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
Time-varying covariates are of great interest in clinical research since they represent dynamic patterns which reflect disease progression. In cancer studies biomarkers values change as functions... Show moreTime-varying covariates are of great interest in clinical research since they represent dynamic patterns which reflect disease progression. In cancer studies biomarkers values change as functions of time and chemotherapy treatment is modified by delaying a course or reducing the dose intensity, according to patient's toxicity levels. In this work, a Functional covariate Cox Model (FunCM) to study the association between time-varying processes and a time-to-event outcome is proposed. FunCM first exploits functional data analysis techniques to represent time-varying processes in terms of functional data. Then, information related to the evolution of the functions over time is incorporated into functional regression models for survival data through functional principal component analysis. FunCM is compared to a standard time-varying covariate Cox model, commonly used despite its limiting assumptions that covariate values are constant in time and measured without errors. Data from MRC BO06/EORTC 80931 randomised controlled trial for treatment of osteosarcoma are analysed. Time-varying covariates related to alkaline phosphatase levels, white blood cell counts and chemotherapy dose during treatment are investigated. The proposed method allows to detect differences between patients with different biomarkers and treatment evolutions, and to include this information in the survival model. These aspects are seldom addressed in the literature and could provide new insights into the clinical research. Show less
