Electronic health records contain enormous amounts of data produced by interactions between millions of patients and their healthcare providers. They are already being used to train deep learning models capable of providing insight into patients' futures that may be used to inform clinicians and improve healthcare services. This thesis builds on the literature of deep learning time-to-event prediction models that may be trained with electronic health record data to predict the distribution of future event times. Advances in this thesis fall into three distinct but related projects.

We propose an improved model evaluation metric for model selection. Various adaptations of Harrell's c-index have been identified as improper when evaluating general right-censored time-to-event models. We use the counting process framework to generalise these metrics, identifying a time-varying risk score for which we prove that our generalised concordance index is proper. We also demonstrate that our metric outperforms other concordance indices when used for model selection and as a secondary loss term in a deep-learning model.

Patient pathways, comprised of sequences of events a patient is susceptible to when first diagnosed with a disease, can be modelled using multi-state models. Our second project explores the extension of two single-event deep learning time-to-event prediction models to the multi-state case. We investigate the use of these models in one synthetic and two real data settings. We evaluate these models using existing evaluation metrics and an adaptation of our proposed concordance index for the multi-state case.

Due to the high-risk nature of clinical decision-making, the tools being used to inform decisions must be reliable. Our final project investigates two approaches to quantifying time-to-event prediction uncertainty using Bayesian neural networks. We produce two new time-to-event prediction Bayesian neural networks, which are tested against their frequentist counterparts and used to provide predictions with quantified uncertainty.