Parameter estimation for additive hazards model with partly interval-censored failure time data using a penalized likelihood approach

In the context of failure time data, interval censoring is a censoring type which has become increasingly prevalent in many areas, including medical, financial, actuarial and sociological studies. In interval-censored data, the actual failure time is neither exactly observed nor right-censored nor left-censored, but one can establish boundaries of an interval within which the survival event has occurred. The aim of this thesis is to develop a maximum penalized log-likelihood (MPL) method which estimates model parameters of the semiparametric additive hazards model with partly interval-censored failure time data. This data will contain exactly observed, left-censored, finite interval-censored and right-censored data. This MPL method estimates the regression coefficients and the underlying non-parametric baseline hazard function, simultaneously, by imposing non-negativity constraints on the baseline hazard and the overall hazard function. We approximate infinite dimensional baseline hazard from a finite number of non-negative basis functions. The chosen MPL method guarantees the smoothness of the baseline hazard estimates, which clearly depicted the trend of how the estimates changed over time. We adopted the augmented Lagrangian method to solve this constraint optimization problem, and the estimates were obtained simultaneously using the Newton and multiplicative iterative (Newton-MI) algorithm followed by line-search steps. The asymptotic properties of these derived constrained MPL estimators were studied when the number of basis functions was fixed and when it went to infinity. We investigated the performance of this proposed MPL method by conducting simulation studies for both right-censored data and partly interval-censored data. Both of the simulation studies demonstrated that our method worked well for small and large datasets as well as small and large censoring proportions. The derived asymptotic standard deviation formula was generally accurate in approximating the standard deviation of the constrained MPL estimates. In addition, we also made comparisons between our MPL method and existing parameter estimation methods developed by Aalen (1980) and Lin & Ying (1994). Results show that our MPL method provided better estimates. In a real data analysis, we applied our MPL method to fit the additive hazards model to a melanoma data set with all types of censoring, which was provided by the Melanoma Institute of Australia.