complete data likelihood in a simple form. An EM algorithm is further derived utilizing this complete likelihood. The resulting algorithm is easy to implement, robust to initialization, and enjoys quick convergence. The proposed method has excellent