The analysis of survival data with a possible cure fraction has attracted much interest in the last two decades. Various models and estimating methods have been proposed for such data and they have been applied in many fields, especially in cancer clinical trials. In the thesis, we consider some new general cure models, which include existing survival models as their special cases. We also consider a nonparametric estimation of cure rate. The estimator is proved consistent and asymptotically normal. We also consider the application of proportional density for cure data and the analysis of length-biased cure data. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-01-26 09:53:08.127