Nonparametric Inference for the Mixture Cure Model When the Cure Status is Partially Known

Abstract

Classical analysis of time-to-event data assumes that all individuals will eventually experience the event of interest. However, when there is evidence of long-term survivors, cure models should be used instead. They assume that the population of individuals is made up of two distinct groups: those who will and those who will not experience the event. A common assumption in cure models is that there is no additional information about the cure status, and the cure indicator is modelled as a latent variable. But this is not entirely valid in many cases, when some censored individuals can be identified as cured, for example, based on a diagnostic test or if the observed lifetime is larger than a cure threshold. Mixture cure models have been usually estimated using parametric or semiparametric models. Recently, a completely nonparametric approach was introduced under the classical assumption that the cure status in unknown. This PhD thesis proposes a novel extension of nonparametric mixture cure models to incorporate the additional information about the cure status. Suitable nonparametric estimators for the main functions are proposed, together with a rough procedure for checking the validity of the model.