Regression analysis of interval-censored failure time data with non proportional hazards models

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Interval-censored failure time data arises when the failure time of interest is known only to lie within an interval or window instead of being observed exactly. Many clinical trials and longitudinal studies may generate interval-censored data. One common area that often produces such data is medical or health 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 the so-called current status data when each study subject is observed only once for the status of the event of interest. That is, instead of observing the survival endpoint directly, we will only know the observation time and whether or not the event of interest has occurred by that time. Such data may occur in many fields as cross-sectional studies and tumorigenicity experiments. Sometimes we also refer current status data as case I interval-censored data and the general case as case II interval-censored data. Recently the semi-parametric statistical analysis of both case I and case II intervalcensored failure time data has attracted a great deal of attention. Many procedures have been proposed for their regression analysis under various models. We will describe the structure of interval-censored data in Chapter 1 and provides two specific examples. Also some special situations like informative censoring and failure time data with missing covariates are discussed. Besides, a brief review of the literature on some important topics, including nonparametric estimation and regression analysis are performed. However, there are still a number of problems that remain unsolved or lack approaches that are simpler, more efficient and could apply to more general situations compared to the existing ones. For regression analysis of interval-censored data, many approaches have been proposed and more specifically most of them are developed for the widely used proportional hazards model. The research in this dissertation focuses on the statistical analysis on non-proportional hazards models. In Chapter 2 we will discuss the regression analysis of interval-censored failure time data with possibly crossing hazards. For the problem of crossing hazards, people assume that the hazard functions with two samples considered may cross each other where most of the existing approaches cannot deal with such situation. Many authors has provided some efficient methods on right-censored failure time data, but little articles could be found on interval-censored data. By applying the short-term and long-term hazard ratio model, we develop a spline-based maximum likelihood estimation procedure to deal with this specific situation. In the method, a splined-based sieve estimation are used to approximate the underlying unknown function. The proposed estimators are shown to be strongly consistent and the asymptotic normality of the estimators of regression parameters are also shown to be true. In addition, we also provided a Cramer-Raw type of criterion to do the model validation. Simulation study was conducted for the assessment of the finite sample properties of the presented procedure and suggests that the method seems to work well for practical situations. Also an illustrative example using a data set from a tumor study is provided. As we discussed in Chapter 1, several semi-parametric and non-parametric methods have been proposed for the analysis of current status data. However, most of them only deal with the situation where observation time is independent of the underlying survival time. In Chapter 3, we consider regression analysis of current status data with informative observation times in additive hazards model. In many studies, the observation time may be correlated to the underlying failure time of interest, which is often referred to as informative censoring. Several authors have discussed the problem and in particular, an estimating equation-based approach for fitting current status data to additive hazards model has been proposed previously when informative censoring occurs. However, it is well known that such procedure may not be efficient and to address this, we propose a sieve maximum likelihood procedure. In particular, an EM algorithm is developed and the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study was conducted for the assessment of the finite sample properties of the presented procedure and suggests that it seems to work well for practical situations. An application to a tumorigenicity experiment is also provided. In Chapter 4, we considered another special case under the additive hazards model, case II interval-censored data with possibly missing covariates. In many areas like demographical, epidemiological, medical and sociological studies, a number of nonparametric or semi-parametric methods have been developed for interval-censored data when the covariates are complete. However, it is well-known that in reality some covariates may suffer missingness due to various reasons, data with missing covariates could be very common in these areas. In the case of missing covariates, a naive method is clearly the complete-case analysis, which deletes the cases or subjects with missing covariates. However, it's apparent that such analysis could result in loss of efficiency and furthermore may lead to biased estimation. To address this, we propose the inverse probability weighted method and reweighting approach to estimate the regression parameters under the additive hazards model when some of the covariates are missing at random. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal. Several numerical results suggest that the proposed method works well in practical situations. Also an application to a health survey is provided. Several directions for future research are discussed in Chapter 5.