Semiparametric regression analysis of interval-censored data with informative dropout

Interval-censored data arise when the event time of interest can only be ascertained through periodic examinations. In medical studies, subjects may not complete the examination schedule for reasons related to the event of interest. In this article, we develop a semiparametric approach to adjust for such informative dropout in regression analysis of interval-censored data. Specifically, we propose a broad class of joint models, under which the event time of interest follows a transformation model with a random effect and the dropout time follows a different transformation model but with the same random effect. We consider nonparametric maximum likelihood estimation and develop an EM algorithm that involves simple and stable calculations. We prove that the resulting estimators of the regression parameters are consistent, asymptotically normal, and asymptotically efficient with a covariance matrix that can be consistently estimated through profile likelihood. In addition, we show how to consistently estimate the survival function when dropout represents voluntary withdrawal and the cumulative incidence function when dropout is an unavoidable terminal event. Furthermore, we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies. Finally, we provide an application to data on the incidence of diabetes from a major epidemiological cohort study

Jackknife Emperical Likelihood Method and its Applications

In this dissertation, we investigate jackknife empirical likelihood methods motivated by recent statistics research and other related fields. Computational intensity of empirical likelihood can be significantly reduced by using jackknife empirical likelihood methods without losing computational accuracy and stability. We demonstrate that proposed jackknife empirical likelihood methods are able to handle several challenging and open problems in terms of elegant asymptotic properties and accurate simulation result in finite samples. These interesting problems include ROC curves with missing data, the difference of two ROC curves in two dimensional correlated data, a novel inference for the partial AUC and the difference of two quantiles with one or two samples. In addition, empirical likelihood methodology can be successfully applied to the linear transformation model using adjusted estimation equations. The comprehensive simulation studies on coverage probabilities and average lengths for those topics demonstrate the proposed jackknife empirical likelihood methods have a good performance in finite samples under various settings. Moreover, some related and attractive real problems are studied to support our conclusions. In the end, we provide an extensive discussion about some interesting and feasible ideas based on our jackknife EL procedures for future studies

Multivariate Probit Models for Interval-Censored Failure Time Data

Survival analysis is an important branch of statistics that analyzes the time to event data. The events of interest can be death, disease occurrence, the failure of a machine part, etc.. One important feature of this type of data is censoring: information on time to event is not observed exactly due to loss to follow-up or non-occurrence of interested event before the trial ends. Censored data are commonly observed in clinical trials and epidemiological studies, since monitoring a person’s health over time after treatment is often required in medical or health studies. In this dissertation we focus on studying multivariate interval-censored data, a special type of survival data. By saying multivariate interval-censored data, we mean that there are multiple failure time events of interest, and these failure times are known only to lie within certain intervals instead of being observed exactly. These events of interest can be associated because of sharing some common characteristics. Multivariate interval-censored data draw more and more attention in epidemiological, social-behavioral and medical studies, in which subjects are examined multiple times and several events of interest are tested at the observation times. There are some existing methods available in literatures for analyzing multivariate interval-censored failure time data. Various models were developed for regression analysis. However, due to the complicated correlation structure between events, analyzing such type of survival data is much more difficult and new efficient methodologies are needed. Chapter 1 of this dissertation illustrates the important concepts of interval-censored data with several real data examples. A literature review of existing regression models and approaches is included as well. Chapter 2 introduces a new normal-frailty multivariate probit model for regression analysis of interval-censored failure time data and proposes an efficient Bayesian approach to get parameter estimates. Simulations and an analysis on a real data set are conducted to evaluate and illustrate the performance of this new method. This new approach is proved efficient and has accurate estimations on both the regression parameters and the baseline survival function. Several appealing properties of the model are discussed here. Chapter 3 proposes a more general multivariate probit model for multivariate interval-censored data. This new model allows arbitrary correlation among the correlated survival times. A new Gibbs sampler is proposed for the joint estimation of the regression parameters, the baseline CDF, and the correlation parameters. Chapter 4 extends the normal frailty multivariate probit model to allow arbitrary pairwise correlations. Simulation studies are conducted to explore the underlying relationship between the normal frailty multivariate probit model and the general multivariate probit model

