Joint survival models: a Bayesian investigation of longitudinal volatility

Thesis

In this thesis, we investigate joint models of longitudinal and time-to-event data. We extend the current literature by developing a model that assigns subject-specific variance to the longitudinal process and links this variance to the survival outcome. During development we provide the theoretical definition of the model and its properties, and explore the practical implications for estimating the parameters. We use Markov Chain Monte Carlo (MCMC) methods, and compare the different samplers used in similar models in the literature with our custom MCMC algorithm, written in C++.

We use the Deviance Information Criterion to perform model comparisons, and we formalise suggestions from the literature to use posterior predictive model checking to construct a goodness-of-fit test for our model. We use the model on two real-world datasets to investigate claims relating to the importance of blood pressure volatility on stroke risk, and examine the consequences of ignoring measurement error.

We amend our model to accommodate competing risk, time-dependent baseline hazard rates, and bivariate longitudinal processes --- at which point we update our MCMC samplers and identify the issues. Finally, we use our code in a separate, but related, collaboration with other researchers to analyse repeated counts data.

Authors: Bester, D

• DOI: 10.5287/ora-zbmjaev8q
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford