Semiparametric Regression Analysis of Right- and Interval-Censored Data

Abstract

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.