Gaussian Process Based Approaches for Survival Analysis

Traditional machine learning focuses on the situation where a fixed number of features are available for each data-point. For medical applications each individual patient will typically have a different set of clinical tests associated with them. This results in a varying number of observed per patient features. An important indicator of interest in medical domains is survival information. Survival data presents its own particular challenges such as censoring. The aim of this thesis is to explore how machine learning ideas can be transferred to the domain of clinical data analysis. We consider two primary challenges; firstly how survival models can be made more flexible through non-linearisation and secondly methods for missing data imputation in order to handle the varying number of observed per patient features. We use the framework of Gaussian process modelling to facilitate conflation of our approaches; allowing the dual challenges of survival data and missing data to be addressed. The results show promise, although challenges remain. In particular when a large proportion of data is missing, greater uncertainty in inferences results. Principled handling of this uncertainty requires propagation through any Gaussian process model used for subsequent regression.