Semiparametric analysis of failure time data with complex structures
Authors:   , Liu Yeqian 
Published: April 2021

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Failure time data arise in many fields including biomedical studies and industrial life testing. Right-censored failure time data are often observed from a cohort of prevalent cases that are subject to length-biased sampling, which are termed as length-biased and right-censored data. Interval-censored failure time data arise when the failure time of interest in a survival study is not exactly observed but known only to fall within some interval or window. One area that often produces such data is medical studies with periodic follow-ups, in which the medical condition of interest such as the onset of a disease is only known to occur between two adjacent examination times. An important special case of interval-censored data is current status data which arise when each study subject is observed only once and the only information available is whether the failure event of interest has occurred or not by the observation time. Sometimes we also refer current status data as case I interval-censored data and the general case as case II interval-censored data. Semiparametric regression analysis of both right-censored and interval-censored failure time data has recently attracted a great deal of attention. Many procedures have been proposed for their regression analysis under various models. However, in many settings, the population include a cured (nonsusceptible) subpopulation, where only individuals in the susceptible subpopulation will go on to experience the event. Since classical survival models implicitly assume that all individuals will eventually experience the event of interest, they cannot be used in such contexts. They would in fact lead to incorrect results such as, among others, an overestimation of the survival of the non-cured subjects. The research in this dissertation focuses on the statistical analysis for right-censored data with length-biased sampling, interval-censored data with a cured subgroup in the presence of potential dependent censoring and measurement errors. Chapter 1 describes specific examples of right-censored and interval-censored failure time data and reviews the literature on some important topics, including nonparametric and semiparametric estimation, regression analysis in the presence of length-biased sampling and a cured subgroup respectively. Chapter 2 discusses regression analysis of length-biased and right-censored data with with partially linear varying effects. For this problem, we consider quantile regression analysis of right-censored and length-biased data and present a semiparametric varying coefficient partially linear model. For estimation of regression parameters, a three-stage procedure that makes use of the inverse probability weighted technique is developed, and the asymptotic properties of the resulting estimators are established. In addition, the approach allows the dependence of the censoring variable on covariates, while most of the existing methods assume the independence between censoring variables and covariates. A simulation study is conducted and suggests that the proposed approach works well in practical situations. Also an illustrative example is provided. Chapter 3 considers regression analysis of current status data in the presence of a cured subgroup and dependent censoring. For the problem, we develop a sieve maximum likelihood estimation approach with the use of latent variables and Bernstein polynomials. For the determination of the proposed estimators, an EM algorithm and the asymptotic properties of the estimators are established. An extensive simulation study conducted to asses the finite sample performance of the method indicates that it performs well for practical situations. An illustrative example using a data set from a tumor toxicological study is provided. Chapter 4 considers regression analysis of interval-censored data in the presence of a cured subgroup and the case where one or more explanatory variables in the model are subject to measurement errors. These errors should be taken into account in the estimation of the model, to avoid biased estimations. A general approach that exists in the literature is the SIMEX algorithm, a method based on simulations which allows one to estimate the effect of measurement error on the bias of the estimators and to reduce this bias. We extend the SIMEX approach to the mixture cure model with interval-censored data. Comprehensive simulations study as well as a real data application are provided. Several directions for future research are discussed in Chapter 5.