Dynamic joint modelling of longitudinal and survival data using a state space framework

The expanding volume and complexity of healthcare data, driven by technological advancements, necessitate advanced approaches for meaningful analysis. Routine tests and monitoring vital biomarkers contribute to this big data, capturing diverse variables irregularly over time, enabling inference into patients' true health states. While this wealth of information has the potential to enhance clinical decision-making, uncovering complex patterns is a growing challenge, demanding modelling solutions for irregular electronic health records data.

Machine learning approaches, while offering high discriminatory accuracy, often lack interpretability and justifications; critical aspects in healthcare applications. Conversely, statistical models may not capture the underlying complex trends and achieve such accuracy. This thesis addresses this gap by proposing interpretable and intricate statistical frameworks that jointly model longitudinal and survival data, aiming to enhance prognostic capabilities in healthcare settings. Built on system identification foundations, the framework offers a unique approach compared to existing joint models for longitudinal and survival data. It develops three interpretable classes of state space dynamic survival models. The first model establishes a simplified foundational model based on linear dynamical relationships, enabling clinicians to comprehend evolving processes and make informed decisions. To address variations in behaviour within the cohort, a mixture model extension is introduced, recognising diverse patient trajectories and potential sub-populations. Lastly, to capture intricate time series patterns, nonlinearities are incorporated, enabling more accurate tracking of biomarkers and improved prognoses.

Comparative analysis against the prevailing risk score for pulmonary arterial hypertension patients reveals that the proposed frameworks improve survival predictions within the crucial one-year timeframe. Unlike the current empirical approach for these patients, a data-driven solution offers objectivity and potential enhancements in predictions. The versatility of the proposed frameworks extends beyond clinical settings, finding applications in domains such as machine failure assessment, business defaults, and student dropouts, wherever joint longitudinal and time-to-event data analysis is imperative.