Analysis of failure time data with interval censoring and bivariate truncation

The failure time data is often subject to censoring and truncation. In the case of censoring, the true failure time is known to fall into a region. The exact value of the failure time is unobserved. The effect of this type of incompleteness is to coarse data. This means that the information that the data give us is "correct" but not "accurate". Another type of incompleteness is truncation. Truncation is where the failure time can be observed only if it falls within a specified region. In this case, the observed data is a biased sample of the population since not all of the subjects in the population are observable.; This dissertation will focus on two types of incompleteness in the failure time data: one is interval censoring and the other one is bivariate truncation. Interval censoring means that the failure time falls into an interval but the exact time is unknown. This type of data is common in many studies where a failure is monitored periodically hence it would only be possible to know that it occurred between two inspection time points. Bivariate truncation is also common in studies of correlated failure times. This is where both of the failure times can be observed if and only if each of them is smaller (or greater) than some threshold.; The motivating examples include two datasets: Breastfeeding data and Panic Disorder data. For Breastfeeding data, a competing risks model with one arm (HIV transmission arm) subject to interval censoring is considered. A nonparametric estimation approach to estimate the crude cumulative probability is derived. This paper also proposes a nonparametric score-type test to compare the crude cumulative probabilities between two groups. This is the main theme of the second chapter of this dissertation. Panic Disorder data is analyzed by assuming a bivariate right truncation model. By comparing with the existing estimation methods, this paper proposes a simple nonparametric estimation approach to determine the bivariate survival function. This estimation procedure is easy to implement and the estimator has nice asymptotic properties. This estimation procedure is the topic of the third chapter of this dissertation.; This paper will begin with a review of the concepts and techniques in the related literature. And it will end with a brief summary and discussion of the relevant future research topics.