Functional biomarkers: the role of longitudinal variation patterns in the prediction of clinical conditions

Functional data analysis (FDA) is a growing methodological framework in medical research that, rather than reducing signals to summary measures, operates on entire trajectories to enable richer insights. In this context, we introduce the term functional biomarkers to refer to biological signals whose most meaningful information is carried not at a single evaluation, but rather in their shape or variation. A bibliometric analysis of 1,199 records spanning 35 years confirmed that the field of medical FDA applications is small but expanding at an annual growth rate of 5.72\%, with neurology, sport medicine, and endocrinology well-represented among recent publications and functional principal component analysis as the most widely used procedure. Despite this growth, nearly half of the reviewed studies provided limited information on key preprocessing steps, raising reproducibility concerns and suggesting the need for more rigorous reporting standards. This thesis presents three original applications of FDA, placing an emphasis on reproducibility and reporting, and exploring different types of medical data. The first application uses WESAD, a publicly available multimodal dataset of high-density physiological recordings from 15 subjects, to evaluate stress detection from wearable sensors. FDA consistently identified tonic electrodermal activity as a key stress biomarker and provided deeper insights into how physiological associations vary across different stressful tasks, outperforming conventional feature-based approaches in capturing the temporal structure of the signals. The second application turns to oncology, analyzing 16,294 weight measurements, unequally and irregularly distributed across 1,811 patients enrolled in the GIM-2 trial, to characterize individual weight trajectories during adjuvant chemotherapy for early breast cancer. While the average weight change was modest, FDA identified longitudinal profiles linked to overall survival, with mid-treatment gains and late-treatment losses appearing less favorable, a pattern not captured by traditional summary measures, supporting the case for time-informed profiling in personalized care. Building on these insights, the final contribution proposes a novel clinical trial design for Phase II studies in multiple sclerosis, where ethical concerns about randomizing patients to a control arm are increasingly pressing. The proposed single-arm design assigns each participant a randomly selected intervention time, allowing them to serve as their own control. Curve alignment reconstructs individual intervention timing from noisy biomarker measurements, and treatment effects are detected by correlating estimated with actual intervention times. Simulations across parameters drawn from the literature demonstrate strong performance. The design extends naturally to the simultaneous analysis of multiple biomarkers, a capability rarely present in classical trial designs, positioning FDA as a driver not only of deeper medical insight, but of methodological innovation in biomarker research.