Nonparametric and Semiparametric Methods for Interval-censored Failure Time Data

Interval-censored failure time data commonly arise in follow-up studies such as clinical trials and epidemiology studies. For their analysis, what interests researcher most includes comparisons of survival functions for different groups and regression analysis. This dissertation, which consists of three parts, consider these problems on two types of interval-censored data by using nonparametric and semiparametric methods. In Chapter 2, we discuss a goodness-of-fit test for checking the proportional odds (PO) model with interval-censored data. The PO model has a feature that allows the ratio of two hazard functions to be monotonic and converge to one. Hence, it provides an important tool for modeling the situation where hazard functions are nonproportional. We derive a procedure for testing the PO model, which is a generalization of Dauxois and Kirmani (2003) for right-censored data. Simulation studies suggest that the proposed test works well and we apply the test to a real dataset from an AIDS cohort study. Chapters 3 considers nonparametric comparison of survival functions. For this, several test procedures have been proposed for interval-censored failure time data in which distributions of censoring intervals are identical among different treatment groups. Sometimes these distributions may not be the same and depend on treatments. A class of test statistics is proposed for situations where the distributions may be different for subjects in different treatment groups. The asymptotic normality of the test statistics is established and the test procedure is evaluated by simulations, which suggest that it works well. An illustrative example is provided. Chapter 4 discusses semiparametric regression analysis of two-sample current status vii data. For their regression analysis, One limitation of commonly used models is that they cannot be used to situations where survival functions cross. We consider a class of two-sample models that include these commonly used models as special cases and especially, are appropriate for crossing survival functions. Some estimating equation-based approaches are presented and the proposed estimates of regression parameters are shown to be consistent and asymptotically normally distributed. The method is evaluated using simulation studies and applied to a set of current status data arising from a tumorgenicity experiment.