Abstract:

This thesis proposes three studies on inference for failure time data subject to interrupted hazards and interval censoring. The first develops statistical methods for designing and analyzing studies in which treatments are deliberately interrupted and reinitiated, but where interest lies in making inferences about continuous treatment use. Such designs are referred to as alternating designs since subjects alternate between periods in which they are and are not taking the treatment of interest. Methods for nonparametric estimation of the distribution of time to event if the treatment were given continuously, comparing the distributions of two such continuously-given treatments, and assessing the effects of covariates are presented. Properties of the alternating treatment design and the classical parallel group design are compared and the proposed methods are illustrated on a data set from an alternating trial.

The second study develops methods for designing and analyzing arm-in-cage experiments which are used to test the efficacy of insect repellents. Efficacy of a repellent is described using a progressive three-state model in which the first two states represent varying degrees of protection and the third state occurs once protection is completely lost. Since subjects follow the same cage visit schedule, transition times between states are interval censored into one of several fixed intervals. This study develops a semiparametric approach for estimating the parameters of interest assuming sojourn times are dependent and examines inference for various hypotheses. Design considerations for arm-in-cage experiments are addressed and the proposed methods are illustrated on data from an arm-in-cage experiment.

The final study addresses inference and identifiability for chain-of-events data subject to interval censoring. This study develops an algorithm for nonparametric estimation of the distribution functions of sojourn times in a four-state progressive disease model when transition times between states are interval censored. Since issues of uniqueness for chain-of-events data are not well understood, the main goal of this final study is to present conditions which determine the identifiable aspects of the distribution functions of sojourn times. The proposed methods are illustrated on a number of examples.