This dissertation focuses on developing new mathematical and statistical methods to properly represent time-varying covariates and model them within the context of time-to-event analysis. This... Show moreThis dissertation focuses on developing new mathematical and statistical methods to properly represent time-varying covariates and model them within the context of time-to-event analysis. This research topic is motivated by specific clinical questions aimed at gaining insights into personalised treatments for cardiological and oncological patients. The main purpose is to enrich the knowledge available for modelling patients’ survival with relevant features related to the time-varying processes of interest.The efforts of this work address the complexities of both (i) developing adequate dynamic characterizations of the processes under study (i.e., representation problem) and (ii) identifying and quantifying the association between time-varying processes and patient survival (i.e., time-to-event modelling problem). In both cases, the main issue is dealing with complex data sources while taking into account the nature of the processes and managing the complex trade-off between clinical interpretability and mathematical formulation.By solving the aforementioned statistical complexities, this work is not only impacting the community of researchers in mathematics and statistics. The development of these novel methodologies may represent a significant step forward in the definition of customized and flexible monitoring tools to support doctors and clinicians in their work.*********This doctoral dissertation was part of a cotutelle agreement between the Politecnico di Milano and Leiden University Show less
