Statistical inference for cure models under monotonicity constraints

The analysis of survival data in the presence of subjects who will never experience the event of interest has become popular over the recent decades. Mixture cure models are commonly used to analyze such data, allowing the investigation of how covariates (e.g., age, gender and treatment) relate to both the cure probabilities and the conditional survival function of the uncured subjects. Mixture cure models consist of two sub-models: an incidence model for the probability of being uncured and a latency model for the survival times of the uncured subjects.
In the presence of censoring, estimation of cure probabilities is challenging since it is not possible to distinguish the cured subjects from the censored uncured ones. An important assumption to avoid overestimating the cure probability is the presence of sufficiently long follow-up, meaning that the support of the uncured survival times is included in that of the censoring times.
This thesis focuses on statistical inference for cure models, with a focus on incorporating monotonicity constraints in both estimation and hypothesis testing. In the first part, we propose a monotone single-index structure for modeling the incidence component of the mixture cure model, utilizing isotonic estimation techniques to ensure monotonicity. The second part addresses the crucial problem of testing the assumption of sufficient follow-up, which is critical for the identifiability and reliability of cure model inference.