Everything Changes Over Time: Transforming Joint Modelling Methodology

Clinicians typically collect data from patients regularly throughout the treatment of an illness. Such longitudinal data provides valuable insights into how things change over time for patients - tracking the progression of the disease, a patient's reaction to particular treatments, the usefulness of intervention strategies, for example. It is common that such data will be collected alongside key event information such as the time to recovery, time to relapse or time to death of patients. Joint models enable the relationships between this survival and longitudinal data to be mathematically represented, frequently linking a linear mixed effects model to a Cox proportional hazards model.

Despite the significant growth in this field of research in recent years, a wider array of models is needed to truly represent natural biological changes over time. With joint models being first introduced in 1996, this relatively young field of research has many opportunities in which novel approaches can be explored. This project will tackle one such avenue of research - the transformation of joint modelling methodology to both allow a better representation of changing effects over time and to handle the common situation where not all patients will react the same to treatments as the population.

To do so, this research would incorporate a stochastic component within a robust linear mixed effects models to represent the longitudinal process. This would accurately model fluctuations in an individual's own average longitudinal response over time whilst down weighing the negative impact of longitudinal outliers, novel research within a joint model setting. In doing so, this would better represent the true longitudinal process of how individuals' biomarkers, for example, change over time and thus impact their survival, providing more precise interpretations and dynamic predictions.