Variations on the accelerated failure time model: Mixture distributions, cure rates, and different censoring scenarios

KRACHEY, ELIZABETH C. Variations on the Accelerated Failure Time Model: Mixture Distributions, Cure Rates, and Different Censoring Scenarios. (Under the direction of Professors Wenbin Lu and Sujit K. Ghosh). The accelerated failure time (AFT) model is a popular model for time-to-event data. It provides a useful alternative when the proportional hazards assumption is in question and it provides an intuitive linear regression interpretation where the logarithm of the survival time is regressed on the covariates. We have explored several deviations from the standard AFT model. Standard survival analysis assumes that in the case of perfect follow-up, every patient will eventually experience the event of interest. However, in some clinical trials, a number of patients may never experience such an event, and in essence, are considered cured from the disease. In such a scenario, the Kaplan-Meier (KM) survival curve will level off at a nonzero proportion. Hence there is a window of time in which most or all of the events occur, while heavy censoring occurs in the tail. The two-component mixture cure model provides a means of adjusting the AFT model to account for this cured fraction. Chapters 1 and 2 propose parametric and semiparametric estimation procedures for this cure rate AFT (CRAFT) model. Parametric estimation is employed to verify the performace of the CRAFT model in a simpler setting. Semiparametric estimation using mixture density estimation is then used to introduce a novel estimation procedure for the CRAFT model. Posterior consistency is established under some regularity conditions providing large sample justification to the proposed model. Simulation studies validate the performance of the proposed model in finite samples and an application to a breast cancer data set illustrates the semiparametric estimation procedure. Survival analysis methods for interval-censoring have been much slower to develop than for the right-censoring case. This is in part because interval-censored data have a more complex censoring mechanism and because the counting process theory developed for right-censored data does not generalize or extend to interval-censored data. Because of the analyical difficulty associated with interval-censored data, recent estimation strategies have focused on the implementation rather than the large sample theoretical justifications of the semiparametric AFT model. Chapter 3 proposes a semiparametric Bayesian estimation procedure for the AFT model under interval-censored data, employing Markov chain Monte Carlo methods to generate samples from the posterior distribution. Posterior consistency is established under certain conditions providing large sample justification to the proposed model. Simulation studies validate the performance of the proposed model in finite samples and an application to a breast cosmesis data set illustrates the method. Variations on the Accelerated Failure Time Model: Mixture Distributions, Cure Rates, and Different Censoring Scenarios by Elizabeth C. Krachey A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fullfillment of the requirements for the Degree of Doctor of Philosophy