Cure Rate Models

Cure rate models have a broad range of application in many fields, such as medicine, public health, and especially in cancer studies. Researchers in these studies are interested in waiting time until occurrence of the event of interest, as well as the proportion of instances where the event never occurs, known in this case as the cure fraction. In general, there are two types of models for estimation of the cure fraction. The first one is the mixture cure rate model. This type of models assumes that the whole population is composed of two groups of subjects, susceptible subjects and insusceptible (or cured) subjects. The second model is non-mixture cure model, based on number of cancer cells which remain after treatment. This thesis devises and presents a review for cure rate models form early studies to recent articles. Since there is not a comprehensive review on cure rate models, my mission was to put all models together in a single and coherent notation. Cure rate models are a part of survival analysis and involve censored subjects. Therefore, analyses cure rate models a sufficient knowledge in survival analysis is required. In Chapter 2, the definitions of censored and truncated subjects are given. In addition, the basic concepts and formulations of survival analysis are explained. Some common parametric and non-parametric, and semi-parametric survival models are explained as well. Chapter 3 and Chapter 4 are the main body of this dissertation, and focus on explaining cure rate models. In Chapter 3, some preliminary tests for existence of cured fraction are described. Early works in mixture cure rate models and some parametric and nonparametric cure models are discussed. In Chapter 4 non-mixture cure rate models and two semi-parametric mixture cure rate models which are adopted from more recent works in cure models are explained. An extensive simulation study has been done for each model type and is discussed in Chapter 5. Simulation setup is the same as in original article and we were able to reproduce their results. In Chapter 6, advanced cure models are implemented for bone marrow transplantation dataset. Chapter 7 presents the conclusion of the study and an overview of future research.