Semiparametric sieve maximum likelihood estimation for interval censored data with/without cure fraction

This thesis focuses on semiparametric sieve maximum likelihood esti- mation of interval censored survival data. It consists of two parts. In the first part, we discuss the accelerated hazards (AH) model, which provides an alternative to the popular proportional hazards (PH) model when the proportionality does not hold. We explore the difficulties that arise when one fits the AH model to interval censored data. We develop a semiparametric sieve maximum likelihood estimator and provide an algorithm for its implementation. We also establish consistency results and set up the rate of convergence. In the second part, we propose a new double semiparametric mixture cure model for analyzing interval censored data with possible cure frac- tion. The proposed model incorporates semiparametric latency and inci- dence parts. Unlike existing works in the literature, where the incidence follows a parametric model, the proposed model allows the incidence to be semiparametric. We develop a spline-based sieve maximum likelihood es- timation approach to analyze such data. Using modern empirical process techniques we establish large sample properties of the estimator, including the consistency, rate of convergence and the asymptotic normality of the finite dimensional parameters. For both parts of the thesis we provide extensive simulation studies to show the finite sample size performance of the proposed estimation algorithm. For illustration purpose, the proposed method are applied to real data.​Doctor of Philosophy (SPMS