Flexible methods for survival data: synthetic patients, imputation and prediction in mixture cure models

Survival analysis is essential in medical research, as it helps to evaluate treatment effects, disease progression, and patient outcomes. However, with the increasing complexity and scope of modern biomedical studies, survival data can present methodological challenges, including issues with reproducibility, missing information, and a rising demand for personalized prognoses. This dissertation aims to develop a comprehensive framework that addresses these challenges by introducing innovations in synthetic data generation, missing data imputation, and dynamic prediction within cure models. The first contribution focuses on reproducibility and data sharing, proposing a flexible approach to generate synthetic survival data that preserves key features of the original data while protecting patient confidentiality. The proposed framework allows researchers to reproduce complex dependence structures between covariates and time-to-event outcomes, thereby supporting transparent and privacy-protecting research in both methodological and applied contexts. The second contribution addresses missing data in cure models, which distinguish between survival and disease progression in cured and uncured individuals. A multiple imputation strategy tailored to the structure of cure models is developed, enabling valid inference when covariate information is incomplete. This approach improves the ability to separate curative from life-prolonging effects, a distinction of central importance in many clinical applications. The final contribution concerns dynamic prediction in the presence of a cure fraction. A modelling framework is proposed to incorporate longitudinal information into cure models, allowing individualized survival predictions to be updated over time as patient profiles evolve. Through simulation studies and real-data applications, the proposed method demonstrates improved predictive performance compared to existing approaches.