Maximum penalized likelihood estimation for semi-parametric regression models with partly interval-censored failure time data

Interval-censored failure time data arise in many areas including demographical, financial, actuarial, medical and sociological studies. By interval censoring we mean that the failure time is not always exactly observed and we can only observe an interval within which the failure event has occurred. The goal of this dissertation is to develop maximum penalized likelihood (MPL) methods for ptoportional hazard (PH), additive hazard (AH) and accelerated failure time (AFT) models with partly interval-censored failure time data, which contains exactly observed, left-censored, finite interval-censored and right-censored data. We fit these three semi-parametric regression models by estimating the underlying non-parametric baseline hazard functions and regression coefficients. For the PH and AFT models, we compute these estimates simultaneously using the Newton and multiplicative iterative (Newton-MI) algorithm with line search steps, where the nonnegativity of baseline hazard functions is imposed in a direct way. For the AH model, we obtain the estimates using the primal-dual interior point algorithm, with which the baseline hazard function and hazard function are constrained to be non-negative simultaneously. The MPL methods provide smoothness for the baseline hazard estimates, which can clearly show the trend of how the baseline hazard estimates are changing over time. The asymptotic properties of these MPL estimators are studied. We investigate the performance of our proposed MPL methods by conducting simulation studies, and the simulation results demonstrate that our methods work well. In addition, we also make comparisons between our MPL methods and some existing methods. In a real data analysis, the proposed MPL methods are applied to the AIDS example provided by Lindsey and Ryan (1998).