Abstract
Many medical studies show that there are subjects who are cured, free of disease, or die of other causes after treatments. Those subjects come from the nonsusceptible population of the disease and cure models may be used to predict the cure rates with suitable covariates. In our thesis, we extend bounded cumulative hazards models, which is one of the two main types of cure models, to a nonparametric setting for estimating the cure rates and assume that the baseline function in the model follows a parametric distribution. We adopt the local polynomial approach and use the local likelihood criterion to derive estimators of cure rates. This way we adopt a flexible method to estimate the cure rate, the important part in cure models, and a convenient way to model the baseline function, which is less useful in practice. We also derive the convex conditions for the extended cure model. We simulate two examples to examine the performance of our proposed methods. Finally, we apply the extended model to two real datasets to predict cure rates with a continuous covariate.