Abstract

In this thesis, we shall attempt to give the NPMLE of the event time distribution and cure-rate based on different types of uncensored and censored data. Cure-mixture model and hidden model are used extensively. We address the non-estimability of the cure-rate when no cures are actually observed, in the uncensored case and some important censoring models. A proof is also given for the almost sure convergence of [Special characters omitted.] F ( x ) to (1 - s), where [Special characters omitted.] F ( x ) is the supremum of the MLE of the underlying distribution function, and s is the true underlying cure-rate, for random censoring and interval censoring (case-1). We describe and illustrate the "max-min formula" derived by Groeneboom and Wellner (1992) for interval censoring (case-1), then modify it to get the MLE of the cure-rate under a cure-mixture model, when some cures are observed. We perform a simulation study to give some numerical results as well. Finally, we discuss a probable approach to find the NPMLE in interval censoring (case-2), as a problem for further research.