Modelling interval-censored event times in the presence of a cure fraction : from building to refining

In standard survival analysis, it is generally assumed that every individual will eventually experience the event of interest. However, this is not always the case, as some individuals may not be susceptible to this event. In the statistical literature, this feature is referred to as the presence of a cure fraction. Moreover, it is frequent that patients come to scheduled visits and that the time to the event is only known up to an interval of time. That is, the data are interval-censored. This thesis develops methods to handle interval-censored data in which there is a fraction of cured individuals. We first study the impact of these features and then propose two flexible models, allowing to use classical parametric maximum likelihood theory. The extension of a variable selection method to our model is also studied. Lastly, we propose a new diagnostic check procedure as well as a goodness-of-fit test to assess the adequacy of our model.