Variations on the Accelerated Failure Time Model: Mixture Distributions, Cure Rates, and Di fferent Censoring Scenarios

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 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 model. 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 analytical 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.