Semiparametric Regression with an Interval-Censored Covariate

In longitudinal studies, investigators are often interested in how the timing of an intermediateevent affects a future outcome. The intermediate event is often asymptomatic and its status can onlybe assessed at periodic examinations. Such an event is interval-censored in that its occurrence isonly known to lie in an interval induced by these examinations. The problem of interval-censoredcovariates has been previously studied only under restrictive conditions. In this dissertation, werelax these assumptions and present semiparametric regression models linking an interval-censoredintermediate event to various response variables.In the first chapter, we consider the case where the response variable of interest is continuous.We link the intermediate event and response through the rectified linear unit function, allowingfor interpretations in terms of duration of exposure to the intermediate event. We propose a nonparametricmaximum likelihood estimation approach using an expectation-maximization algorithm.We demonstrate the proposed approach through simulation studies and show that our method is robustto differential censoring patterns induced by missing visits. We present an application regressingsystolic blood pressure on interval-censored diabetes exposure.In the second chapter, we address the case where the response variable of interest is a rightcensoredevent time. We generalize the relationship between the outcome and intermediate event bylinking them through any non-constant function. We demonstrate the method through simulationstudies and a real data application.In the third chapter, we extend our previous work to longitudinal repeated measurements of acontinuous variable. We account for within-subject correlation through Gaussian-distributed randomeffects. We allow for time-dependent covariates to influence both the response and the occurrenceof the intermediate event. We demonstrate the approach through simulation studies and repeat theanalysis of Chapter 1 using repeated measurements of systolic blood pressure.In a brief fourth chapter, we develop regression models with an interval-censored covariate forresponse variables belonging to the exponential family. This extension provides researchers accessto analogs of generalized linear models such as logistic regression and the log-linear model. Wedemonstrate the performance of the approach, both with and without repeated measures, throughsimulation studies.Doctor of Philosoph

Semiparametric Regression Analysis of Right- and Interval-Censored Data

Right-censored data arise when the event time can only be observed up to the end of the follow-up, while interval-censored data arise when the event time is only known to lie within an interval. There is a large body of statistical literature on right-censored and interval-censored data, but the existing methods cannot properly handle certain complexities. In the first project, we consider efficient semiparametric estimation of the accelerated failure time (AFT) model with partly interval-censored (PIC) data, which arise when the event time may be right-censored for some subjects and interval-censored for the others because of different observation schemes. We generalize the Buckley-James estimator to PIC data and develop a one-step estimator by deriving and estimating the efficient score for the regression parameters. We then establish the asymptotic properties of the estimators, conduct extensive simulation studies, and apply our methods to data derived from an AIDS study. In the second project, we consider the setting when subjects may not complete the examination schedule for reasons related to the event of interest. To make a valid inference about the interval-censored event time of interest, we jointly model the event time of interest and the dropout time using transformation models with a shared random effect. We consider nonparametric maximum likelihood estimation (NPMLE) and develop a simple and stable Expectation-maximization (EM) algorithm. We then prove the asymptotic properties of the resulting estimators and show how to predict the event time of interest when dropout is an unavoidable terminal event. Finally, we provide an application to data on the incidence of diabetes from the Atherosclerosis Risk in Communities (ARIC) study. In the third project, we formulate the effects of covariates on the joint distribution of multiple right- and interval-censored events through semiparametric proportional hazards models with random effects. We consider NPMLE, develop an EM algorithm, and establish the asymptotic properties of the resulting estimators. We leverage the joint modelling to provide dynamic prediction of disease incidence based on the evolving event history and provide an application to the ARIC study.Doctor of Philosoph